241 results on '"Mayhall, Nicholas J."'
Search Results
2. Minimal evolution times for fast, pulse-based state preparation in silicon spin qubits
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Long, Christopher K., Mayhall, Nicholas J., Economou, Sophia E., Barnes, Edwin, Barnes, Crispin H. W., Martins, Frederico, Arvidsson-Shukur, David R. M., and Mertig, Normann
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Quantum Physics - Abstract
Standing as one of the most significant barriers to reaching quantum advantage, state-preparation fidelities on noisy intermediate-scale quantum processors suffer from quantum-gate errors, which accumulate over time. A potential remedy is pulse-based state preparation. We numerically investigate the minimal evolution times (METs) attainable by optimizing (microwave and exchange) pulses on silicon hardware. We investigate two state preparation tasks. First, we consider the preparation of molecular ground states and find the METs for H$_2$, HeH$^+$, and LiH to be 2.4 ns, 4.4 ns, and 27.2 ns, respectively. Second, we consider transitions between arbitrary states and find the METs for transitions between arbitrary four-qubit states to be below 50 ns. For comparison, connecting arbitrary two-qubit states via one- and two-qubit gates on the same silicon processor requires approximately 200 ns. This comparison indicates that pulse-based state preparation is likely to utilize the coherence times of silicon hardware more efficiently than gate-based state preparation. Finally, we quantify the effect of silicon device parameters on the MET. We show that increasing the maximal exchange amplitude from 10 MHz to 1 GHz accelerates the METs, e.g., for H$_2$ from 84.3 ns to 2.4 ns. This demonstrates the importance of fast exchange. We also show that increasing the maximal amplitude of the microwave drive from 884 kHz to 56.6 MHz shortens state transitions, e.g., for two-qubit states from 1000 ns to 25 ns. Our results bound both the state-preparation times for general quantum algorithms and the execution times of variational quantum algorithms with silicon spin qubits., Comment: 9 + (7) pages, 6 figs, comments are welcomed
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- 2024
3. Restricted Open-shell cluster Mean-Field theory for Strongly Correlated Systems
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Bachhar, Arnab and Mayhall, Nicholas J.
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Physics - Chemical Physics - Abstract
The cluster-based Mean Field method (cMF) and it's second order perturbative correction[1], was introduced by Jim\'enez-Hoyos and Scuseria to reduce the cost of modeling strongly correlated systems by dividing an active space up into small clusters, which are individually solved in the mean-field presence of each other. In that work, clusters with unpaired electrons are treated naturally, by allowing the $\alpha$ and $\beta$ orbitals to spin polarize. While that provided significant energetic stabilization, the resulting cMF wavefunction was spin-contaminated, making it difficult to use as a reference state for spin-pure post-cMF methods. In this work, we propose the Restricted Open-shell cMF (RO-cMF) method, extending the cMF approach to systems with open-shell clusters, while not permitting spin-polarization. While the resulting RO-cMF energies are necessarily higher in energy than the unrestricted orbital cMF, the new RO-cMF provides a simple reference state for post-cMF methods that recover the missing inter-cluster correlations. We provide a detailed explanation of the method, and report demonstrative calculations of exchange coupling constants for three systems: a di-iron complex, a di-chromium complex, and a dimerized organic radical. We also report the first perturbatively corrected RO-cMF-PT2 results as well.
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- 2024
4. Parameterization and optimizability of pulse-level VQEs
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Sherbert, Kyle M, Amer, Hisham, Economou, Sophia E, Barnes, Edwin, and Mayhall, Nicholas J
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Quantum Physics - Abstract
In conventional variational quantum eigensolvers (VQEs), trial states are prepared by applying series of parameterized gates to a reference state, with the gate parameters being varied to minimize the energy of the target system. Recognizing that the gates are intermediates which are ultimately compiled into a set of control pulses to be applied to each qubit in the lab, the recently proposed ctrl-VQE algorithm takes the amplitudes, frequencies, and phases of the pulse as the variational parameters used to minimize the molecular energy. In this work, we explore how all three degrees of freedom interrelate with one another. To this end, we consider several distinct strategies to parameterize the control pulses, assessing each one through numerical simulations of a transmon-like device. For each parameterization, we contrast the pulse duration required to prepare a good ansatz, and the difficulty to optimize that ansatz from a well-defined initial state. We deduce several guiding heuristics to implement practical ctrl-VQE in hardware, which we anticipate will generalize for generic device architectures., Comment: 13 pages (10 of main text), 6 figures
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- 2024
5. Physically motivated improvements of Variational Quantum Eigensolvers
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Vaquero-Sabater, Nonia, Carreras, Abel, Orús, Román, Mayhall, Nicholas J., and Casanova, David
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Quantum Physics - Abstract
The Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum Eigensolver (ADAPT-VQE) has emerged as a pivotal promising approach for electronic structure challenges in quantum chemistry with noisy quantum devices. Nevertheless, to surmount existing technological constraints, this study endeavors to enhance ADAPT-VQE's efficacy. Leveraging insights from electronic structure theory, we concentrate on optimizing state preparation without added computational burden and guiding ansatz expansion to yield more concise wavefunctions with expedited convergence toward exact solutions. These advancements culminate in shallower circuits and, as demonstrated, reduced measurement requirements. This research delineates these enhancements and assesses their performance across mono, di, and tridimensional arrangements of H4 models, as well as in the water molecule. Ultimately, this work attests to the viability of physically-motivated strategies in fortifying ADAPT-VQE's efficiency, marking a significant stride in quantum chemistry simulations.
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- 2024
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6. Accurate and Interpretable Representation of Correlated Electronic Structure via Tensor Product Selected CI
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Braunscheidel, Nicole M., Bachhar, Arnab, and Mayhall, Nicholas J.
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Physics - Chemical Physics - Abstract
The task of computing wavefunctions that are accurate, yet simple enough mathematical objects to use for reasoning has long been a challenge in quantum chemistry. The difficulty in drawing physical conclusions from a wavefunction is often related to the generally large number of configurations with similar weights. In Tensor Product Selected CI, we use a locally correlated tensor product state basis, which has the effect of concentrating the weight of a state onto a smaller number of physically interpretable degrees of freedom. In this paper, we apply TPSCI to a series of three molecular systems ranging in separability, one of which is the first application of TPSCI to an open-shell bimetallic system. For each of these systems, we obtain accurate solutions to large active spaces, and analyze the resulting wavefunctions through a series of different approaches including (i) direct inspection of the TPS basis coefficients, (ii) construction of Bloch effective Hamiltonians, and (iii) computation of cluster correlation functions.
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- 2024
7. Reducing measurement costs by recycling the Hessian in adaptive variational quantum algorithms
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Ramôa, Mafalda, Santos, Luis Paulo, Mayhall, Nicholas J., Barnes, Edwin, and Economou, Sophia E.
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Quantum Physics - Abstract
Adaptive protocols enable the construction of more efficient state preparation circuits in variational quantum algorithms (VQAs) by utilizing data obtained from the quantum processor during the execution of the algorithm. This idea originated with ADAPT-VQE, an algorithm that iteratively grows the state preparation circuit operator by operator, with each new operator accompanied by a new variational parameter, and where all parameters acquired thus far are optimized in each iteration. In ADAPT-VQE and other adaptive VQAs that followed it, it has been shown that initializing parameters to their optimal values from the previous iteration speeds up convergence and avoids shallow local traps in the parameter landscape. However, no other data from the optimization performed at one iteration is carried over to the next. In this work, we propose an improved quasi-Newton optimization protocol specifically tailored to adaptive VQAs. The distinctive feature in our proposal is that approximate second derivatives of the cost function are recycled across iterations in addition to parameter values. We implement a quasi-Newton optimizer where an approximation to the inverse Hessian matrix is continuously built and grown across the iterations of an adaptive VQA. The resulting algorithm has the flavor of a continuous optimization where the dimension of the search space is augmented when the gradient norm falls below a given threshold. We show that this inter-optimization exchange of second-order information leads the Hessian in the state of the optimizer to better approximate the exact Hessian. As a result, our method achieves a superlinear convergence rate even in situations where the typical quasi-Newton optimizer converges only linearly. Our protocol decreases the measurement costs in implementing adaptive VQAs on quantum hardware as well as the runtime of their classical simulation.
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- 2024
8. How to really measure operator gradients in ADAPT-VQE
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Anastasiou, Panagiotis G., Mayhall, Nicholas J., Barnes, Edwin, and Economou, Sophia E.
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Quantum Physics - Abstract
ADAPT-VQE is one of the leading VQE algorithms which circumvents the choice-of-ansatz conundrum by iteratively growing compact and arbitrarily accurate problem-tailored ans\"atze. However, for hardware-efficient operator pools, the gradient-measurement step of the algorithm requires the estimation of $O(N^8)$ observables, which may represent a bottleneck for relevant system sizes on real devices. We present an efficient strategy for measuring the pool gradients based on simultaneously measuring commuting observables. We argue that our approach is relatively robust to shot-noise effects, and show that measuring the pool gradients is in fact only $O(N)$ times as expensive as a naive VQE iteration. Our proposed measurement strategy significantly ameliorates the measurement overhead of ADAPT-VQE and brings us one step closer to practical implementations on real devices., Comment: 8 pages, 2 figures
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- 2023
9. Generalization of the tensor product selected CI method for molecular excited states
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Braunscheidel, Nicole M., Abraham, Vibin, and Mayhall, Nicholas J.
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Physics - Chemical Physics - Abstract
In a recent paper [JCTC, 2020, 16, 6098], we introduced a new approach for accurately approximating full CI ground states in large electronic active-spaces, called Tensor Product Selected CI (TPSCI). In TPSCI, a large orbital active space is first partitioned into disjoint sets (clusters) for which the exact, local many-body eigenstates are obtained. Tensor products of these locally correlated many-body states are taken as the basis for the full, global Hilbert space. By folding correlation into the basis states themselves, the low-energy eigenstates become increasingly sparse, creating a more compact selected CI expansion. While we demonstrated that this approach can improve accuracy for a variety of systems, there is even greater potential for applications to excited states, particularly those which have some excited state character. In this paper, we report on the accuracy of TPSCI for excited states, including a far more efficient implementation in the Julia programming language. In traditional SCI methods that use a Slater determinant basis, accurate excitation energies are obtained only after a linear extrapolation and at a large computational cost. We find that TPSCI with perturbative corrections provides accurate excitation energies for several excited states of various polycyclic aromatic hydrocarbons (PAH) with respect to the extrapolated result (i.e. near exact result). Further, we use TPSCI to report highly accurate estimates of the lowest 31 eigenstates for a tetracene tetramer system with an active space of 40 electrons in 40 orbitals, giving direct access to the initial bright states and the resulting 18 doubly excited (biexcitonic) states.
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- 2023
10. Quantum simulation of molecular response properties
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Kumar, Ashutosh, Asthana, Ayush, Abraham, Vibin, Crawford, T. Daniel, Mayhall, Nicholas J., Zhang, Yu, Cincio, Lukasz, Tretiak, Sergei, and Dub, Pavel A.
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Quantum Physics ,Physics - Chemical Physics - Abstract
Accurate modeling of the response of molecular systems to an external electromagnetic field is challenging on classical computers, especially in the regime of strong electronic correlation. In this paper, we develop a quantum linear response (qLR) theory to calculate molecular response properties on near-term quantum computers. Inspired by the recently developed variants of the quantum counterpart of equation of motion (qEOM) theory, the qLR formalism employs "killer condition" satisfying excitation operator manifolds that offers a number of theoretical advantages along with reduced quantum resource requirements. We also used the qEOM framework in this work to calculate state-specific response properties. Further, through noise-less quantum simulations, we show that response properties calculated using the qLR approach are more accurate than the ones obtained from the classical coupled-cluster based linear response models due to the improved quality of the ground-state wavefunction obtained using the ADAPT-VQE algorithm.
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- 2023
11. Projection-Based Molecular Quantum Embedding via Singular-Value-Informed Orbital Partitioning
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Claudino, Daniel C., primary, Smith, Robert L., additional, and Mayhall, Nicholas J., additional
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- 2024
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12. TETRIS-ADAPT-VQE: An adaptive algorithm that yields shallower, denser circuit ans\'atze
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Anastasiou, Panagiotis G., Chen, Yanzhu, Mayhall, Nicholas J., Barnes, Edwin, and Economou, Sophia E.
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Quantum Physics - Abstract
Adaptive quantum variational algorithms are particularly promising for simulating strongly correlated systems on near-term quantum hardware, but they are not yet viable due, in large part, to the severe coherence time limitations on current devices. In this work, we introduce an algorithm called TETRIS-ADAPT-VQE, which iteratively builds up variational ans\"atze a few operators at a time in a way dictated by the problem being simulated. This algorithm is a modified version of the ADAPT-VQE algorithm in which the one-operator-at-a-time rule is lifted to allow for the addition of multiple operators with disjoint supports in each iteration. TETRIS-ADAPT-VQE results in denser but significantly shallower circuits, without increasing the number of CNOT gates or variational parameters. Its advantage over the original algorithm in terms of circuit depths increases with the system size. Moreover, the expensive step of measuring the energy gradient with respect to each candidate unitary at each iteration is performed only a fraction of the time compared to ADAPT-VQE. These improvements bring us closer to the goal of demonstrating a practical quantum advantage on quantum hardware., Comment: 10 pages, 7 figures
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- 2022
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13. New Local Explorations of the Unitary Coupled Cluster Energy Landscape
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Grimsley, Harper R. and Mayhall, Nicholas J.
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Physics - Chemical Physics ,Quantum Physics - Abstract
The recent quantum information boom has effected a resurgence of interest in unitary coupled cluster (UCC) theory. Our group's interest in local energy landscapes of unitary ans\"atze prompted us to investigate the classical approach of truncating the Taylor series expansion (instead of a perturbative expansion) of UCCSD energy at second-order. This amounts to an approach where electron correlation energy is estimated by taking a single Newton-Raphson step from Hartree-Fock toward UCCSD. Such an approach has been explored previously, but the accuracy was not extensively studied. In this paper, we investigate the performance and observe similar pathologies to linearized coupled cluster with singles and doubles. We introduce the use of derivatives of order three or greater to help partially recover the variational lower bound of true UCCSD, restricting these derivatives to those of the "unmixed" category in order to simplify the model. By testing the approach on several potential energy surfaces and reaction energies, we find this "diagonal" approximation to higher order terms to be effective at reducing sensitivity near singularities for strongly correlated regimes, while not significantly diminishing the accuracy of weakly correlated systems., Comment: 11 pages, 7 figures (including SI)
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- 2022
14. Symmetry breaking slows convergence of the ADAPT Variational Quantum Eigensolver
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Bertels, Luke W., Grimsley, Harper R., Economou, Sophia E., Barnes, Edwin, and Mayhall, Nicholas J.
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Quantum Physics - Abstract
Because quantum simulation of molecular systems is expected to provide the strongest advantage over classical computing methods for systems exhibiting strong electron correlation, it is critical that the performance of VQEs be assessed for strongly correlated systems. For classical simulation, strong correlation often results in symmetry-breaking of the Hartree-Fock reference, leading to L\"owdin's well-known ``symmetry dilemma'' whereby accuracy in the energy can be increased by breaking spin or spatial symmetries. Here, we explore the impact of symmetry breaking on the performance of ADAPT-VQE using two strongly correlated systems: (i) the ``fermionized" anisotropic Heisenberg model, where the anisotropy parameter controls the correlation in the system, and (ii) symmetrically-stretched linear \ce{H4}, where correlation increases with increasing H-H separation. In both of these cases, increasing the level of correlation of the system leads to spontaneous symmetry breaking (parity and $\hat{S}^{2}$, respectively) of the mean-field solutions. We analyze the role that symmetry breaking in the reference states and orbital mappings of the fermionic Hamiltonians have on the compactness and performance of ADAPT-VQE. We observe that improving the energy of the reference states by breaking symmetry has a deleterious effect on ADAPT-VQE by increasing the length of the ansatz necessary for energy convergence and exacerbating the problem of ``gradient troughs"., Comment: 16 pages, 5 figures
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- 2022
15. Scaling adaptive quantum simulation algorithms via operator pool tiling
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Van Dyke, John S., Shirali, Karunya, Barron, George S., Mayhall, Nicholas J., Barnes, Edwin, and Economou, Sophia E.
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Quantum Physics ,Condensed Matter - Strongly Correlated Electrons - Abstract
Adaptive variational quantum simulation algorithms use information from the quantum computer to dynamically create optimal trial wavefunctions for a given problem Hamiltonian. A key ingredient in these algorithms is a predefined operator pool from which trial wavefunctions are constructed. Finding suitable pools is critical for the efficiency of the algorithm as the problem size increases. Here, we present a technique called operator pool tiling that facilitates the construction of problem-tailored pools for arbitrarily large problem instances. By first performing an ADAPT-VQE calculation on a smaller instance of the problem using a large, but computationally inefficient operator pool, we extract the most relevant operators and use them to design more efficient pools for larger instances. We demonstrate the method here on strongly correlated quantum spin models in one and two dimensions, finding that ADAPT automatically finds a highly effective ansatz for these systems. Given that many problems, such as those arising in condensed matter physics, have a naturally repeating lattice structure, we expect the pool tiling method to be a widely applicable technique apt for such systems., Comment: 9 pages, 4 figures
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- 2022
16. Quantum self-consistent equation-of-motion method for computing molecular excitation energies, ionization potentials, and electron affinities on a quantum computer
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Asthana, Ayush, Kumar, Ashutosh, Abraham, Vibin, Grimsley, Harper, Zhang, Yu, Cincio, Lukasz, Tretiak, Sergei, Dub, Pavel A., Economou, Sophia E., Barnes, Edwin, and Mayhall, Nicholas J.
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Quantum Physics ,Condensed Matter - Strongly Correlated Electrons ,Physics - Chemical Physics - Abstract
Near-term quantum computers are expected to facilitate material and chemical research through accurate molecular simulations. Several developments have already shown that accurate ground-state energies for small molecules can be evaluated on present-day quantum devices. Although electronically excited states play a vital role in chemical processes and applications, the search for a reliable and practical approach for routine excited-state calculations on near-term quantum devices is ongoing. Inspired by excited-state methods developed for the unitary coupled-cluster theory in quantum chemistry, we present an equation-of-motion-based method to compute excitation energies following the variational quantum eigensolver algorithm for ground-state calculations on a quantum computer. We perform numerical simulations on H$_2$, H$_4$, H$_2$O, and LiH molecules to test our quantum self-consistent equation-of-motion (q-sc-EOM) method and compare it to other current state-of-the-art methods. q-sc-EOM makes use of self-consistent operators to satisfy the vacuum annihilation condition, a critical property for accurate calculations. It provides real and size-intensive energy differences corresponding to vertical excitation energies, ionization potentials and electron affinities. We also find that q-sc-EOM is more suitable for implementation on NISQ devices as it is expected to be more resilient to noise compared with the currently available methods.
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- 2022
17. Coupled electron pair-type approximations for tensor product state wavefunctions
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Abraham, Vibin and Mayhall, Nicholas J.
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Physics - Chemical Physics - Abstract
Size extensivity, defined as the correct scaling of energy with system size, is a desirable property for any many-body method. Traditional CI methods are not size extensive hence the error increases as the system gets larger. Coupled electron pair approximation (CEPA) methods can be constructed as simple extensions of truncated configuration interaction (CI) that ensures size extensivity. One of the major issues with the CEPA and its variants is that singularities arise in the amplitude equations when the system starts to be strongly correlated. In this work, we extend the traditional Slater determinant-based coupled electron pair approaches like CEPA-0, averaged coupled-pair functional (ACPF) and average quadratic coupled-cluster (AQCC) to a new formulation based on tensor product states (TPS). We show that a TPS basis can often be chosen such that it removes the singularities that commonly destroy the accuracy of CEPA-based methods. A suitable TPS representation can be formed by partitioning the system into separate disjoint clusters and forming the final wavefunction as the tensor product of the many body states of these clusters. We demonstrate the application of these methods on simple bond breaking systems such as CH$_4$ and F$_2$ where determinant based CEPA methods fail. We further apply the TPS-CEPA approach to stillbene isomerization and few planar $\pi-$conjugated systems. Overall the results show that the TPS-CEPA method can remove the singularities and provide improved numerical results compared to common electronic structure methods.
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- 2022
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18. How Much Entanglement Do Quantum Optimization Algorithms Require?
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Chen, Yanzhu, Zhu, Linghua, Liu, Chenxu, Mayhall, Nicholas J., Barnes, Edwin, and Economou, Sophia E.
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Quantum Physics - Abstract
Many classical optimization problems can be mapped to finding the ground states of diagonal Ising Hamiltonians, for which variational quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) provide heuristic methods. Because the solutions of such classical optimization problems are necessarily product states, it is unclear how entanglement affects their performance. An Adaptive Derivative-Assembled Problem-Tailored (ADAPT) variation of QAOA improves the convergence rate by allowing entangling operations in the mixer layers whereas it requires fewer CNOT gates in the entire circuit. In this work, we study the entanglement generated during the execution of ADAPT-QAOA. Through simulations of the weighted Max-Cut problem, we show that ADAPT-QAOA exhibits substantial flexibility in entangling and disentangling qubits. By incrementally restricting this flexibility, we find that a larger amount of entanglement entropy at earlier stages coincides with faster convergence at later stages. In contrast, while the standard QAOA quickly generates entanglement within a few layers, it cannot remove excess entanglement efficiently. Our results demonstrate that the role of entanglement in quantum optimization is subtle and provide guidance for building favorable features into quantum optimization algorithms., Comment: 15 pages, 7 figures. Comments are welcome
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- 2022
19. ADAPT-VQE is insensitive to rough parameter landscapes and barren plateaus
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Grimsley, Harper R., Barron, George S., Barnes, Edwin, Economou, Sophia E., and Mayhall, Nicholas J.
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Quantum Physics ,Physics - Chemical Physics - Abstract
Variational quantum eigensolvers (VQEs) represent a powerful class of hybrid quantum-classical algorithms for computing molecular energies. Various numerical issues exist for these methods, however, including barren plateaus and large numbers of local minima. In this work, we consider Adaptive, Problem-Tailored (ADAPT)-VQE ans\"atze, and examine how they are impacted by these local minima. We find that while ADAPT-VQE does not remove local minima, the gradient-informed, one-operator-at-a-time circuit construction seems to accomplish two things: First, it provides an initialization strategy that is dramatically better than random initialization, and which is applicable in situations where chemical intuition cannot help with initialization, i.e., when Hartree-Fock is a poor approximation to the ground state. Second, even if an ADAPT-VQE iteration converges to a local trap at one step, it can still "burrow" toward the exact solution by adding more operators, which preferentially deepens the occupied trap. This same mechanism helps highlight a surprising feature of ADAPT-VQE: It should not suffer optimization problems due to "barren plateaus". Even if barren plateaus appear in the parameter landscape, our analysis and simulations reveal that ADAPT-VQE avoids such regions by design.
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- 2022
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20. Adaptive variational algorithms for quantum Gibbs state preparation
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Warren, Ada, Zhu, Linghua, Mayhall, Nicholas J., Barnes, Edwin, and Economou, Sophia E.
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Quantum Physics - Abstract
The preparation of Gibbs thermal states is an important task in quantum computation with applications in quantum simulation, quantum optimization, and quantum machine learning. However, many algorithms for preparing Gibbs states rely on quantum subroutines which are difficult to implement on near-term hardware. Here, we address this by (i) introducing an objective function that, unlike the free energy, is easily measured, and (ii) using dynamically generated, problem-tailored ans\"atze. This allows for arbitrarily accurate Gibbs state preparation using low-depth circuits. To verify the effectiveness of our approach, we numerically demonstrate that our algorithm can prepare high-fidelity Gibbs states across a broad range of temperatures and for a variety of Hamiltonians., Comment: 7 pages, 3 figures
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- 2022
21. Minimizing state preparation times in pulse-level variational molecular simulations
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Asthana, Ayush, Liu, Chenxu, Meitei, Oinam Romesh, Economou, Sophia E., Barnes, Edwin, and Mayhall, Nicholas J.
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Quantum Physics ,Physics - Chemical Physics - Abstract
Quantum simulation on NISQ devices is severely limited by short coherence times. A variational pulse-shaping algorithm known as ctrl-VQE was recently proposed to address this issue by eliminating the need for parameterized quantum circuits, which lead to long state preparation times. Here, we find the shortest possible pulses for ctrl-VQE to prepare target molecular wavefunctions for a given device Hamiltonian describing coupled transmon qubits. We find that the time-optimal pulses that do this have a bang-bang form consistent with Pontryagin's maximum principle. We further investigate how the minimal state preparation time is impacted by truncating the transmons to two versus more levels. We find that leakage outside the computational subspace (something that is usually considered problematic) speeds up the state preparation, further reducing device coherence-time demands. This speedup is due to an enlarged solution space of target wavefunctions and to the appearance of additional channels connecting initial and target states.
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- 2022
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22. Avoiding symmetry roadblocks and minimizing the measurement overhead of adaptive variational quantum eigensolvers
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Shkolnikov, V. O., Mayhall, Nicholas J., Economou, Sophia E., and Barnes, Edwin
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Quantum Physics - Abstract
Quantum simulation of strongly correlated systems is potentially the most feasible useful application of near-term quantum computers. Minimizing quantum computational resources is crucial to achieving this goal. A promising class of algorithms for this purpose consists of variational quantum eigensolvers (VQEs). Among these, problem-tailored versions such as ADAPT-VQE that build variational ans\"atze step by step from a predefined operator pool perform particularly well in terms of circuit depths and variational parameter counts. However, this improved performance comes at the expense of an additional measurement overhead compared to standard VQEs. Here, we show that this overhead can be reduced to an amount that grows only linearly with the number $n$ of qubits, instead of quartically as in the original ADAPT-VQE. We do this by proving that operator pools of size $2n-2$ can represent any state in Hilbert space if chosen appropriately. We prove that this is the minimal size of such "complete" pools, discuss their algebraic properties, and present necessary and sufficient conditions for their completeness that allow us to find such pools efficiently. We further show that, if the simulated problem possesses symmetries, then complete pools can fail to yield convergent results, unless the pool is chosen to obey certain symmetry rules. We demonstrate the performance of such symmetry-adapted complete pools by using them in classical simulations of ADAPT-VQE for several strongly correlated molecules. Our findings are relevant for any VQE that uses an ansatz based on Pauli strings., Comment: 15+10 pages, 7 figures
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- 2021
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23. Author Correction: Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus
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Grimsley, Harper R., Barron, George S., Barnes, Edwin, Economou, Sophia E., and Mayhall, Nicholas J.
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- 2023
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24. Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus
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Grimsley, Harper R., Barron, George S., Barnes, Edwin, Economou, Sophia E., and Mayhall, Nicholas J.
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- 2023
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25. Preparing Bethe Ansatz Eigenstates on a Quantum Computer
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Van Dyke, John S., Barron, George S., Mayhall, Nicholas J., Barnes, Edwin, and Economou, Sophia E.
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Quantum Physics - Abstract
Several quantum many-body models in one dimension possess exact solutions via the Bethe ansatz method, which has been highly successful for understanding their behavior. Nevertheless, there remain physical properties of such models for which analytic results are unavailable, and which are also not well-described by approximate numerical methods. Preparing Bethe ansatz eigenstates directly on a quantum computer would allow straightforward extraction of these quantities via measurement. We present a quantum algorithm for preparing Bethe ansatz eigenstates of the spin-1/2 XXZ spin chain that correspond to real-valued solutions of the Bethe equations. The algorithm is polynomial in the number of T gates and circuit depth, with modest constant prefactors. Although the algorithm is probabilistic, with a success rate that decreases with increasing eigenstate energy, we employ amplitude amplification to boost the success probability. The resource requirements for our approach are lower than other state-of-the-art quantum simulation algorithms for small error-corrected devices, and thus may offer an alternative and computationally less-demanding demonstration of quantum advantage for physically relevant problems., Comment: 14 pages, 9 figures
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- 2021
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26. Spin-flip pair-density functional theory: A practical approach to treat static and dynamical correlations in large molecules
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Meitei, Oinam Romesh and Mayhall, Nicholas J.
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Condensed Matter - Strongly Correlated Electrons ,Physics - Chemical Physics - Abstract
We present a practical approach to treat static and dynamical correlation accurately in large multi-configurational systems. The static correlation is accounted for using the spin-flip approach which is well known for capturing static correlation accurately at low-computational expense. Unlike previous approaches to add dynamical correlation to spin-flip models which use perturbation theory or coupled-cluster theory, we explore the ability to use the on-top pair-density functional theory approaches recently developed by Gagliardi and co-workers (JCTC, 10, 3669, 2014). External relaxations are carried out in the spin-flip calculations though a restricted active space framework for which a truncation scheme for the orbitals used in the external excitation is presented. The performance of the approach is demonstrated by computing energy gaps between ground and excited states for diradicals, triradicals and linear polyacene chains ranging from naphthalene to dodecacene. Accurate results are obtained using the new approach for these challenging open-shell molecular systems.
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- 2021
27. Gate-free state preparation for fast variational quantum eigensolver simulations: ctrl-VQE
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Meitei, Oinam Romesh, Gard, Bryan T., Barron, George S., Pappas, David P., Economou, Sophia E., Barnes, Edwin, and Mayhall, Nicholas J.
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Quantum Physics ,Condensed Matter - Strongly Correlated Electrons ,Physics - Chemical Physics - Abstract
The variational quantum eigensolver (VQE) is currently the flagship algorithm for solving electronic structure problems on near-term quantum computers. This hybrid quantum/classical algorithm involves implementing a sequence of parameterized gates on quantum hardware to generate a target quantum state, and then measuring the expectation value of the molecular Hamiltonian. Due to finite coherence times and frequent gate errors, the number of gates that can be implemented remains limited on current quantum devices, preventing accurate applications to systems with significant entanglement, such as strongly correlated molecules. In this work, we propose an alternative algorithm (which we refer to as ctrl-VQE) where the quantum circuit used for state preparation is removed entirely and replaced by a quantum control routine which variationally shapes a pulse to drive the initial Hartree-Fock state to the full CI target state. As with VQE, the objective function optimized is the expectation value of the qubit-mapped molecular Hamiltonian. However, by removing the quantum circuit, the coherence times required for state preparation can be drastically reduced by directly optimizing the pulses. We demonstrate the potential of this method numerically by directly optimizing pulse shapes which accurately model the dissociation curves of the hydrogen molecule (covalent bond) and helium hydride ion (ionic bond), and we compute the single point energy for LiH with four transmons.
- Published
- 2020
28. An adaptive quantum approximate optimization algorithm for solving combinatorial problems on a quantum computer
- Author
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Zhu, Linghua, Tang, Ho Lun, Barron, George S., Calderon-Vargas, F. A., Mayhall, Nicholas J., Barnes, Edwin, and Economou, Sophia E.
- Subjects
Quantum Physics - Abstract
The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves combinatorial optimization problems. While there is evidence suggesting that the fixed form of the standard QAOA ansatz is not optimal, there is no systematic approach for finding better ans\"atze. We address this problem by developing an iterative version of QAOA that is problem-tailored, and which can also be adapted to specific hardware constraints. We simulate the algorithm on a class of Max-Cut graph problems and show that it converges much faster than the standard QAOA, while simultaneously reducing the required number of CNOT gates and optimization parameters. We provide evidence that this speedup is connected to the concept of shortcuts to adiabaticity., Comment: 11 pages, 7 figures; v3: additional analysis, analytical results, and simulations of larger systems
- Published
- 2020
29. Preserving Symmetries for Variational Quantum Eigensolvers in the Presence of Noise
- Author
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Barron, George S., Gard, Bryan T., Altman, Orien J., Mayhall, Nicholas J., Barnes, Edwin, and Economou, Sophia E.
- Subjects
Quantum Physics - Abstract
One of the most promising applications of noisy intermediate-scale quantum computers is the simulation of molecular Hamiltonians using the variational quantum eigensolver. We show that encoding symmetries of the simulated Hamiltonian in the VQE ansatz reduces both classical and quantum resources compared to other, widely available ansatze. Through simulations of the H$_2$ molecule, we verify that these improvements persist in the presence of noise. This simulation is performed with IBM software using noise models from real devices. We also demonstrate how these techniques can be used to find molecular excited states of various symmetries using a noisy processor. We use error mitigation techniques to further improve the quality of our results.
- Published
- 2020
- Full Text
- View/download PDF
30. Selected Configuration Interaction in a Basis of Cluster State Tensor Products
- Author
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Abraham, Vibin and Mayhall, Nicholas J.
- Subjects
Condensed Matter - Strongly Correlated Electrons ,Physics - Chemical Physics - Abstract
Selected configuration interaction (SCI) methods are currently enjoying a resurgence due to several recent developments which improve either the overall computational efficiency or the compactness of the resulting SCI vector. These recent advances have made it possible to get full CI (FCI) quality results for much larger orbital active spaces, compared to conventional approaches. However, due to the starting assumption that the FCI vector has only a small number of significant Slater determinants, SCI becomes intractable for systems with strong correlation. This paper introduces a method for developing SCI algorithms in a way which exploits local molecular structure to significantly reduce the number of SCI variables. The proposed method is defined by first grouping the orbitals into clusters over which we can define many particle cluster states. We then directly perform the SCI algorithm in a basis of tensor products of cluster states instead of Slater determinants. While the approach is general for arbitrarily defined cluster states, we find significantly improved performance by defining cluster states through a Tucker decomposition of the global (and sparse) SCI vector. To demonstrate the potential of this method, called tensor product selected configuration interaction (TPSCI), we present numerical results for a diverse set of examples: 1) modified Hubbard model with different inter- and intra-cluster hopping terms, 2) less obviously clusterable cases of bond breaking in N2 and F2, and 3) ground state energies of large planar {\pi}-conjugated systems with active spaces of up to 42 electrons in 42 orbitals. These numerical results show that TPSCI can be used to significantly reduce the number of SCI variables in the variational space, and thus paving a path for extending these deterministic and variational SCI approaches to a wider range of physical systems.
- Published
- 2020
- Full Text
- View/download PDF
31. qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor
- Author
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Tang, Ho Lun, Shkolnikov, V. O., Barron, George S., Grimsley, Harper R., Mayhall, Nicholas J., Barnes, Edwin, and Economou, Sophia E.
- Subjects
Quantum Physics - Abstract
Quantum simulation, one of the most promising applications of a quantum computer, is currently being explored intensely using the variational quantum eigensolver. The feasibility and performance of this algorithm depend critically on the form of the wavefunction ansatz. Recently in Nat. Commun. 10, 3007 (2019), an algorithm termed ADAPT-VQE was introduced to build system-adapted ans\"atze with substantially fewer variational parameters compared to other approaches. This algorithm relies heavily on a predefined operator pool with which it builds the ansatz. However, Nat. Commun. 10, 3007 (2019) did not provide a prescription for how to select the pool, how many operators it must contain, or whether the resulting ansatz will succeed in converging to the ground state. In addition, the pool used in that work leads to state preparation circuits that are too deep for a practical application on near-term devices. Here, we address all these key outstanding issues of the algorithm. We present a hardware-efficient variant of ADAPT-VQE that drastically reduces circuit depths using an operator pool that is guaranteed to contain the operators necessary to construct exact ans\"atze. Moreover, we show that the minimal pool size that achieves this scales linearly with the number of qubits. Through numerical simulations on $\text{H}_4$, LiH and $\text{H}_6$, we show that our algorithm ("qubit-ADAPT") reduces the circuit depth by an order of magnitude while maintaining the same accuracy as the original ADAPT-VQE. A central result of our approach is that the additional measurement overhead of qubit-ADAPT compared to fixed-ansatz variational algorithms scales only linearly with the number of qubits. Our work provides a crucial step forward in running algorithms on near-term quantum devices., Comment: 15 pages, 6 figures; v2 includes a new proof that the minimal operator pool size scales linearly in the number of qubits. Explicit examples of such pools are also now included
- Published
- 2019
- Full Text
- View/download PDF
32. Is the Trotterized UCCSD Ansatz chemically well-defined?
- Author
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Grimsley, Harper R., Claudino, Daniel, Economou, Sophia E., Barnes, Edwin, and Mayhall, Nicholas J.
- Subjects
Quantum Physics - Abstract
The variational quantum eigensolver (VQE) has emerged as one of the most promising near-term quantum algorithms that can be used to simulate many-body systems such as molecular electronic structures. Serving as an attractive ansatz in the VQE algorithm, unitary coupled cluster (UCC) theory has seen a renewed interest in recent literature. However, unlike the original classical UCC theory, implementation on a quantum computer requires a finite-order Suzuki-Trotter decomposition to separate the exponentials of the large sum of Pauli operators. While previous literature has recognized the non-uniqueness of different orderings of the operators in the Trotterized form of UCC methods, the question of whether or not different orderings matter at the chemical scale has not been addressed. In this letter, we explore the effect of operator ordering on the Trotterized UCCSD ansatz, as well as the much more compact $k$-UpCCGSD ansatz recently proposed by Lee et al. We observe a significant, system-dependent variation in the energies of Trotterizations with different operator orderings. The energy variations occur on a chemical scale, sometimes on the order of hundreds of kcal/mol. This letter establishes the need to define not only the operators present in the ansatz, but also the order in which they appear. This is necessary for adhering to the quantum chemical notion of a ``model chemistry'', in addition to the general importance of scientific reproducibility. As a final note, we suggest a useful strategy to select out of the combinatorial number of possibilities, a single well-defined and effective ordering of the operators., Comment: 6 pages, 2 figures
- Published
- 2019
- Full Text
- View/download PDF
33. Efficient Symmetry-Preserving State Preparation Circuits for the Variational Quantum Eigensolver Algorithm
- Author
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Gard, Bryan T., Zhu, Linghua, Barron, George S., Mayhall, Nicholas J., Economou, Sophia E., and Barnes, Edwin
- Subjects
Quantum Physics - Abstract
The variational quantum eigensolver is one of the most promising approaches for performing chemistry simulations using noisy intermediate-scale quantum (NISQ) processors. The efficiency of this algorithm depends crucially on the ability to prepare multi-qubit trial states on the quantum processor that either include, or at least closely approximate, the actual energy eigenstates of the problem being simulated while avoiding states that have little overlap with them. Symmetries play a central role in determining the best trial states. Here, we present efficient state preparation circuits that respect particle number, total spin, spin projection, and time-reversal symmetries. These circuits contain the minimal number of variational parameters needed to fully span the appropriate symmetry subspace dictated by the chemistry problem while avoiding all irrelevant sectors of Hilbert space. We show how to construct these circuits for arbitrary numbers of orbitals, electrons, and spin quantum numbers, and we provide explicit decompositions and gate counts in terms of standard gate sets in each case. We test our circuits in quantum simulations of the $H_2$ and $LiH$ molecules and find that they outperform standard state preparation methods in terms of both accuracy and circuit depth., Comment: 19 pages, 15 figures (v3 significant updates to match published version)
- Published
- 2019
- Full Text
- View/download PDF
34. An adaptive variational algorithm for exact molecular simulations on a quantum computer
- Author
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Grimsley, Harper R., Economou, Sophia E., Barnes, Edwin, and Mayhall, Nicholas J.
- Subjects
Quantum Physics ,Condensed Matter - Strongly Correlated Electrons ,Physics - Chemical Physics - Abstract
Quantum simulation of chemical systems is one of the most promising near-term applications of quantum computers. The variational quantum eigensolver, a leading algorithm for molecular simulations on quantum hardware, has a serious limitation in that it typically relies on a pre-selected wavefunction ansatz that results in approximate wavefunctions and energies. Here we present an arbitrarily accurate variational algorithm that instead of fixing an ansatz upfront, this algorithm grows it systematically one operator at a time in a way dictated by the molecule being simulated. This generates an ansatz with a small number of parameters, leading to shallow-depth circuits. We present numerical simulations, including for a prototypical strongly correlated molecule, which show that our algorithm performs much better than a unitary coupled cluster approach, in terms of both circuit depth and chemical accuracy. Our results highlight the potential of our adaptive algorithm for exact simulations with present-day and near-term quantum hardware., Comment: 11 pages, 3 figures; published version
- Published
- 2018
- Full Text
- View/download PDF
35. Negative exchange interactions in coupled few-electron quantum dots
- Author
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Deng, Kuangyin, Calderon-Vargas, F. A., Mayhall, Nicholas J., and Barnes, Edwin
- Subjects
Condensed Matter - Mesoscale and Nanoscale Physics - Abstract
It has been experimentally shown that negative exchange interactions can arise in a linear three-dot system when a two-electron double quantum dot is exchange coupled to a larger quantum dot containing on the order of one hundred electrons. The origin of this negative exchange can be traced to the larger quantum dot exhibiting a spin triplet-like rather than singlet-like ground state. Here, we show using a microscopic model based on the configuration interaction (CI) method that both triplet-like and singlet-like ground states are realized depending on the number of electrons. In the case of only four electrons, a full CI calculation reveals that triplet-like ground states occur for sufficiently large dots. These results hold for symmetric and asymmetric quantum dots in both Si and GaAs, showing that negative exchange interactions are robust in few-electron double quantum dots and do not require large numbers of electrons., Comment: 8 pages, 3 figures
- Published
- 2017
- Full Text
- View/download PDF
36. Scaling adaptive quantum simulation algorithms via operator pool tiling
- Author
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Van Dyke, John S., primary, Shirali, Karunya, additional, Barron, George S., additional, Mayhall, Nicholas J., additional, Barnes, Edwin, additional, and Economou, Sophia E., additional
- Published
- 2024
- Full Text
- View/download PDF
37. Accurate and Interpretable Representation of Correlated Electronic Structure via Tensor Product Selected CI
- Author
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Braunscheidel, Nicole M, primary, Bachhar, Arnab, additional, and Mayhall, Nicholas J., additional
- Published
- 2024
- Full Text
- View/download PDF
38. Quantum Simulation of Molecular Response Properties in the NISQ Era
- Author
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Kumar, Ashutosh, primary, Asthana, Ayush, additional, Abraham, Vibin, additional, Crawford, T. Daniel, additional, Mayhall, Nicholas J., additional, Zhang, Yu, additional, Cincio, Lukasz, additional, Tretiak, Sergei, additional, and Dub, Pavel A., additional
- Published
- 2023
- Full Text
- View/download PDF
39. Gate-free state preparation for fast variational quantum eigensolver simulations
- Author
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Meitei, Oinam Romesh, Gard, Bryan T., Barron, George S., Pappas, David P., Economou, Sophia E., Barnes, Edwin, and Mayhall, Nicholas J.
- Published
- 2021
- Full Text
- View/download PDF
40. Computational Quantum Chemistry for Multiple-Site Heisenberg Spin Couplings Made Simple: Still Only One Spin–Flip Required
- Author
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Mayhall, Nicholas J and Head-Gordon, Martin
- Subjects
DFT ,Heisenberg Hamiltonian ,ab initio ,exchange coupling constant ,organometallic chemistry ,spin−flip ,Physical Sciences ,Chemical Sciences - Abstract
We provide a simple procedure for using inexpensive ab initio calculations to compute exchange coupling constants, J(AB), for multiradical molecules containing both an arbitrary number of radical sites and an arbitrary number of unpaired electrons. For a system comprised of 2M unpaired electrons, one needs only to compute states having the Ŝ(z) quantum number M - 1. Conveniently, these are precisely the states that are accessed by the family of single spin-flip methods. Building an effective Hamiltonian with these states allows one to extract all of the J(AB) constants in the molecule. Unlike approaches based on density functional theory, this procedure relies on neither spin-contaminated states nor nonunique spin-projection formulas. A key benefit is that it is possible to obtain completely spin-pure exchange coupling constants with inexpensive ab initio calculations. A couple of examples are provided to illustrate the approach, including a 4-nickel cubane complex and a 6-chromium horseshoe complex with 18 entangled electrons.
- Published
- 2015
41. Advances in molecular quantum chemistry contained in the Q-Chem 4 program package
- Author
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Shao, Yihan, Gan, Zhengting, Epifanovsky, Evgeny, Gilbert, Andrew TB, Wormit, Michael, Kussmann, Joerg, Lange, Adrian W, Behn, Andrew, Deng, Jia, Feng, Xintian, Ghosh, Debashree, Goldey, Matthew, Horn, Paul R, Jacobson, Leif D, Kaliman, Ilya, Khaliullin, Rustam Z, Kuś, Tomasz, Landau, Arie, Liu, Jie, Proynov, Emil I, Rhee, Young Min, Richard, Ryan M, Rohrdanz, Mary A, Steele, Ryan P, Sundstrom, Eric J, Woodcock, H Lee, Zimmerman, Paul M, Zuev, Dmitry, Albrecht, Ben, Alguire, Ethan, Austin, Brian, Beran, Gregory JO, Bernard, Yves A, Berquist, Eric, Brandhorst, Kai, Bravaya, Ksenia B, Brown, Shawn T, Casanova, David, Chang, Chun-Min, Chen, Yunqing, Chien, Siu Hung, Closser, Kristina D, Crittenden, Deborah L, Diedenhofen, Michael, DiStasio, Robert A, Do, Hainam, Dutoi, Anthony D, Edgar, Richard G, Fatehi, Shervin, Fusti-Molnar, Laszlo, Ghysels, An, Golubeva-Zadorozhnaya, Anna, Gomes, Joseph, Hanson-Heine, Magnus WD, Harbach, Philipp HP, Hauser, Andreas W, Hohenstein, Edward G, Holden, Zachary C, Jagau, Thomas-C, Ji, Hyunjun, Kaduk, Benjamin, Khistyaev, Kirill, Kim, Jaehoon, Kim, Jihan, King, Rollin A, Klunzinger, Phil, Kosenkov, Dmytro, Kowalczyk, Tim, Krauter, Caroline M, Lao, Ka Un, Laurent, Adèle D, Lawler, Keith V, Levchenko, Sergey V, Lin, Ching Yeh, Liu, Fenglai, Livshits, Ester, Lochan, Rohini C, Luenser, Arne, Manohar, Prashant, Manzer, Samuel F, Mao, Shan-Ping, Mardirossian, Narbe, Marenich, Aleksandr V, Maurer, Simon A, Mayhall, Nicholas J, Neuscamman, Eric, Oana, C Melania, Olivares-Amaya, Roberto, O’Neill, Darragh P, Parkhill, John A, Perrine, Trilisa M, Peverati, Roberto, Prociuk, Alexander, Rehn, Dirk R, Rosta, Edina, Russ, Nicholas J, Sharada, Shaama M, Sharma, Sandeep, Small, David W, and Sodt, Alexander
- Subjects
Chemical Sciences ,Physical Chemistry ,Theoretical and Computational Chemistry ,quantum chemistry ,electron correlation ,electronic structure theory ,Q-Chem ,computational modelling ,software ,density functional theory ,Atomic ,Molecular ,Nuclear ,Particle and Plasma Physics ,Physical Chemistry (incl. Structural) ,Chemical Physics ,Physical chemistry ,Theoretical and computational chemistry - Abstract
A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Møller-Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube.
- Published
- 2015
42. Computational quantum chemistry for single Heisenberg spin couplings made simple: Just one spin flip required
- Author
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Mayhall, Nicholas J and Head-Gordon, Martin
- Subjects
Physical Sciences ,Chemical Sciences ,Engineering ,Chemical Physics - Abstract
We highlight a simple strategy for computing the magnetic coupling constants, J, for a complex containing two multiradical centers. On the assumption that the system follows Heisenberg Hamiltonian physics, J is obtained from a spin-flip electronic structure calculation where only a single electron is excited (and spin-flipped), from the single reference with maximum Ŝz, M, to the M - 1 manifold, regardless of the number of unpaired electrons, 2M, on the radical centers. In an active space picture involving 2M orbitals, only one β electron is required, together with only one α hole. While this observation is extremely simple, the reduction in the number of essential configurations from exponential in M to only linear provides dramatic computational benefits. This (M, M - 1) strategy for evaluating J is an unambiguous, spin-pure, wave function theory counterpart of the various projected broken symmetry density functional theory schemes, and likewise gives explicit energies for each possible spin-state that enable evaluation of properties. The approach is illustrated on five complexes with varying numbers of unpaired electrons, for which one spin-flip calculations are used to compute J. Some implications for further development of spin-flip methods are discussed.
- Published
- 2014
43. Increasing spin-flips and decreasing cost: Perturbative corrections for external singles to the complete active space spin flip model for low-lying excited states and strong correlation
- Author
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Mayhall, Nicholas J and Head-Gordon, Martin
- Subjects
Physical Sciences ,Chemical Sciences ,Engineering ,Chemical Physics - Abstract
An approximation to the spin-flip extended configuration interaction singles method is developed using a second-order perturbation theory approach. In addition to providing significant efficiency advantages, the new framework is general for an arbitrary number of spin-flips, with the current implementation being applicable for up to around 4 spin-flips. Two new methods are introduced: one which is developed using non-degenerate perturbation theory, spin-flip complete active-space (SF-CAS(S)), and a second quasidegenerate perturbation theory method, SF-CAS(S)1. These two approaches take the SF-CAS wavefunction as the reference, and then perturbatively includes the effect of single excitations. For the quasidegenerate perturbation theory method, SF-CAS(S)1, the subscripted "1" in the acronym indicates that a truncated denominator expansion is used to obtain an energy-independent down-folded Hamiltonian. We also show how this can alternatively be formulated in terms of an extended Lagrangian, by introducing an orthonormality constraint on the first-order wavefunction. Several numerical examples are provided, which demonstrate the ability of SF-CAS(S) and SF-CAS(S)1 to describe bond dissociations, singlet-triplet gaps of organic molecules, and exchange coupling parameters for binuclear transition metal complexes.
- Published
- 2014
44. A Quasidegenerate Second-Order Perturbation Theory Approximation to RAS‑nSF for Excited States and Strong Correlations
- Author
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Mayhall, Nicholas J, Goldey, Matthew, and Head-Gordon, Martin
- Subjects
Theoretical and Computational Chemistry ,Biochemistry and Cell Biology ,Computer Software ,Chemical Physics - Abstract
We present a modification of the recently developed Restricted Active Space with n Spin Flips method (RAS-nSF), which provides significant efficiency advantages. In the RAS-nSF configuration interaction wave function, an arbitrary number of spin-flips are performed within an orbital active space (often simply the singly occupied orbitals), with state-specific orbital relaxation being described by single excitations into and out of the active space (termed hole and particle states, respectively). As the number of hole and particle states dominates the cost of the calculation, we present an attractive simplification in which the orbital relaxation effects (via hole and particle states) are treated perturbatively rather than variationally. The physical justification for this simplification stems from the spin-flip methodology itself, which suggests that the underlying molecular orbitals (high-spin ROHF) are capable of providing a decent description of the target (spin-flipped) electronic states. The current approach termed SF-CAS(h,p)n (Spin-Flip Complete Active-Space with perturbative Hole and Particle states) yields spin-pure energies and eigenfunctions due to the spin-free formulation. A description of the theory is presented, and a number of numerical examples are investigated to determine the accuracy of the approximation. Computational speedups of over 100 times were demonstrated on a 254 electron, 358 basis function calculation on a Cu(II) porphyrin derivatized with a verdazyl group.
- Published
- 2014
45. Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm
- Author
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Gard, Bryan T., Zhu, Linghua, Barron, George S., Mayhall, Nicholas J., Economou, Sophia E., and Barnes, Edwin
- Published
- 2020
- Full Text
- View/download PDF
46. Avoiding symmetry roadblocks and minimizing the measurement overhead of adaptive variational quantum eigensolvers
- Author
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Shkolnikov, V. O., primary, Mayhall, Nicholas J., additional, Economou, Sophia E., additional, and Barnes, Edwin, additional
- Published
- 2023
- Full Text
- View/download PDF
47. Tribute to Krishnan Raghavachari
- Author
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Hratchian, Hrant P., Karton, Amir, and Mayhall, Nicholas J.
- Published
- 2024
- Full Text
- View/download PDF
48. Cluster many-body expansion: A many-body expansion of the electron correlation energy about a cluster mean field reference.
- Author
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Abraham, Vibin and Mayhall, Nicholas J.
- Subjects
- *
ELECTRON configuration , *HUBBARD model , *TENSOR products , *BINDING energy , *TWO-dimensional models , *CONJUGATED systems - Abstract
The many-body expansion (MBE) is an efficient tool that has a long history of use for calculating interaction energies, binding energies, lattice energies, and so on. In the past, applications of MBE to correlation energy have been unfeasible for large systems, but recent improvements to computing resources have sparked renewed interest in capturing the correlation energy using the generalized nth order Bethe–Goldstone equation. In this work, we extend this approach, originally proposed for a Slater determinant, to a tensor product state (TPS) based wavefunction. By partitioning the active space into smaller orbital clusters, our approach starts from a cluster mean field reference TPS configuration and includes the correlation contribution of the excited TPSs using the MBE. This method, named cluster MBE (cMBE), improves the convergence of MBE at lower orders compared to directly doing a block-based MBE from a RHF reference. We present numerical results for strongly correlated systems, such as the one- and two-dimensional Hubbard models and the chromium dimer. The performance of the cMBE method is also tested by partitioning the extended π space of several large π-conjugated systems, including a graphene nano-sheet with a very large active space of 114 electrons in 114 orbitals, which would require 1066 determinants for the exact FCI solution. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
49. Quantum self-consistent equation-of-motion method for computing molecular excitation energies, ionization potentials, and electron affinities on a quantum computer
- Author
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Asthana, Ayush, primary, Kumar, Ashutosh, additional, Vibin, Abraham, additional, Grimsley, Harper, additional, Zhang, Yu, additional, Cincio, Lukasz, additional, Tretiak, Sergei, additional, Dub, Pavel A., additional, Economou, Sophia E, additional, Barnes, Edwin, additional, and Mayhall, Nicholas J., additional
- Published
- 2023
- Full Text
- View/download PDF
50. Energy Transfer in Metal-Organic Frameworks
- Author
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Zhu, Jie, primary, Shaikh, Shaunak, additional, Mayhall, Nicholas J., additional, and Morris, Amanda J., additional
- Published
- 2018
- Full Text
- View/download PDF
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