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Abstract Exploring the ground state properties of many-body quantum systems conventionally involves adiabatic processes, alongside exact diagonalization, in the context of quantum annealing or adiabatic quantum computation. Shortcuts to adiabaticity by counter-diabatic driving serve to accelerate these processes by suppressing energy excitations. Motivated by this, we develop variational quantum algorithms incorporating the auxiliary counter-diabatic interactions, comparing them with digitized adiabatic algorithms. These algorithms are then implemented on gate-based quantum circuits to explore the ground states of the Fermi-Hubbard model on honeycomb lattices, utilizing systems with up to 26 qubits. The comparison reveals that the counter-diabatic inspired ansatz is superior to traditional Hamiltonian variational ansatz. Furthermore, the number and duration of Trotter steps are analyzed to understand and mitigate errors. Given the model’s relevance to materials in condensed matter, our study paves the way for using variational quantum algorithms with counterdiabaticity to explore quantum materials in the noisy intermediate-scale quantum era.

Anomalous heat transfer (AHT), a process by which heat spontaneously flows from a cold system into a hot one, superficially contradicts the Clausius statement of the second law of thermodynamics. Here we provide a full classification of mechanisms of AHT in nonequilibrium quantum systems from a quantum-information perspective. For initial states in local equilibrium, we find that AHT can arise from three resources: initial correlation, intrasystem interaction, and intrasystem temperature inhomogeneity. In particular, for qubit systems, we prove that initial quantum coherence is necessary for AHT if the intersystem interactions are limited to the two-body type. We explicitly show AHT dominated by each of the mechanisms in a three-qubit system. Our classification scheme may offer a guideline for developing high-efficiency quantum autonomous thermal machines.

Abstract Two classes of quantum-annealing-inspired-algorithms (QAIA), namely different variants of simulated coherent Ising machine and simulated bifurcation, have been proposed for efficiently solving combinatorial optimization problems recently. In order to certify the superiority of these algorithms, standardized comparisons among them and against other physics-based algorithms are necessary. In this work, for Max-Cut problems up to 20,000 nodes, we benchmark QAIA against quantum annealing and other physics-based algorithms. We found that ballistic simulated bifurcation excelled for chimera and small-scale graphs, achieving nearly a 50-fold reduction in time-to-solution compared to quantum annealing. For large-scale graphs, discrete simulated bifurcation achieves the lowest time-to-target and outperforms D-Wave Advantage system when tasked with finding the maximum cut value in pegasus graphs. Our results suggest that QAIA represents a promising means for solving combinatorial optimization problems in practice, and can act as a natural baseline for competing quantum algorithms.

The Variational Quantum Eigensolver (VQE) algorithm, as applied to finding the ground state of a Hamiltonian, is particularly well-suited for deployment on noisy intermediate-scale quantum (NISQ) devices. Here, we utilize the VQE algorithm with a quantum circuit ansatz inspired by the Density Matrix Renormalization Group (DMRG) algorithm. To ameliorate the impact of realistic noise on the performance of the method, we employ zero-noise extrapolation. We find that, with realistic error rates, our DMRG–VQE hybrid algorithm delivers good results for strongly correlated systems. We illustrate our approach with the Heisenberg model on a Kagome lattice patch and demonstrate that DMRG–VQE hybrid methods can locate and faithfully represent the physics of the ground state of such systems. Moreover, the parameterized ansatz circuit used in this work is low depth and requires a reasonably small number of parameters, so it is efficient for NISQ devices.

Storage of information, in any form, relies on patterns standing out from thermal fluctuations. In this work, the authors highlight a fundamental tradeoff quantifying the minimum amount of nonequilibrium resources needed to achieve a target level of accuracy in the processing of information.

Abstract Exceptional points (EPs), the degeneracy points of non-Hermitian systems, have recently attracted great attention because of their potential of enhancing the sensitivity of quantum sensors. Unlike the usual degeneracies in Hermitian systems, at EPs, both the eigenenergies and eigenvectors coalesce. Although EPs have been widely explored, the range of EPs studied is largely limited by the underlying systems, for instance, higher-order EPs are hard to achieve. Here we propose an extendable method to simulate non-Hermitian systems and study EPs with quantum circuits. The system is inherently parity-time (PT) broken due to the non-symmetric controlling effects of the circuit. Inspired by the quantum Zeno effect, the circuit structure guarantees the success rate of the post-selection. A sample circuit is implemented in a quantum programming framework, and the phase transition at EP is demonstrated. Considering the scalable and flexible nature of quantum circuits, our model is capable of simulating large-scale systems with higher-order EPs.

The simulation of quantum dynamics on a digital quantum computer with parametrized circuits has widespread applications in fundamental and applied physics and chemistry. In this context, using the hybrid quantum-classical algorithm, combining classical optimizers and quantum computers, is a competitive strategy for solving specific problems. We put forward its use for optimal quantum control. We simulate the wave-packet expansion of a trapped quantum particle on a quantum device with a finite number of qubits. We then use circuit learning based on gradient descent to work out the intrinsic connection between the control phase transition and the quantum speed limit imposed by unitary dynamics. We further discuss the robustness of our method against errors and demonstrate the absence of barren plateaus in the circuit. The combination of digital quantum simulation and hybrid circuit learning opens up new prospects for quantum optimal control.

Optical neural network (ONNs) are emerging as attractive proposals for machine-learning applications. However, the stability of ONNs decreases with the circuit depth, limiting the scalability of ONNs for practical uses. Here we demonstrate how to compress the circuit depth to scale only logarithmically in terms of the dimension of the data, leading to an exponential gain in terms of noise robustness. Our low-depth (LD)-ONN is based on an architecture, called Optical CompuTing Of dot-Product UnitS (OCTOPUS), which can also be applied individually as a linear perceptron for solving classification problems. We present both numerical and theoretical evidence showing that LD-ONN can exhibit a significant improvement on robustness, compared with previous ONN proposals based on singular-value decomposition.

The variational quantum-classical algorithms are the most promising approach for achieving quantum advantage on near-term quantum simulators. Among these methods, the variational quantum eigensolver has attracted a lot of attention in recent years. While it is very effective for simulating the ground state of many-body systems, its generalization to excited states becomes very resource demanding. Here, we show that this issue can significantly be improved by exploiting the symmetries of the Hamiltonian. The improvement is even more effective for higher energy eigenstates. We introduce two methods for incorporating the symmetries. In the first approach, called hardware symmetry preserving, all the symmetries are included in the design of the circuit. In the second approach, the cost function is updated to include the symmetries. The hardware symmetry preserving approach indeed outperforms the second approach. However, integrating all symmetries in the design of the circuit could be extremely challenging. Therefore, we introduce hybrid symmetry preserving method in which symmetries are divided between the circuit and the classical cost function. This allows to harness the advantage of symmetries while preventing sophisticated circuit design.

Current quantum simulators suffer from multiple limitations such as short coherence time, noisy operations, faulty readout and restricted qubit connectivity in some platforms. Variational quantum algorithms are the most promising approach in near-term quantum simulation to achieve practical quantum advantage over classical computers. Here, we explore variational quantum algorithms, with different levels of qubit connectivity, for digital simulation of the ground state of long-range interacting systems as well as generation of spin squeezed states. We find that as the interaction becomes more long-ranged, the variational algorithms become less efficient, achieving lower fidelity and demanding more optimization iterations. In particular, when the system is near its criticality the efficiency is even lower. Increasing the connectivity between distant qubits improves the results, even with less quantum and classical resources. Our results show that by mixing circuit layers with different levels of connectivity one can sensibly improve the performance. Interestingly, the order of layers becomes very important and grouping the layers with long-distance connectivity at the beginning of the circuit outperforms other permutations. The same design of circuits can also be used to variationally produce spin squeezed states, as a resource for quantum metrology.

We investigate the black hole evaporation process in Lovelock gravity with diverse dimensions. By selecting the appropriate coefficients, the space-time solutions can possess a unique AdS vacuum with a fixed cosmological constant Λ=−(d−1)(d−2)2ℓ2. The black hole solutions can be divided into two cases: d>2k+1 and d=2k+1. In the case of d>2k+1, the black hole is in an analogy with the Schwarzschild AdS black hole, and the life time is bounded by a time of the order of ℓd−2k+1, which reduces Page's result on the Einstein gravity in k=1. In the case of d=2k+1, the black hole resembles the three dimensional black hole. The black hole vacuum corresponds to T=0, so the black hole will take infinite time to evaporate away for any initial states, which obeys the third law of thermodynamics. In the asymptotically flat limit ℓ→∞, the system reduces to the pure Lovelock gravity that only possesses the highest k-th order term. For an initial mass M0, the life time of the black hole is in the order of M0d−2k+1d−2k−1.

In this work, we explore all possible scenarios in the evaporation process of a spherical neutral AdS black hole in four-dimensional conformal gravity, where the equations of states are branched. In one branch, the final states correspond to the extremal black hole where the total decay time is divergent given any initial mass. In the other branch, the black holes always evaporate completely with in a finite time; the total decay time depends linearly on the AdS radius, when the mass is taken to be infinity.

Nonadiabatic geometric quantum computation (NGQC) and nonadiabatic holonomic quantum computation (NHQC) have been proposed to reduce the run time of geometric quantum gates. However, in terms of robustness against experimental control errors, the existing NGQC and NHQC scenarios have no advantage over standard dynamical gates in most cases. Here, we give the reasons why nonadiabatic geometric gates are sensitive to the control errors and, further, we propose a scheme of super-robust nonadiabatic geometric quantum control, in which the super-robust condition can guarantee both high speed and robustness of the geometric gate. To illustrate the working mechanism of super-robust geometric quantum gates, we give two simple examples of SR-NGQC and SR-NHQC for two- and three-level quantum systems, respectively. Theoretical and numerical results with the experimental parameters indicate that our scheme can significantly improve the gate performance compared to the previous NGQC, NHQC, and standard dynamical schemes. Super-robust geometric quantum computation can be applied to various physical platforms such as superconducting qubits, quantum dots, and trapped ions. All of these sufficiently show that our scheme provides a promising way towards robust geometric quantum computation.

Abstract For a pair of incompatible quantum measurements, the total uncertainty can be bounded by a state-independent constant. However, such a bound can be violated if the quantum system is entangled with another quantum system (called memory); the quantum correlation between the systems can reduce the measurement uncertainty. On the other hand, in a curved spacetime, the presence of the Hawking radiation can reduce quantum correlation. The interplay of quantum correlation in the curved spacetime has become an interesting arena for studying uncertainty relations. Here we demonstrate that the bounds of the entropic uncertainty relations, in the presence of memory, can be formulated in terms of the Holevo quantity, which limits how much information can be encoded in a quantum system. Specifically, we considered examples with Dirac fields with and without spin, near the event horizon of a Schwarzschild black hole, the Holevo bound provides a better bound than the previous bound based on the mutual information. Furthermore, as the memory moves away from the black hole, the difference between the total uncertainty and the new lower bound remains a constant, not depending on any property of the black hole.

A set of multipartite orthogonal product states is locally irreducible, if it is not possible to eliminate one or more states from the set by orthogonality-preserving local measurements. An effective way to prove that a set is locally irreducible is to show that only trivial orthogonality-preserving local measurement can be performed to this set. In general, it is difficult to show that such an orthogonality-preserving local measurement must be trivial. In this work, we develop two basic techniques to deal with this problem. Using these techniques, we successfully show the existence of unextendible product bases (UPBs) that are locally irreducible in every bipartition in $d\otimes d\otimes d$ for any $d\geq 3$, and $3\otimes3\otimes 3$ achieves the minimum dimension for the existence of such UPBs. These UPBs exhibit the phenomenon of strong quantum nonlocality without entanglement. Our result solves an open question given by Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)] and Yuan et al. [Phys. Rev. A 102, 042228 (2020)]. It also sheds new light on the connections between UPBs and strong quantum nonlocality.

Simulation of quantum field theory using quantum systems would in principle allow avoidance of the exponential overhead required for classical simulations. Here, the authors use a multilevel trapped ion to simulate the processes of self-interaction and particle-antiparticle creation/annihilation.

A crucial subroutine in quantum computing is to load the classical data of N complex numbers into the amplitude of a superposed n=⌈log_{2}N⌉-qubit state. It has been proven that any algorithm universally implementing this subroutine would need at least O(N) constant weight operations. However, the proof assumes that only n qubits are used, whereas the circuit depth could be reduced by extending the space and allowing ancillary qubits. Here we investigate this space-time tradeoff in quantum state preparation with classical data. We propose quantum algorithms with O(n^{2}) circuit depth to encode any N complex numbers using only single- and two-qubit gates, and local measurements with ancillary qubits. Different variances of the algorithm are proposed with different space and runtime. In particular, we present a scheme with O(N^{2}) ancillary qubits, O(n^{2}) circuit depth, and O(n^{2}) average runtime, which exponentially improves the conventional bound. While the algorithm requires more ancillary qubits, it consists of quantum circuit blocks that only simultaneously act on a constant number of qubits, and at most O(n) qubits are entangled. We also prove a fundamental lower bound Ω(n) for the minimum circuit depth and runtime with an arbitrary number of ancillary qubits, aligning with our scheme with O(n^{2}). The algorithms are expected to have wide applications in both near-term and universal quantum computing.

Abstract Molecular vibroic spectroscopy, where the transitions involve non-trivial Bosonic correlation due to the Duschinsky Rotation, is strongly believed to be in a similar complexity class as Boson Sampling. At finite temperature, the problem is represented as a Boson Sampling experiment with correlated Gaussian input states. This molecular problem with temperature effect is intimately related to the various versions of Boson Sampling sharing the similar computational complexity. Here we provide a full description to this relation in the context of Gaussian Boson Sampling. We find a hierarchical structure, which illustrates the relationship among various Boson Sampling schemes. Specifically, we show that every instance of Gaussian Boson Sampling with an initial correlation can be simulated by an instance of Gaussian Boson Sampling without initial correlation, with only a polynomial overhead. Since every Gaussian state is associated with a thermal state, our result implies that every sampling problem in molecular vibronic transitions, at any temperature, can be simulated by Gaussian Boson Sampling associated with a product of vacuum modes. We refer such a generalized Gaussian Boson Sampling motivated by the molecular sampling problem as Vibronic Boson Sampling.

We investigate the Unruh quantum Otto heat engine with level degeneracy. An effectively two-level system, where the ground state is non-degenerate and the excited state is n-fold degenerate, is acting as the working substance, and the vacuum of massless free scalar field serves as a thermal bath via the Unruh effect. We calculate the heat and work at each step of the Unruh quantum Otto cycle and study the features of the heat engine. The efficiency of the heat engine depends only on the excited energy values of the two-level system, not on its level degeneracy. However, the degeneracy acts as a kind of thermodynamic resource and helps us to extract more work than in the non-degenerate case. The extractable work has a finite upper bound, corresponding to n→∞.

We propose a geometric quantum computation (GQC) scheme, called Floquet GQC (FGQC), where error-resilient geometric gates based on periodically driven two-level systems can be constructed via a non-Abelian geometric phase proposed in a recent study [V. Novičenko and G. Juzeliūnas, Phys. Rev. A 100, 012127 (2019)10.1103/PhysRevA.100.012127]. Based on Rydberg atoms, we give possible implementations of universal FGQC single-qubit gates and a nontrivial FGQC two-qubit gate. By using numerical simulation, we evaluate the performance of the FGQC Z and X gates in the presence of both decoherence and a certain kind of systematic control error. For the currently available coherence time of the Rydberg state, T_{2}≈32μs, the numerical results show that the X and Z gate fidelities are about 0.900 and 0.899, respectively. In addition, we find that FGQC is robust against global control error; both analytical demonstration and numerical evidence are given. As the coherence time of various qubits grows, FGQC may provide a promising error-resilient quantum computation scheme in the future.

Transferring quantum information is a fundamental task, but doing so with high fidelity is a challenging task. Here, the authors implement the perfect state transfer protocol to a photonic qubit, entangled with a second one in a different location, across eleven coupled waveguides.

Nonadiabatic geometric quantum computation (NGQC) has been developed to realize fast and robust geometric gate. However, the conventional NGQC is that all of the gates are performed with exactly the same amount of time, whether the geometric rotation angle is large or small, due to the limitation of cyclic condition. Here, we propose an unconventional scheme, called nonadiabatic noncyclic geometric quantum computation (NNGQC), that arbitrary single- and two-qubit geometric gate can be constructed via noncyclic non-Abelian geometric phase. Consequently, this scheme makes it possible to accelerate the implemented geometric gates against the effects from the environmental decoherence. Furthermore, this extensible scheme can be applied in various quantum platforms, such as superconducting qubit and Rydberg atoms. Specifically, for single-qubit gate, we make simulations with practical parameters in neutral atom system to show the robustness of NNGQC and also compare with NGQC using the recent experimental parameters to show that the NNGQC can significantly suppress the decoherence error. In addition, we also demonstrate that nontrivial two-qubit geometric gate can be realized via unconventional Rydberg blockade regime within current experimental technologies. Therefore, our scheme provides a promising way for fast and robust neutral-atom-based quantum computation.

Antiferromagnets (AFMs) are widely believed to be superior to ferromagnets in spintronics because of their high stability due to the vanishingly small stray field. It is thus expected that the order parameter of AFMs should always align along the easy axis of the crystalline anisotropy. In contrast to this conventional wisdom, we find that the AFM order parameter switches away from the easy axis below a critical anisotropy strength when an AFM is properly tailored into a nanostructure. The switching time first decreases and then increases with the damping. Above the critical anisotropy, the AFM order parameter is stable and precesses under a microwave excitation. However, the absorption peak is not at resonance frequency even for magnetic damping as low as 0.01. To resolve these anomalies, we first ascertain the hidden role of dipolar interaction that reconstructs the energy landscape of the nanosystem and propose a model of a damped nonlinear pendulum to explain the switching behavior. In this framework, the second anomaly appears when an AFM is close to the boundary between underdamped and overdamped phases, where the observed absorption line shape has a small quality factor and thus is not reliable any longer. Our results should be significant to extract the magnetic parameters through resonance techniques.

In many non-linear systems, such as plasma oscillation, boson condensation, chemical reaction, and even predatory-prey oscillation, the coarse-grained dynamics are governed by an equation containing anti-symmetric transitions, known as the anti-symmetric Lotka-Volterra (ALV) equations. In this work, we prove the existence of a novel bifurcation mechanism for the ALV equations, where the equilibrium state can be drastically changed by flipping the stability of a pair of fixed points. As an application, we focus on the implications of the bifurcation mechanism for evolutionary networks; we found that the bifurcation point can be determined quantitatively by the microscopic quantum entanglement. The equilibrium state can be critically changed from one type of global demographic condensation to another state that supports global cooperation for homogeneous networks. In other words, our results indicate that there exist a class of many-body systems where the macroscopic properties are invariant with a certain amount of microscopic entanglement, but they can be changed abruptly once the entanglement exceeds a critical value. Furthermore, we provide numerical evidence showing that the emergence of bifurcation is robust against the change of the network topologies, and the critical values are in good agreement with our theoretical prediction. These results show that the bifurcation mechanism could be ubiquitous in many physical systems, in addition to evolutionary networks.

In studying open quantum systems, the environment is often approximated as a collection of non-interacting harmonic oscillators, a configuration also known as the star-bath model. It is also well known that the star-bath can be transformed into a nearest-neighbor interacting chain of oscillators. The chain-bath model has been widely used in renormalization group approaches. The transformation can be obtained by recursion relations or orthogonal polynomials. Based on a simple linear algebraic approach, we propose a bath partition strategy to reduce the system-bath coupling strength. As a result, the non-interacting star-bath is transformed into a set of weakly coupled multiple parallel chains. The transformed bath model allows complex problems to be practically implemented on quantum simulators, and it can also be employed in various numerical simulations of open quantum dynamics.

The quantitative adiabatic condition (QAC), or quantitative condition, is a convenient ( a priori ) tool for estimating the adiabaticity of quantum evolutions. However, the range of the applicability of QAC is not well understood. It has been shown that QAC can become insufficient for guaranteeing the validity of the adiabatic approximation, but under what conditions the QAC would become necessary has become controversial. Furthermore, it is believed that the inability for the QAC to reveal quantum adiabaticity is due to induced resonant transitions. However, it is not clear how to quantify these transitions in general. Here we present a progress to this problem by finding an exact relation that can reveal how transition amplitudes are related to QAC directly. As a posteriori condition for quantum adiabaticity, our result is universally applicable to any (nondegenerate) quantum system and gives a clear picture on how QAC could become insufficient or unnecessary for the adiabatic approximation, which is a problem that has gained considerable interest in the literature in recent years.

Quantum computers can in principle simulate quantum physics exponentially faster than their classical counterparts, but some technical hurdles remain. We propose methods which substantially improve the performance of a particular form of simulation, ab initio quantum chemistry, on fault-tolerant quantum computers; these methods generalize readily to other quantum simulation problems. Quantum teleportation plays a key role in these improvements and is used extensively as a computing resource. To improve execution time, we examine techniques for constructing arbitrary gates which perform substantially faster than circuits based on the conventional Solovay–Kitaev algorithm (Dawson and Nielsen 2006 Quantum Inform. Comput. 6 81). For a given approximation error ϵ , arbitrary single-qubit gates can be produced fault-tolerantly and using a restricted set of gates in time which is O (log ϵ ) or O (log log ϵ ); with sufficient parallel preparation of ancillas, constant average depth is possible using a method we call programmable ancilla rotations. Moreover, we construct and analyze efficient implementations of first- and second-quantized simulation algorithms using the fault-tolerant arbitrary gates and other techniques, such as implementing various subroutines in constant time. A specific example we analyze is the ground-state energy calculation for lithium hydride.