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Computational models are an essential tool for the design, characterization, and discovery of novel materials. Hard computational tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their simulation, analysis, and data resources. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions., Comment: 65 pages, 15 figures; comments welcome

Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with improvements in control electronics, are enabling increasingly advanced demonstrations of the necessary operations for applying quantum error correction. Here, we perform quantum error correction on superconducting qubits connected in a heavy-hexagon lattice. The full processor can encode a logical qubit with distance three and perform several rounds of fault-tolerant syndrome measurements that allow the correction of any single fault in the circuitry. Furthermore, by using dynamic circuits and classical computation as part of our syndrome extraction protocols, we can exploit real-time feedback to reduce the impact of energy relaxation error in the syndrome and flag qubits. We show that the logical error varies depending on the use of a perfect matching decoder compared to a maximum likelihood decoder. We observe a logical error per syndrome measurement round as low as $\sim0.04$ for the matching decoder and as low as $\sim0.03$ for the maximum likelihood decoder. Our results suggest that more significant improvements to decoders are likely on the horizon as quantum hardware has reached a new stage of development towards fully fault-tolerant operations., Comment: 15 pages, 6 figures, 5 tables

Arbitrarily long quantum computations require quantum memories that can be repeatedly measured without being corrupted. Here, we preserve the state of a quantum memory, notably with the additional use of flagged error events. All error events were extracted using fast, mid-circuit measurements and resets of the physical qubits. Among the error decoders we considered, we introduce a perfect matching decoder that was calibrated from measurements containing up to size-4 correlated events. To compare the decoders, we used a partial post-selection scheme shown to retain ten times more data than full post-selection. We observed logical errors per round of $2.2\pm0.1\times10^{-2}$ (decoded without post-selection) and $5.1\pm0.7\times10^{-4}$ (full post-selection), which was less than the physical measurement error of $7\times10^{-3}$ and therefore surpasses a pseudo-threshold for repeated logical measurements., Comment: 16 pages, 14 figures, 5 tables, for peer-review

Two-dimensional electron gases (2DEGs) with high mobility, engineered in semiconductor heterostructures host a variety of ordered phases arising from strong correlations, which emerge at sufficiently low temperatures. The 2DEG can be further controlled by surface gates to create quasi-one dimensional systems, with potential spintronic applications. Here we address the long-standing challenge of cooling such electrons to below 1$\,$mK, potentially important for identification of topological phases and spin correlated states. The 2DEG device was immersed in liquid $^3$He, cooled by the nuclear adiabatic demagnetization of copper. The temperature of the 2D electrons was inferred from the electronic noise in a gold wire, connected to the 2DEG by a metallic ohmic contact. With effective screening and filtering, we demonstrate a temperature of 0.9$\,\pm\,$0.1$\,$mK, with scope for significant further improvement. This platform is a key technological step, paving the way to observing new quantum phenomena, and developing new generations of nanoelectronic devices exploiting correlated electron states., Comment: 9 pages, 5 figures plus 5 pages of supplementary information

The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to computational hardness assumptions, cannot be computed classically. It is an important challenge to find quantum kernels that provide an advantage in the classification of real-world data. We introduce a class of quantum kernels that can be used for data with a group structure. The kernel is defined in terms of a unitary representation of the group and a fiducial state that can be optimized using a technique called kernel alignment. We apply this method to a learning problem on a coset-space that embodies the structure of many essential learning problems on groups. We implement the learning algorithm with $27$ qubits on a superconducting processor., Comment: 18 pages, 8 figures

In this work we extend a multi-qubit benchmarking technique known as the Binned Output Generation (BOG) in order to discriminate between coherent and incoherent noise sources in the multi-qubit regime. While methods exist to discriminate coherent from incoherent noise at the single and few-qubit level, these methods scale poorly beyond a few qubits or must make assumptions about the form of the noise. On the other end of the spectrum, system-level benchmarking techniques exist, but fail to discriminate between coherent and incoherent noise sources. We experimentally verify the BOG against Randomized Benchmarking (RB) (the industry standard benchmarking technique) in the two-qubit regime, then apply this technique to a six qubit linear chain, a regime currently inaccessible to RB. In this experiment we inject an instantaneous coherent Z-type noise on each qubit and demonstrate that the measured coherent noise scales correctly with the magnitude of the injected noise, while the measured incoherent noise remains unchanged as expected. This demonstrates a robust technique to measure coherent errors in a variety of hardware.

Extracting the Hamiltonian of interacting quantum-information processing systems is a keystone problem in the realization of complex phenomena and large-scale quantum computers. The remarkable growth of the field increasingly requires precise, widely-applicable, and modular methods that can model the quantum electrodynamics of the physical circuits, and even of their more-subtle renormalization effects. Here, we present a computationally-efficient method satisfying these criteria. The method partitions a quantum device into compact lumped or quasi-distributed cells. Each is first simulated individually. The composite system is then reduced and mapped to a set of simple subsystem building blocks and their pairwise interactions. The method operates within the quasi-lumped approximation and, with no further approximation, systematically accounts for constraints, couplings, parameter renormalizations, and non-perturbative loading effects. We experimentally validate the method on large-scale, state-of-the-art superconducting quantum processors. We find that the full method improves the experimental agreement by a factor of two over taking standard coupling approximations when tested on the most sensitive and dressed Hamiltonian parameters of the measured devices., Comment: For related code, see #QiskitMetal https://qiskit.org/metal | 13 pages, 4 figures, 1 table

The execution of quantum circuits on real systems has largely been limited to those which are simply time-ordered sequences of unitary operations followed by a projective measurement. As hardware platforms for quantum computing continue to mature in size and capability, it is imperative to enable quantum circuits beyond their conventional construction. Here we break into the realm of dynamic quantum circuits on a superconducting-based quantum system. Dynamic quantum circuits involve not only the evolution of the quantum state throughout the computation, but also periodic measurements of a subset of qubits mid-circuit and concurrent processing of the resulting classical information within timescales shorter than the execution times of the circuits. Using noisy quantum hardware, we explore one of the most fundamental quantum algorithms, quantum phase estimation, in its adaptive version, which exploits dynamic circuits, and compare the results to a non-adaptive implementation of the same algorithm. We demonstrate that the version of real-time quantum computing with dynamic circuits can offer a substantial and tangible advantage when noise and latency are sufficiently low in the system, opening the door to a new realm of available algorithms on real quantum systems., Comment: 7 pages, 4 figures, plus supplement

Nonreciprocal microwave devices play several critical roles in high-fidelity, quantum-nondemolition (QND) measurement schemes. They separate input from output, impose unidirectional routing of readout signals, and protect the quantum systems from unwanted noise originated by the output chain. However, state-of-the-art, cryogenic circulators and isolators are disadvantageous in scalable superconducting quantum processors because they use magnetic materials and strong magnetic fields. Here, we realize an active isolator formed by coupling two nondegenerate Josephson mixers in an interferometric scheme. Nonreciprocity is generated by applying a phase gradient between the same-frequency pumps feeding the Josephson mixers, which play the role of the magnetic field in a Faraday medium. To demonstrate the applicability of this Josephson-based isolator for quantum measurements, we incorporate it into the output line of a superconducting qubit, coupled to a fast resonator and a Purcell filter. We also utilize a wideband, superconducting directional coupler for coupling the readout signals into and out of the qubit-resonator system and a quantum-limited Josephson amplifier for boosting the readout fidelity. By using this novel quantum setup, we demonstrate fast, high-fidelity, QND measurements of the qubit while providing more than 20 dB of protection against amplified noise reflected off the Josephson amplifier.

As interest in quantum computing grows, there is a pressing need for standardized API's so that algorithm designers, circuit designers, and physicists can be provided a common reference frame for designing, executing, and optimizing experiments. There is also a need for a language specification that goes beyond gates and allows users to specify the time dynamics of a quantum experiment and recover the time dynamics of the output. In this document we provide a specification for a common interface to backends (simulators and experiments) and a standarized data structure (Qobj --- quantum object) for sending experiments to those backends via Qiskit. We also introduce OpenPulse, a language for specifying pulse level control (i.e. control of the continuous time dynamics) of a general quantum device independent of the specific hardware implementation., Comment: 68 pages. More information and schemas can be found in the Qiskit repository https://github.com/Qiskit/

Quantum computation, a completely different paradigm of computing, benefits from theoretically proven speed-ups for certain problems and opens up the possibility of exactly studying the properties of quantum systems. Yet, because of the inherent fragile nature of the physical computing elements, qubits, achieving quantum advantages over classical computation requires extremely low error rates for qubit operations as well as a significant overhead of physical qubits, in order to realize fault-tolerance via quantum error correction. However, recent theoretical work has shown that the accuracy of computation based off expectation values of quantum observables can be enhanced through an extrapolation of results from a collection of varying noisy experiments. Here, we demonstrate this error mitigation protocol on a superconducting quantum processor, enhancing its computational capability, with no additional hardware modifications. We apply the protocol to mitigate errors on canonical single- and two-qubit experiments and then extend its application to the variational optimization of Hamiltonians for quantum chemistry and magnetism. We effectively demonstrate that the suppression of incoherent errors helps unearth otherwise inaccessible accuracies to the variational solutions using our noisy processor. These results demonstrate that error mitigation techniques will be critical to significantly enhance the capabilities of near-term quantum computing hardware., Comment: 6 pages, 4 figures in main text. 4 pages, 4 figures in supplementary information

Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern recognition, with support vector machines (SVMs) being the most well-known method for classification problems. However, there are limitations to the successful solution to such problems when the feature space becomes large, and the kernel functions become computationally expensive to estimate. A core element to computational speed-ups afforded by quantum algorithms is the exploitation of an exponentially large quantum state space through controllable entanglement and interference. Here, we propose and experimentally implement two novel methods on a superconducting processor. Both methods represent the feature space of a classification problem by a quantum state, taking advantage of the large dimensionality of quantum Hilbert space to obtain an enhanced solution. One method, the quantum variational classifier builds on [1,2] and operates through using a variational quantum circuit to classify a training set in direct analogy to conventional SVMs. In the second, a quantum kernel estimator, we estimate the kernel function and optimize the classifier directly. The two methods present a new class of tools for exploring the applications of noisy intermediate scale quantum computers [3] to machine learning., Comment: Fixed typos, added figures and discussion about quantum error mitigation

The ability to perform fast, high-fidelity readout of quantum bits (qubits) is essential to the goal of building a quantum computer. However, coupling a fast measurement channel to a superconducting qubit typically also speeds up its relaxation via spontaneous emission. Here we use impedance engineering to design a filter by which photons may easily leave the resonator at the cavity frequency but not at the qubit frequency. We implement this broadband filter in both an on-chip and off-chip configuration., Comment: 5 pages, 3 figures

We characterize a superconducting qubit before and after embedding it along with its package in an absorptive medium. We observe a drastic improvement in the effective qubit temperature and over a tenfold improvement in the relaxation time up to 5.7 $\mu$s. Our results suggest the presence of external radiation inside the cryogenic apparatus can be a limiting factor for both qubit initialization and coherence. We infer from simple calculations that relaxation is not limited by thermal photons in the sample prior to embedding, but by dissipation arising from quasiparticle generation., Comment: 3 figures

Thin films of TiN were sputter-deposited onto Si and sapphire wafers with and without SiN buffer layers. The films were fabricated into RF coplanar waveguide resonators, and internal quality factor measurements were taken at millikelvin temperatures in both the many photon and single photon limits, i.e. high and low power regimes, respectively. At high power, internal quality factors ($Q_i$'s) higher than $10^7$ were measured for TiN with predominantly a (200)-TiN orientation. Films that showed significant (111)-TiN texture invariably had much lower $Q_i$'s, on the order of $10^5$. Our studies show that the (200)-TiN is favored for growth at high temperature on either bare Si or SiN buffer layers. However, growth on bare sapphire or Si(100) at low temperature resulted in primarily a (111)-TiN orientation. Ellipsometry and Auger measurements indicate that the (200)-TiN growth on the bare Si substrates is correlated with the formation of a thin, $\approx 2$ nm, layer of SiN during the pre-deposition procedure. In the single photon regime, $Q_i$ of these films exceeded $8\times10^5$, while thicker SiN buffer layers led to reduced $Q_i$'s at low power., Comment: Submitted to APL July 2010