Quantum information processing is steadily progressing from a purely academic discipline towards applications throughout science and industry. Transitioning from lab-based, proof-of-concept experiments to robust, integrated realizations of quantum information processing hardware is an important step in this process. However, the nature of traditional laboratory setups does not offer itself readily to scaling up system sizes or allow for applications outside of laboratory-grade environments. This transition requires overcoming challenges in engineering and integration without sacrificing the state-of-the-art performance of laboratory implementations. Here, we present a 19-inch rack quantum computing demonstrator based on ${}^{40}{\mathrm{Ca}}^{+}$ optical qubits in a linear Paul trap to address many of these challenges. We outline the mechanical, optical, and electrical subsystems. Furthermore, we describe the automation and remote access components of the quantum computing stack. We conclude by describing characterization measurements relevant to quantum computing including site-resolved single-qubit interactions, and entangling operations mediated by the Mølmer-Sørensen interaction delivered via two distinct addressing approaches. Using this setup, we produce maximally entangled Greenberger-Horne-Zeilinger states with up to 24 ions without the use of postselection or error mitigation techniques; on par with well-established conventional laboratory setups.

Stochastic modeling of complex systems plays an essential, yet often computationally intensive, role across the quantitative sciences. Recent advances in quantum information processing have elucidated the potential for quantum simulators to exhibit memory advantages for such tasks. Heretofore, the focus has been on lossless memory compression, wherein the advantage is typically in terms of lessening the amount of information tracked by the model, while—arguably more practical—reductions in memory dimension are not always possible. Here, we address the case of lossy compression for quantum stochastic modeling of continuous-time processes, introducing a method for coarse graining in quantum state space that drastically reduces the requisite memory dimension for modeling temporal dynamics while retaining near-exact statistics. In contrast to classical coarse graining, this compression is not based on sacrificing temporal resolution and brings memory-efficient high-fidelity stochastic modeling within reach of present quantum technologies.

Estimating and reducing the overhead of fault-tolerance (FT) schemes is a crucial step toward realizing scalable quantum computers. Of particular interest are schemes based on two-dimensional (2D) topological codes such as the surface and color codes that have high thresholds but lack a natural implementation of a non-Clifford gate. In this work, we directly compare two leading FT implementations of the $T$ gate in 2D color codes under circuit noise across a wide range of parameters in regimes of practical interest. We report that implementing the $T$ gate via code switching to a three-dimensional (3D) color code does not offer substantial savings over state distillation in terms of either space or space-time overhead. We find a circuit-noise threshold of $0.07(1)\mathrm{\%}$ for the $T$ gate via code switching, almost an order of magnitude below that achievable by state distillation in the same setting. To arrive at these results, we provide and simulate an optimized code-switching procedure, and bound the effect of various conceivable improvements. Many intermediate results in our analysis may be of independent interest. For example, we optimize the 2D color code for circuit noise yielding its largest threshold to date $0.37(1)\mathrm{\%}$, and adapt and optimize the restriction decoder finding a threshold of $0.80(5)\mathrm{\%}$ for the 3D color code with perfect measurements under $Z$ noise. Our work provides a much-needed direct comparison of the overhead of state distillation and code switching, and sheds light on the choice of future FT schemes and hardware designs.

Single-shot error correction corrects data noise using only a single round of noisy measurements on the data qubits, removing the need for intensive measurement repetition. We introduce a general concept of confinement for quantum codes, which roughly stipulates qubit errors cannot grow without triggering more measurement syndromes. We prove confinement is sufficient for single-shot decoding of adversarial errors and linear confinement is sufficient for single-shot decoding of local stochastic errors. Further to this, we prove that all three-dimensional homological product codes exhibit confinement in their $X$ components and are therefore single shot for adversarial phase-flip noise. For local stochastic phase-flip noise, we numerically explore these codes and again find evidence of single-shot protection. Our Monte Carlo simulations indicate sustainable thresholds of $3.08(4)\mathrm{\%}$ and $2.90(2)\mathrm{\%}$ for three-dimensional (3D) surface and toric codes, respectively, the highest observed single-shot thresholds to date. To demonstrate single-shot error correction beyond the class of topological codes, we also run simulations on a randomly constructed family of 3D homological product codes.

The out-of-time-ordered correlation (OTOC) and entanglement are two physically motivated and widely used probes of the “scrambling” of quantum information, a phenomenon that has drawn great interest recently in quantum gravity and many-body physics. We argue that the corresponding notions of scrambling can be fundamentally different, by proving an asymptotic separation between the time scales of the saturation of OTOC and that of entanglement entropy in a random quantum-circuit model defined on graphs with a tight bottleneck, such as tree graphs. Our result counters the intuition that a random quantum circuit mixes in time proportional to the diameter of the underlying graph of interactions. It also provides a more rigorous justification for an argument in our previous work [Shor P.W., Scrambling time and causal structure of the photon sphere of a Schwarzschild black hole, arXiv:1807.04363 (2018)], that black holes may be slow information scramblers, which in turn relates to the black-hole information problem. The bounds we obtain for OTOC are interesting in their own right in that they generalize previous studies of OTOC on lattices to the geometries on graphs in a rigorous and general fashion.

We present a numerically exact method to compute the full counting statistics of heat transfer in non-Markovian open quantum systems, which is based on the time-evolving matrix product operator algorithm. This approach is applied to the paradigmatic spin-boson model in order to calculate the mean and fluctuations of the heat transferred to the environment during thermal equilibration. We show that system-reservoir correlations make a significant contribution to the heat statistics at low temperature and present a variational theory that quantitatively explains our numerical results. We also demonstrate a fluctuation-dissipation relation connecting the mean and variance of the heat distribution at high temperature. Our results reveal that system-bath interactions make a significant contribution to heat transfer even when the dynamics of the open system is effectively Markovian. The method presented here provides a flexible and general tool to predict the fluctuations of heat transfer in open quantum systems in nonperturbative regimes.

The variational quantum eigensolver (VQE) is a method of choice to solve the electronic structure problem for molecules on near-term gate-based quantum computers. However, the circuit depth is expected to grow significantly with the problem size. Increased depth can both degrade the accuracy of the results and reduce trainability. In this work, we propose an approach to reduce ansatz circuit depth. Our approach, called “PermVQE,” adds an additional optimization loop to the VQE that permutes qubits in order to solve for the qubit Hamiltonian that maximally localizes correlations in the ground state. The choice of permutations is based on mutual information, which is a measure of interaction between electrons and/or holes in spin-orbitals. Encoding strongly entangled spin-orbitals into proximal qubits on a quantum chip naturally reduces the circuit depth needed to prepare the ground state. For representative molecular systems, $\mathrm{LiH}$, ${\mathrm{H}}_2$, $({\mathrm{H}}_2{)}_2$, ${\mathrm{H}}_4^{\ne }$, ${\mathrm{H}}_3^{+}$, and ${\mathrm{N}}_2$, we demonstrate that placing entangled qubits in close proximity leads to shallower depth circuits required to reach a given eigenvalue-eigenvector accuracy. The approach is designed for hardware-efficient ansatz of any qubit connectivity, and examples are demonstrated for linear and two-dimensional grid architectures. The main ideas can also be applied to simulate molecules with other ansatz as well as variational quantum algorithms beyond the VQE. In particular, we demonstrate the beneficial effect of qubit permutations to build fermionic–adaptive derivative assembled pseudo-Trotter ansatz on a linear qubit connectivity architecture with nearly a twofold reduction of the number of controlled not gates.

Driven-dissipative quantum systems generically do not satisfy simple notions of detailed balance based on the time symmetry of correlation functions. We show that such systems can nonetheless exhibit a hidden time-reversal symmetry, which most directly manifests itself in a doubled version of the original system prepared in an appropriate entangled thermofield double state. This hidden time-reversal symmetry has a direct operational utility: it provides a general method for finding exact solutions of nontrivial steady states. Special cases of this approach include the coherent quantum absorber and complex-$P$ function methods from quantum optics. We also show that hidden time-reversal symmetry has observable consequences even in single-system experiments, and can be broken by the nontrivial combination of nonlinearity, thermal fluctuations, and driving. To illustrate our ideas, we analyze concrete examples of driven qubits and nonlinear cavities. These systems exhibit hidden time-reversal symmetry but not conventional detailed balance.

Quantum dots (QDs) defined with electrostatic gates are a leading platform for a scalable quantum computing implementation. However, with increasing numbers of qubits, the complexity of the control parameter space also grows. Traditional measurement techniques, relying on complete or near-complete exploration via two-parameter scans (images) of the device response, quickly become impractical with increasing numbers of gates. Here we propose to circumvent this challenge by introducing a measurement technique relying on one-dimensional projections of the device response in the multidimensional parameter space. Dubbed the “ray-based classification (RBC) framework,” we use this machine learning approach to implement a classifier for QD states, enabling automated recognition of qubit-relevant parameter regimes. We show that RBC surpasses the $82\mathrm{\%}$ accuracy benchmark from the experimental implementation of image-based classification techniques from prior work, while reducing the number of measurement points needed by up to $70\mathrm{\%}$. The reduction in measurement cost is a significant gain for time-intensive QD measurements and is a step forward toward the scalability of these devices. We also discuss how the RBC-based optimizer, which tunes the device to a multiqubit regime, performs when tuning in the two-dimensional and three-dimensional parameter spaces defined by plunger and barrier gates that control the QDs. This work provides experimental validation of both efficient state identification and optimization with machine learning techniques for nontraditional measurements in quantum systems with high-dimensional parameter spaces and time-intensive measurements.

We introduce a hierarchy of semidefinite relaxations of the set of quantum correlations in generalized contextuality scenarios. This constitutes a simple and versatile tool for bounding the magnitude of quantum contextuality. To illustrate its utility, we use it to determine the maximal quantum violation of several noncontextuality inequalities whose maximum violations were previously unknown. We then go further and use it to prove that certain preparation-contextual correlations cannot be explained with pure states, thereby showing that mixed states are an indispensable resource for contextuality. In the second part of the paper, we turn our attention to the simulation of preparation-contextual correlations in general operational theories. We introduce the information cost of simulating preparation contextuality, which quantifies the additional, otherwise forbidden, information required to simulate contextual correlations in either classical or quantum models. In both cases, we show that the simulation cost can be efficiently bounded using a variant of our hierarchy of semidefinite relaxations, and we calculate it exactly in the simplest contextuality scenario of parity-oblivious multiplexing.

We derive a theoretical framework for the experimental certification of non-Gaussian features of quantum states using double homodyne detection. We rank experimental non-Gaussian states according to the recently defined stellar hierarchy and we propose practical Wigner negativity witnesses. We simulate various use-cases ranging from fidelity estimation to witnessing Wigner negativity. Moreover, we extend results on the robustness of the stellar hierarchy of non-Gaussian states. Our results illustrate the usefulness of double homodyne detection as a practical measurement scheme for retrieving information about continuous-variable quantum states, and show that certification of high-order non-Gaussian features can be carried out experimentally with current technology.

Quantum control, which refers to the active manipulation of physical systems described by the laws of quantum mechanics, constitutes an essential ingredient for the development of quantum technology. Here we apply differentiable programming (DP) and natural evolution strategies (NES) to the optimal transport of Majorana zero modes in superconducting nanowires, a key element to the success of Majorana-based topological quantum computation. We formulate the motion control of Majorana zero modes as an optimization problem for which we propose a new categorization of four different regimes with respect to the critical velocity of the system and the total transport time. In addition to correctly recovering the anticipated smooth protocols in the adiabatic regime, our algorithms uncover efficient but strikingly counterintuitive motion strategies in the nonadiabatic regime. The emergent picture reveals a simple but high-fidelity strategy that makes use of pulselike jumps at the beginning and the end of the protocol with a period of constant velocity in between the jumps, which we dub the jump-move-jump protocol. We provide a transparent semianalytical picture, which uses the sudden approximation and a reformulation of the Majorana motion in a moving frame, to illuminate the key characteristics of the jump-move-jump control strategy. We verify that the jump-move-jump protocol remains robust against the presence of interactions or disorder, and corroborate its high efficacy on a realistic proximity-coupled nanowire model. Our results demonstrate that machine learning for quantum control can be applied efficiently to quantum many-body dynamical systems with performance levels that make it relevant to the realization of large-scale quantum technology.

Experimental results are presented on the efficiency limits for a quantum interface between a matter-based qubit and a photonic qubit. Using a trapped ion in an optical cavity, we obtain a single ion-entangled photon at the cavity output with a probability of 0.69(3). The performance of our system is shown to saturate the upper limit to photon-collection probability from a quantum emitter in a cavity, set by the emitter’s electronic structure and by the cavity parameters. The probability for generating and detecting the ion-entangled fiber-coupled photon is 0.462(3), a fivefold increase over the previous best performance. Finally, the generation and detection of up to 15 sequential polarized photons demonstrates the ability of a trapped ion to serve as a multiphoton source. The comparison between measured probabilities and predicted bounds is relevant for quantum emitters beyond trapped ions, in particular, for the design of future systems optimizing photon collection from, and absorption in, quantum matter.

In most quantum sensing schemes, interactions between the constituent particles of the sensor are expected to lead to thermalization and degraded sensitivity. However, recent theoretical and experimental work has shown that the phenomenon of quantum many-body scarring can slow down, or even prevent, thermalization. We show that scarring can be exploited for quantum sensing that is robust against certain strong interactions. In the ideal case of perfect scars with harmonic energy gaps, the optimal sensing time can diverge despite the strong interactions. We demonstrate the idea with two examples: a spin-1 model with Dzyaloshinskii-Moriya interaction and a spin-1/2 mixed-field Ising model. We also briefly discuss some nonideal perturbations and the addition of periodic controls to suppress their effect on sensing.

We present the meta-variational quantum eigensolver (VQE), an algorithm capable of learning the ground-state energy profile of a parameterized Hamiltonian. If the meta-VQE is trained with a few data points, it delivers an initial circuit parameterization that can be used to compute the ground-state energy of any parameterization of the Hamiltonian within a certain trust region. We test this algorithm with an XXZ spin chain, an electronic ${\mathrm{H}}_4$ Hamiltonian, and a single-transmon quantum simulation. In all cases, the meta-VQE is able to learn the shape of the energy functional and, in some cases, it results in improved accuracy in comparison with individual VQE optimization. The meta-VQE algorithm introduces both a gain in efficiency for parameterized Hamiltonians in terms of the number of optimizations and a good starting point for the quantum circuit parameters for individual optimizations. The proposed algorithm can be readily mixed with other improvements in the field of variational algorithms to shorten the distance between the current state of the art and applications with quantum advantage.

Digital-analog quantum computation aims to reduce the currently infeasible resource requirements needed for near-term quantum information processing by replacing sequences of one- and two-qubit gates with a unitary transformation generated by the systems’ underlying Hamiltonian. Inspired by this paradigm, we consider superconducting architectures and extend the cross-resonance effect, up to first order in perturbation theory, from a two-qubit interaction to an analog Hamiltonian acting on one-dimensional (1D) chains and two-dimensional (2D) square lattices, which, in an appropriate reference frame, results in a purely two-local Hamiltonian. By augmenting the analog Hamiltonian dynamics with single-qubit gates we show how one may generate a larger variety of distinct analog Hamiltonians. We then synthesize unitary sequences, in which we toggle between the various analog Hamiltonians as needed, simulating the dynamics of Ising, $XY$, and Heisenberg spin models. Our dynamics simulations are Trotter error-free for the Ising and $XY$ models in 1D. We also show that the Trotter errors for 2D $XY$ and 1D Heisenberg chains are reduced, with respect to a digital decomposition, by a constant factor. In order to realize these important near-term speedups, we discuss the practical considerations needed to accurately characterize and calibrate our analog Hamiltonians for use in quantum simulations. We conclude with a discussion of how the Hamiltonian toggling techniques could be extended to derive new analog Hamiltonians, which may be of use in more complex digital-analog quantum simulations for various models of interacting spins.

Many quantum computational tasks have inherent symmetries, suggesting a path to enhancing their efficiency and performance. Exploiting this observation, we propose representation matching, a generic probabilistic protocol for reducing the cost of quantum computation in a quantum network. We show that the representation-matching protocol is capable of reducing the communication or memory cost to almost the minimum in various tasks, including remote execution of unitary gate arrays, permutation gates, and unitary conjugation, as well as the storage and retrieval of unitary gates.

We investigate, in a four-photon interference experiment in a laser-written waveguide structure, how symmetries control the suppression of many-body output events of a $J_x$ unitary. We show that totally destructive interference does not require mutual indistinguishability between all but only between symmetrically paired particles, in agreement with recent theoretical predictions. The outcome of the experiment is well described by a quantitative simulation that accounts for higher-order emission of the photon source, imbalances in the scattering network, partial distinguishability, and photon loss.

We develop a method to connect the infinite-dimensional description of optical continuous-variable quantum key distribution (QKD) protocols to a finite-dimensional formulation. The secure key rates of the optical QKD protocols can then be evaluated using recently developed reliable numerical methods for key-rate calculations. We apply this method to obtain asymptotic key rates for discrete-modulated continuous-variable QKD protocols, which are of practical significance due to their experimental simplicity and potential for large-scale deployment in quantum-secured networks. Importantly, our security proof does not require the photon-number cutoff assumption relied upon in previous works. We also demonstrate that our method can provide practical advantages over the flag-state squasher when applied to discrete-variable protocols.

In order to characterize and calibrate quantum processing devices, a large amount of measurement data has to be collected. Active qubit reset increases the speed at which data can be gathered but requires additional hardware and/or calibration. The experimental apparatus can, however, be operated at elevated repetition rates without reset. In this case, the outcome of a first measurement serves as the initial state for the next experiment. Rol et al. have used this restless operation mode to accelerate the calibration of a single-qubit gate by measuring fixed-length sequences of Clifford gates that compose to $X$ gates [Phys. Rev. Appl. 7, 041001 (2017)]. However, we find that when measuring pulse sequences that compose to arbitrary operations, distortion appears in the measured data. Here, we extend the restless methodology by showing how to efficiently analyze restless measurements and correct distortions to achieve an identical outcome and accuracy as compared to measurements in which the superconducting qubits are reset. This allows us to rapidly characterize and calibrate qubits. We illustrate this bias-corrected restless measurements method by measuring a Rabi oscillation at a $250\mathrm{kHz}$ repetition rate without any reset, for a qubit with a decay rate of $1/2\pi T_1=3\mathrm{kHz}$. We also show that we can measure a single- and a two-qubit average gate fidelity using randomized benchmarking 20 and 8 times faster, respectively, than measurements that reset the qubits through $T_1$ decay.