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arXiv:2306.03060 · Proceedings of the National Academy of Sciences

Accreditation of analogue quantum simulators

Andrew Jackson, Theodoros Kapourniotis, Animesh Datta

Published Jan 31, 2024• 5 citations
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Abstract

We present an accreditation protocol for analogue, i.e., continuous-time, quantum simulators. For a given simulation task, it provides an upper bound on the variation distance between the probability distributions at the output of an erroneous and error-free analogue quantum simulator. As its overheads are independent of the size and nature of the simulation, the protocol is ready for immediate usage and practical for the long term. It builds on the recent theoretical advances of strongly universal Hamiltonians and quantum accreditation as well as experimental progress toward the realization of programmable hybrid analogue-digital quantum simulators.

DOI
10.1073/pnas.2309627121

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We present an accreditation protocol for analogue, i.e., continuous-time, quantum simulators. For a given simulation task, it provides an upper bound on the variation distance between the probability distributions at the output of an erroneous and error-free analogue quantum simulator. As its overheads are independent of the size and nature of the simulation, the protocol is ready for immediate usage and practical for the long term. It builds on the recent theoretical advances of strongly universal Hamiltonians and quantum accreditation as well as experimental progress toward the realization of programmable hybrid analogue-digital quantum simulators.
We improve on the results of [A. Jackson et al. Proc. Natl. Acad. Sci. U.S.A 121 (6). 2024] on the verification of analogue quantum simulators by eliminating the use of universal Hamiltonians, removing the need for two-qubit gates, and no longer assuming error is represented by identical maps across simulations. This new protocol better reflects the reality of extant analogue simulators. It integrates well with recent complexity theoretic results, leading to a near-term feasible simulation-based route to establishing quantum advantage.
We develop a family of quantum accreditation protocols for quantum circuits with non-Clifford two-qubit gates. The latter includes families of gates such as the fSim and XY families of gates, native to existing hardwares. We provide practical and scalable protocols that upper-bound the total variation distance between the probability distributions of error-free and erroneous quantum computations. We also establish the robustness of our protocols to small perturbations and generalize Pauli twirling to non-Pauli single-qubit bases, which may be of independent interest.
We provide and experimentally demonstrate an accreditation protocol that upper bounds the variation distance between noisy and noiseless probability distributions of the outputs of arbitrary quantum computations. We accredit the outputs of 24 quantum circuits executed on programmable superconducting hardware, ranging from depth-9 circuits on 10 qubits to depth-21 circuits on 4 qubits. Our protocol requires implementing the ``target'' quantum circuit along with a number of random Clifford circuits and subsequently postprocessing the outputs of these Clifford circuits. Importantly, the number of Clifford circuits is chosen to obtain the bound with the desired confidence and accuracy and is independent of the size and nature of the target circuit. We thus demonstrate a practical and scalable method of ascertaining the correctness of the outputs of arbitrary-sized noisy quantum computers---the ultimate arbiter of the utility of the computer itself.
Analogue quantum simulators offer a promising route to explore quantum many-body dynamics beyond classical reach in the near term. However, their vulnerability to noise limits the accuracy of simulations. Here, we establish a new framework for mitigating noise in analogue quantum simulation, operating in a time-continuous manner. To our knowledge, this is the first protocol that is fully analogue and that achieves exact noise cancellation. Our method requires a small number of ancillary qubits, whose interaction with the system−-−combined with classical post-processing of joint measurement data−-−is tailored to cancel the effect of noise. Furthermore, the protocol is Hamiltonian-independent, robust to realistic ancilla noise, and avoids any discretization, preserving the continuous-time nature of the system's dynamics. This work opens a new direction for achieving high-fidelity analogue quantum simulation in the presence of noise.
Abstract Current development in programmable analogue quantum simulators (AQS), whose physical implementation can be realised in the near-term compared to those of large-scale digital quantum computers, highlights the need for robust testing techniques in analogue platforms. Methods to properly certify or benchmark AQS should be efficiently scalable, and also provide a way to deal with errors from state preparation and measurement (SPAM). Up to now, attempts to address this combination of requirements have generally relied on model-specific properties. We put forward a new approach, applying a well-known digital noise characterisation technique called randomized benchmarking (RB) to the analogue setting. RB is a scalable experimental technique that provides a measure of the average error-rate of a gate-set on a quantum hardware, incorporating SPAM errors. We present the original form of digital RB, the necessary alterations to translate it to the analogue setting and introduce the analogue randomized benchmarking protocol (ARB). In ARB we measure the average error-rate per time evolution of a family of Hamiltonians and we illustrate this protocol with two case-studies of analogue models; classically simulating the system by incorporating several physically motivated noise scenarios. We find that for the noise models tested, the data fit with the theoretical predictions and we gain values for the average error rate for differing unitary sets. We compare our protocol with other relevant RB methods, where both advantages (physically motivated unitaries) and disadvantages (difficulty in reversing the time-evolution) are discussed.
Analog quantum simulators emulate complex many-body dynamics through native continuous-time evolution under hardware-defined interactions. Yet once a platform is specified, its interaction structure is largely fixed by the underlying hardware, restricting the Hamiltonians that can be realized and limiting programmability. Here we introduce universal analog quantum simulation (UAQS), a hybrid framework that systematically expands the range of accessible quantum evolutions within a given analog platform. UAQS employs optimized continuous-time control fields to engineer target dynamics directly, avoiding decomposition into discrete gate sequences. By preserving native analog evolution while extending the set of achievable Hamiltonians, UAQS transforms fixed-interaction analog devices into programmable simulators. Numerical studies on representative architectures, including superconducting circuits and Rydberg-atom arrays, show that UAQS accurately reproduces non-trivial many-body dynamics beyond the intrinsic interaction structure of the hardware. These results establish UAQS as a practical route toward programmable analog quantum simulation.