We present an accreditation protocol for the outputs of noisy intermediate-scale quantum devices. By testing entire circuits rather than individual gates, our accreditation protocol can provide an upper-bound on the variation distance between noisy and noiseless probability distribution of the outputs of the target circuit of interest. Our accreditation protocol requires implementing quantum circuits no larger than the target circuit, therefore it is practical in the near term and scalable in the long term. Inspired by trap-based protocols for the verification of quantum computations, our accreditation protocol assumes that single-qubit gates have bounded probability of error. We allow for arbitrary spatial and temporal correlations in the noise affecting state preparation, measurements, single-qubit and two-qubit gates. We describe how to implement our protocol on real-world devices, and we also present a novel cryptographic protocol (which we call 'mesothetic' protocol) inspired by our accreditation protocol.
We present an accreditation protocol for the outputs of noisy intermediate-scale quantum devices. By testing entire circuits rather than individual gates, our accreditation protocol can provide an upper-bound on the variation distance between noisy and noiseless probability distribution of the outputs of the target circuit of interest. Our accreditation protocol requires implementing quantum circuits no larger than the target circuit, therefore it is practical in the near term and scalable in the long term. Inspired by trap-based protocols for the verification of quantum computations, our accreditation protocol assumes that single-qubit gates have bounded probability of error. We allow for arbitrary spatial and temporal correlations in the noise affecting state preparation, measurements, single-qubit and two-qubit gates. We describe how to implement our protocol on real-world devices, and we also present a novel cryptographic protocol (which we call 'mesothetic' protocol) inspired by our accreditation protocol.
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.
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.
Correcting errors due to noise in quantum circuits run on current and near-term quantum hardware is essential for any convincing demonstration of quantum advantage. Indeed, in many cases it has been shown that noise renders quantum circuits efficiently classically simulable, thereby destroying any quantum advantage potentially offered by an ideal (noiseless) implementation of these circuits. Although the technique of quantum error correction (QEC) allows correcting these errors very accurately, QEC usually requires a large overhead of physical qubits which is not reachable with currently available quantum hardware. This has been the motivation behind the field of quantum error mitigation, which aims at developing techniques to correct an important part of the errors in quantum circuits, while also being compatible with current and near-term quantum hardware. In this work, we present a technique for quantum error mitigation which is based on a technique from quantum verification, the so-called accreditation protocol, together with postselection. Our technique allows for correcting the expectation value of an observable O, which is the output of multiple runs of noisy quantum circuits, where the noise in these circuits is at the level of preparations, gates, and measurements. We discuss the sample complexity of our procedure and provide rigorous guarantees of errors being mitigated under some realistic assumptions on the noise. Our technique is tailored to time-dependent behaviors, as we allow for the output states to be different between different runs of the accreditation protocol. We validate our findings by running our technique on currently available quantum hardware.
Using near-term quantum computers to achieve a quantum advantage requires efficient strategies to improve the performance of the noisy quantum devices presently available. We develop and experimentally validate two efficient error mitigation protocols named ``Noiseless Output Extrapolation" and ``Pauli Error Cancellation" that can drastically enhance the performance of quantum circuits composed of noisy cycles of gates. By combining popular mitigation strategies such as probabilistic error cancellation and noise amplification with efficient noise reconstruction methods, our protocols can mitigate a wide range of noise processes that do not satisfy the assumptions underlying existing mitigation protocols, including non-local and gate-dependent processes. We test our protocols on a four-qubit superconducting processor at the Advanced Quantum Testbed. We observe significant improvements in the performance of both structured and random circuits, with up to 86% improvement in variation distance over the unmitigated outputs. Our experiments demonstrate the effectiveness of our protocols, as well as their practicality for current hardware platforms.
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.
Abstract We study the distribution over measurement outcomes of noisy random quantum circuits in the regime of low fidelity, which corresponds to the setting where the computation experiences at least one gate-level error with probability close to one. We model noise by adding a pair of weak, unital, single-qubit noise channels after each two-qubit gate, and we show that for typical random circuit instances, correlations between the noisy output distribution pnoisy p noisy and the corresponding noiseless output distribution pideal p ideal shrink exponentially with the expected number of gate-level errors. Specifically, the linear cross-entropy benchmark F that measures this correlation behaves as F=exp(−2sϵ±O(sϵ2)) F = exp ( - 2 s ϵ ± O ( s ϵ 2 ) ) , where ϵ ϵ is the probability of error per circuit location and s is the number of two-qubit gates. Furthermore, if the noise is incoherent—for example, depolarizing or dephasing noise—the total variation distance between the noisy output distribution pnoisy p noisy and the uniform distribution punif p unif decays at precisely the same rate. Consequently, the noisy output distribution can be approximated as pnoisy≈Fpideal+(1−F)punif p noisy ≈ F p ideal + ( 1 - F ) p unif . In other words, although at least one local error occurs with probability 1−F 1 - F , the errors are scrambled by the random quantum circuit and can be treated as global white noise, contributing completely uniform output. Importantly, we upper bound the average total variation error in this approximation by O(Fϵs) O ( F ϵ s ) . Thus, the “white-noise approximation” is meaningful when ϵs≪1 ϵ s ≪ 1 , a quadratically weaker condition than the ϵs≪1 ϵ s ≪ 1