Abstract
The accumulation of noise in quantum computers is the dominant issue stymieing the push of quantum algorithms beyond their classical counterparts. We do not expect to be able to afford the overhead required for quantum error correction in the next decade, so in the meantime we must rely on low-cost, unscalable error mitigation techniques to bring quantum computing to its full potential. This paper presents a new error mitigation technique based on quantum phase estimation that can also reduce errors in expectation value estimation (e.g., for variational algorithms). The general idea is to apply phase estimation while effectively post-selecting for the system register to be in the starting state, which allows us to catch and discard errors which knock us away from there. We refer to this technique as "verified phase estimation" (VPE) and show that it can be adapted to function without the use of control qubits in order to simplify the control circuitry for near-term implementations. Using VPE, we demonstrate the estimation of expectation values on numerical simulations of intermediate scale quantum circuits with multiple orders of magnitude improvement over unmitigated estimation at near-term error rates (even after accounting for the additional complexity of phase estimation). Our numerical results suggest that VPE can mitigate against any single errors that might occur; i.e., the error in the estimated expectation values often scale as O(p^2), where p is the probability of an error occurring at any point in the circuit. This property, combined with robustness to sampling noise reveal VPE as a practical technique for mitigating errors in near-term quantum experiments.
Highlights
Error mitigation is likely essential for near-term quantum computations to realize valuable applications
In this paper we present a new error mitigation technique based on quantum phase estimation that can reduce errors in expectation value estimation
We present a new method for error mitigation, based on verification of the system register in a single-control quantum phase estimation routine
Summary
Error mitigation is likely essential for near-term quantum computations to realize valuable applications. We show that the set of experiments that pass this condition contain all the necessary information to perform quantum phase estimation This yields a powerful error mitigation technique, as in most cases errors will not return the system to this initial state. Our techniques apply to variants of phase estimation that might involve postprocessing on a single control qubit [33,34], or when performing recently developed control-free variants [35,36] We further develop it into a simple scheme for verified expectation value estimation by dividing a target Hamiltonian into a sum of fast-forwardable terms. V, we implement these ideas, studying the mitigation power of verified expectation value estimation in a variety of systems and implementations developed earlier in the text under various noise models, and testing the convergence of the protocol under sampling noise
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have