Practical Quantum Error Mitigation for Near-Future Applications

By Suguru Endo, Simon C. Benjamin, Ying Li. Physical Review X, 2017

733 citations recorded by the source corpus.

It is vital to minimise the impact of errors for near-future quantum devices that will lack the resources for full fault tolerance. Two quantum error mitigation (QEM) techniques have been introduced recently, namely error extrapolation [Li 2017,Temme 2017] and quasi-probability decomposition [Temme 2017]. To enable practical implementation of these ideas, here we account for the inevitable imperfections in the experimentalist's knowledge of the error model itself. We describe a protocol for systematically measuring the effect of errors so as to design efficient QEM circuits. We find that the effect of localised Markovian errors can be fully eliminated by inserting or replacing some gates with certain single-qubit Clifford gates and measurements. Finally, having introduced an exponential variant of the extrapolation method we contrast the QEM techniques using exact numerical simulation of up to 19 qubits in the context of a 'SWAP test' circuit. Our optimised methods dramatically reduce the circuit's output error without increasing the qubit count or time requirements.

Subfields: Artificial Intelligence, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/9bbf679d0fd8d3e802842b0318347946b4fd9d1a

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Citations in the corpus

Quantum error mitigation (2022, methodology): “Endo et al. (2018) have shown that such basis can be constructed using single-qubit Clifford gates and Z -measurement with reasonable fidelity, while the characterisation can be carried out efficiently using gate set tomography.”
Probabilistic error cancellation with sparse Pauli–Lindblad models on noisy quantum processors (2022, methodology): “Although Λ − 1 is not a physical operation, it can be expressed as a linear combination of gates and state-preparation operations [9, 12].”
Variational quantum algorithms (2020, methodology): “First, Richardson extrapolation was proposed [74, 89, 205], and it was shown that single- and multi-exponential extrapolation work well for Markovian gate errors, with the latter subsequently shown to have very broad efficacy [206, 207].”
Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator (2018, background): “[118] Suguru Endo, Simon C Benjamin, and Ying Li, “Practical Quantum Error Mitigation for Near-Future Applications,” arXiv.”
Error mitigation with Clifford quantum-circuit data (2020, background): “In addition, we also show an exponential fit for ZNE [17].”
Theory of variational quantum simulation (2018, methodology): “As the variational method only uses shallow quantum circuits, error mitigation techniques can be applied to suppress errors [41, 63–70].”
The future of quantum computing with superconducting qubits (2022, background): “Probabilistic error cancellation (PEC) 10,72 aims to approximate an ideal quantum circuit via a weighted sum of noisy circuits that can be implemented on a given quantum computer.”
Fundamental limits of quantum error mitigation (2021, methodology): “Although this analysis is suﬃcient for many present methods of error mitigation, it is possible to also improve estimates of (cid:104) 𝐴 (cid:105) by scaling the number of distorted outputs we process in a single round (e.g., extrapolation [11] and subspace expansion [27]).”
Variational Quantum Computation of Excited States (2018, methodology): “[7, 39] can be readily applied to our algorithm.”
Evidence for the utility of quantum computing before fault tolerance (2023, background): “2a highlight the reduced bias from exponential extrapolation 19 in comparison with linear extrapolation.”
Error mitigation extends the computational reach of a noisy quantum processor (2018, methodology): “In the absence of classical cross-talk, the IY is negligible, else a cancellation may be employed as in reference [13].”