Generalized quantum subspace expansion

Abstract

One of the major challenges for erroneous quantum computers is undoubtedly the control over the effect of noise. Considering the rapid growth of available quantum resources that are not fully fault-tolerant, it is crucial to develop practical hardware-friendly quantum error mitigation (QEM) techniques to suppress unwanted errors. Here, we propose a novel generalized quantum subspace expansion method which can handle stochastic, coherent, and algorithmic errors in quantum computers. By fully exploiting the substantially extended subspace, we can efficiently mitigate the noise present in the spectra of a given Hamiltonian, without relying on any information of noise. The performance of our method is discussed under two highly practical setups: the quantum subspaces are mainly spanned by powers of the noisy state ${\rho }^m$ and a set of error-boosted states, respectively. We numerically demonstrate in both situations that we can suppress errors by orders of magnitude, and show that out protocol inherits the advantages of previous error-agnostic QEM techniques as well as overcoming their drawbacks.

6+14 pages, 4+10 figures

References in corpus (8)

• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Hybrid quantum-classical algorithms and quantum error mitigation
• Error mitigation for universal gates on encoded qubits
• The Dominant Eigenvector of a Noisy Quantum State
• Dual-state purification for practical quantum error mitigation
• Error mitigation and quantum-assisted simulation in the error corrected regime
• Quantum Error Mitigation Relying on Permutation Filtering
• Qubit-efficient exponential suppression of errors

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