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Perturbative model of noisy quantum signal processing

Andrew K. Tan1,*, Yuan Liu1,†, Minh C. Tran2,‡, and Isaac L. Chuang1,3

  • 1Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 2Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 3Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • *aktan@mit.edu
  • †yuanliu@mit.edu
  • ‡minhtran@mit.edu
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Phys. Rev. A 107, 042429 – Published 24 April, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.042429

Abstract

Recent progress in quantum signal processing (QSP) and its generalization, quantum singular value transformation, has led to a grand unification of quantum algorithms. However, inherent experimental noise in quantum devices severely limits the length of realizable QSP sequences. We consider a model of QSP with generic perturbative noise in the signal processing basis and present a diagrammatic notation useful for analyzing such errors. To demonstrate our technique, we study a specific coherent error, that of under- or overrotation of the signal processing operator parametrized by ε≪1. For this coherent error model, it is shown that while Pauli Z errors are not recoverable without additional resources, Pauli X and Y errors can be arbitrarily suppressed by coherently appending a noisy recovery QSP without the use of additional resources or ancillas. Furthermore, through a careful accounting of errors using our diagrammatic tools, we provide an upper and lower bound on the length of this recovery QSP operator. We anticipate that the perturbative technique and the diagrammatic notation proposed here will facilitate future study of generic noise in QSP and quantum algorithms.

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Physics Subject Headings (PhySH)

Corrections

27 July, 2023

Correction: The omission of factors 1/k! in Eqs. (27) and (28) has been fixed. The previously published Figures 8 and 10 contained diagrams that reflected the error of the missing factors and have been replaced.

Article Text

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Outline

Information

Phys. Rev. A 107, 042429– Published 24 April, 2023
  • Received 22 February 2023
  • Accepted 6 April 2023
  • Corrected 27 July 2023
Article part of CHORUS
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