4 research outputs found
Zero noise extrapolation on logical qubits by scaling the error correction code distance
In this work, we migrate the quantum error mitigation technique of Zero-Noise
Extrapolation (ZNE) to fault-tolerant quantum computing. We employ ZNE on
\emph{logically encoded} qubits rather than \emph{physical} qubits. This
approach will be useful in a regime where quantum error correction (QEC) is
implementable but the number of qubits available for QEC is limited. Apart from
illustrating the utility of a traditional ZNE approach (circuit-level unitary
folding) for the QEC regime, we propose a novel noise scaling ZNE method
specifically tailored to QEC: \emph{distance scaled ZNE (DS-ZNE)}. DS-ZNE
scales the distance of the error correction code, and thereby the resulting
logical error rate, and utilizes this code distance as the scaling `knob' for
ZNE. Logical qubit error rates are scaled until the maximum achievable code
distance for a fixed number of physical qubits, and lower error rates (i.e.,
effectively higher code distances) are achieved via extrapolation techniques
migrated from traditional ZNE. Furthermore, to maximize physical qubit
utilization over the ZNE experiments, logical executions at code distances
lower than the maximum allowed by the physical qubits on the quantum device are
parallelized to optimize device utilization. We validate our proposal with
numerical simulation and confirm that ZNE lowers the logical error rates and
increases the effective code distance beyond the physical capability of the
quantum device. For instance, at a physical code distance of 11, the DS-ZNE
effective code distance is 17, and at a physical code distance of 13, the
DS-ZNE effective code distance is 21. When the proposed technique is compared
against unitary folding ZNE under the constraint of a fixed number of
executions of the quantum device, DS-ZNE outperforms unitary folding by up to
92\% in terms of the post-ZNE logical error rate.Comment: 8 pages, 5 figure
Automated quantum error mitigation based on probabilistic error reduction
Current quantum computers suffer from a level of noise that prohibits
extracting useful results directly from longer computations. The figure of
merit in many near-term quantum algorithms is an expectation value measured at
the end of the computation, which experiences a bias in the presence of
hardware noise. A systematic way to remove such bias is probabilistic error
cancellation (PEC). PEC requires a full characterization of the noise and
introduces a sampling overhead that increases exponentially with circuit depth,
prohibiting high-depth circuits at realistic noise levels. Probabilistic error
reduction (PER) is a related quantum error mitigation method that
systematically reduces the sampling overhead at the cost of reintroducing bias.
In combination with zero-noise extrapolation, PER can yield expectation values
with an accuracy comparable to PEC.Noise reduction through PER is broadly
applicable to near-term algorithms, and the automated implementation of PER is
thus desirable for facilitating its widespread use. To this end, we present an
automated quantum error mitigation software framework that includes noise
tomography and application of PER to user-specified circuits. We provide a
multi-platform Python package that implements a recently developed Pauli noise
tomography (PNT) technique for learning a sparse Pauli noise model and exploits
a Pauli noise scaling method to carry out PER.We also provide software tools
that leverage a previously developed toolchain, employing PyGSTi for gate set
tomography and providing a functionality to use the software Mitiq for PER and
zero-noise extrapolation to obtain error-mitigated expectation values on a
user-defined circuit.Comment: 11 pages, 9 figure
Automated quantum error mitigation based on probabilistic error reduction
Current quantum computers suffer from a level of noise that prohibits extracting useful results directly from longer computations. The figure of merit in many near-term quantum algorithms is an expectation value measured at the end of the computation, which experiences a bias in the presence of hardware noise. A systematic way to remove such bias is probabilistic error cancellation (PEC). PEC requires a full characterization of the noise and introduces a sampling overhead that increases exponentially with circuit depth, prohibiting high-depth circuits at realistic noise levels. Probabilistic error reduction (PER) is a related quantum error mitigation method that systematically reduces the sampling overhead at the cost of reintroducing bias. In combination with zero-noise extrapolation, PER can yield expectation values with an accuracy comparable to PEC.Noise reduction through PER is broadly applicable to near-term algorithms, and the automated implementation of PER is thus desirable for facilitating its widespread use. To this end, we present an automated quantum error mitigation software framework that includes noise tomography and application of PER to user-specified circuits. We provide a multi-platform Python package that implements a recently developed Pauli noise tomography (PNT) technique for learning a sparse Pauli noise model and exploits a Pauli noise scaling method to carry out PER.We also provide software tools that leverage a previously developed toolchain, employing PyGSTi for gate set tomography and providing a functionality to use the software Mitiq for PER and zero-noise extrapolation to obtain error-mitigated expectation values on a user-defined circuit.This is a pre-print of the article McDonough, Benjamin, Andrea Mari, Nathan Shammah, Nathaniel T. Stemen, Misty Wahl, William J. Zeng, and Peter P. Orth. "Automated quantum error mitigation based on probabilistic error reduction." arXiv preprint arXiv:2210.08611 (2022).
DOI: 10.48550/arXiv.2210.08611.
Copyright 2022 The Authors.
Posted with permission
Mitiq : a software package for error mitigation on noisy quantum computers
We introduce Mitiq, a Python package for error mitigation on noisy quantum computers. Error mitigation techniques can reduce the impact of noise on near-term quantum computers with minimal overhead in quantum resources by relying on a mixture of quantum sampling and classical post-processing techniques. Mitiq is an extensible toolkit of different error mitigation methods, including zero-noise extrapolation, probabilistic error cancellation, and Clifford data regression. The library is designed to be compatible with generic backends and interfaces with different quantum software frameworks. We describe Mitiq using code snippets to demonstrate usage and discuss features and contribution guidelines. We present several examples demonstrating error mitigation on IBM and Rigetti superconducting quantum processors as well as on noisy simulators