[Paper Review] Automated quantum error mitigation based on probabilistic error reduction

Benjamin McDonough, Andrea Mari+5 more|arXiv (Cornell University)|Jan 1, 2022

Quantum Computing Algorithms and Architecture21 references13 citations

TL;DR

This paper presents an automated software framework for quantum error mitigation using probabilistic error reduction (PER) combined with virtual zero-noise extrapolation (vZNE). It enables efficient noise characterization via Pauli noise tomography (PNT) or gate set tomography (GST), generates noise-scaled circuits for PER, and applies vZNE to achieve error-mitigated expectation values with significantly reduced sampling overhead compared to probabilistic error cancellation (PEC), while maintaining comparable accuracy.

ABSTRACT

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.

Motivation & Objective

• To address the high sampling overhead of probabilistic error cancellation (PEC) in near-term quantum computing.
• To develop an automated, end-to-end software pipeline for applying probabilistic error reduction (PER) to user-defined quantum circuits.
• To integrate noise characterization (PNT and GST) with PER and virtual zero-noise extrapolation (vZNE) for scalable error mitigation.
• To enable practical, reproducible error mitigation on noisy intermediate-scale quantum (NISQ) devices through a multi-platform Python package.

Proposed method

• Uses Pauli noise tomography (PNT) to extract a sparse Pauli noise model from benchmarking circuits with weak assumptions on noise correlations.
• Employs gate set tomography (GST) via PyGSTi to obtain detailed noisy superoperators for quantum gates.
• Applies canonical noise scaling to generate noise-scaled channel representations G(ξ)i that depend on a tunable noise level ξ.
• Generates sampled circuits from the noise-scaled representations to estimate expectation values at multiple ξ values.
• Uses virtual zero-noise extrapolation (vZNE) with exponential fitting to extrapolate to the noiseless limit (ξ → 0).
• Integrates the entire workflow into a multi-platform Python package using Mitiq and PyGSTi, enabling automated execution from circuit input to error-mitigated output.

Experimental results

Research questions

• RQ1 Can probabilistic error reduction (PER) combined with virtual zero-noise extrapolation (vZNE) achieve error-mitigated expectation values with accuracy comparable to PEC but with reduced sampling overhead?
• RQ2 How can Pauli noise tomography (PNT) be effectively integrated into an automated error mitigation pipeline for NISQ devices?
• RQ3 What is the performance gain of PER over PEC in terms of sampling overhead for deep quantum circuits?
• RQ4 Can the proposed framework be implemented as a general-purpose, multi-platform software tool for practical use across different quantum hardware platforms?

Key findings

• PER with vZNE reduces the required sampling overhead from γ(0)²/δ² ≈ 53/δ² for PEC to only γ(0.5)²/δ² + 2/δ² ≈ 9/δ² at noise strengths ξ ∈ [0.5, 1, 2] for a 15-step Trotter simulation.
• The framework successfully mitigates noise in a 4-qubit transverse field Ising model simulation, achieving agreement with the noiseless result using vZNE on PER data.
• The sampling overhead for PEC increases dramatically as ξ approaches zero due to negative quasiprobability coefficients, while PER maintains lower variance and reduced cost.
• The software framework enables automated execution of the full error mitigation workflow, including circuit parsing, tomography, circuit generation, execution, and analysis, with execution time dominated by circuit generation (~1 hour on a laptop for 10 Trotter steps).
• The integration of PNT with PER and vZNE enables scalable noise characterization with constant complexity in qubit count, making it suitable for larger systems.
• The open-source implementation with tutorial notebooks ensures reproducibility and facilitates adoption across multiple quantum platforms.