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

Interventions to improve system-level coproduction in the Cystic Fibrosis Learning Network

Background Coproduction is defined as patients and clinicians collaborating equally and reciprocally in healthcare and is a crucial concept for quality improvement (QI) of health services. Learning Health Networks (LHNs) provide insights to integrate coproduction with QI efforts from programmes from various health systems.Objective We describe interventions to develop and maintain patient and family partner (PFP) coproduction, measured by PFP-reported and programme-reported scales. We aim to increase percentage of programmes with PFPs reporting active QI work within their programme, while maintaining satisfaction in PFP-clinician relationships.Methods Conducted in the Cystic Fibrosis Learning Network (CFLN), an LHN comprising over 30 cystic fibrosis (CF) programmes, people with CF, caregivers and clinicians cocreated interventions in readiness awareness, inclusive PFP recruitment, onboarding process, partnership development and leadership opportunities. Interventions were adapted by CFLN programmes and summarised in a change package for existing programmes and the orientation of new ones. We collected monthly assessments for PFP and programme perceptions of coproduction and PFP self-rated competency of QI skills and satisfaction with programme QI efforts. We used control charts to analyse coproduction scales and run charts for PFP self-ratings.Results Between 2018 and 2022, the CFLN expanded to 34 programmes with 52% having ≥1 PFP reporting active QI participation. Clinicians from 76% of programmes reported PFPs were actively participating or leading QI efforts. PFPs reported increased QI skills competency (17%–32%) and consistently high satisfaction and feeling valued in their work.Conclusions Implementing system-level programmatic strategies to engage and sustain partnerships between clinicians and patients and families with CF improved perceptions of coproduction to conduct QI work. Key adaptable strategies for programmes included onboarding and QI training, supporting multiple PFPs simultaneously and developing financial recognition processes. Interventions may be applicable in other health conditions beyond CF seeking to foster the practice of coproduction