# Unifying and benchmarking state-of-the-art quantum error mitigation techniques

@inproceedings{Bultrini2021UnifyingAB, title={Unifying and benchmarking state-of-the-art quantum error mitigation techniques}, author={Daniel Bultrini and Max Hunter Gordon and Piotr Czarnik and Andrew Arrasmith and Patrick J. Coles and Lukasz Cincio}, year={2021} }

Daniel Bultrini,1, 2, ∗ Max Hunter Gordon,3, ∗ Piotr Czarnik,1 Andrew Arrasmith,1, 4 Patrick J. Coles,1, 4 and Lukasz Cincio1, 4 Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, INF 229, D-69120 Heidelberg, Germany Instituto de Física Teórica, UAM/CSIC, Universidad Autónoma de Madrid, Madrid, Spain Quantum Science Center, Oak Ridge, TN 37931, USA

#### 5 Citations

Extending quantum probabilistic error cancellation by noise scaling

- Physics
- Physical Review A
- 2021

We propose a general framework for quantum error mitigation that combines and generalizes two techniques: probabilistic error cancellation (PEC) and zero-noise extrapolation (ZNE). Similarly to PEC,… Expand

Quantum Error Mitigation Relying on Permutation Filtering

- Physics, Computer Science
- ArXiv
- 2021

This treatise shows that the proposed filter design algorithm always converge to the global optimum, and that the optimal filters can provide substantial improvements over the existing permutation-based methods in the presence of narrowband quantum noise, corresponding to large-depth, high-error-rate quantum circuits. Expand

A Practical Framework for Quantum Error Mitigation

- Physics
- 2021

Quantum error mitigation is expected to play a crucial role in the practical applications of quantum machines for the foreseeable future. Thus it is important to put the numerous quantum error… Expand

Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?

- Computer Science, Physics
- ArXiv
- 2021

This work shows that, for a broad class of EM strategies, exponential cost concentration cannot be resolved without committing exponential resources elsewhere, and finds numerical evidence that Clifford Data Regression (CDR) can aid the training process in certain settings where cost concentration is not too severe. Expand

Biology and medicine in the landscape of quantum advantages

- Physics, Computer Science
- 2021

Quantum computing holds significant potential for applications in biology and medicine, spanning from the simulation of biomolecules to machine learning approaches for subtyping cancers on the basis… Expand

#### References

SHOWING 1-10 OF 42 REFERENCES

Generalized quantum subspace expansion

- Physics
- 2021

Nobuyuki Yoshioka, 2, ∗ Hideaki Hakoshima, Yuichiro Matsuzaki, Yuuki Tokunaga, Yasunari Suzuki, 5 and Suguru Endo † Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo… Expand

Error mitigation by training with fermionic linear optics

- Physics
- 2021

Noisy intermediate-scale quantum (NISQ) computers could solve quantum-mechanical simulation problems that are beyond the capabilities of classical computers. However, NISQ devices experience… Expand

Error mitigation extends the computational reach of a noisy quantum processor

- Medicine, Computer Science
- Nature
- 2019

This work applies the error mitigation protocol to mitigate errors in canonical single- and two-qubit experiments and extends its application to the variational optimization of Hamiltonians for quantum chemistry and magnetism. Expand

Resource-efficient Purification-based Quantum Error Mitigation

- Physics
- 2021

To achieve the practical applications of near-term noisy quantum devices, low-cost ways to mitigate the noise damages in the devices are essential. In many applications, the noiseless state we want… Expand

Learning the quantum algorithm for state overlap

- Computer Science, Physics
- New Journal of Physics
- 2018

This work finds algorithms that have shorter depths than the Swap Test, including one that has constant depth (independent of problem size) and applies this approach to the hardware-specific connectivity and gate alphabets used by Rigetti's and IBM's quantum computers. Expand

Low-cost error mitigation by symmetry verification

- Physics
- Physical Review A
- 2018

We investigate the performance of error mitigation via measurement of conserved symmetries on near-term devices. We present two protocols to measure conserved symmetries during the bulk of an… Expand

Unified approach to data-driven quantum error mitigation

- Physics, Computer Science
- 2020

A novel, scalable error mitigation method that conceptually unifies ZNE and CDR, called variable-noise Clifford data regression (vnCDR), significantly outperforms these individual methods in numerical benchmarks. Expand

Error Mitigation via Verified Phase Estimation

- Physics, Computer Science
- 2020

This paper presents a new error mitigation technique based on quantum phase estimation that can also reduce errors in expectation value estimation and demonstrates the estimation of expectation values on numerical simulations of intermediate scale quantum circuits with multiple orders of magnitude improvement over unmitigated estimation at near-term error rates. Expand

The Dominant Eigenvector of a Noisy Quantum State

- Physics
- New Journal of Physics
- 2021

Although near-term quantum devices have no comprehensive solution for correcting errors, numerous techniques have been proposed for achieving practical value. Two works have recently introduced the… Expand

Noise-Resilient Quantum Dynamics Using Symmetry-Preserving Ansatzes

- Mathematics, Physics
- 2019

We describe and demonstrate a method for the computation of quantum dynamics on small, noisy universal quantum computers. This method relies on the idea of `restarting' the dynamics; at least one… Expand