Symmetry boosts quantum computer performance

TL;DR

This paper demonstrates that implementing symmetric errors in quantum subroutines can significantly enhance the fidelity of quantum computations, with potential improvements up to a factor of 10, especially in algorithms like Shor's.

Contribution

The authors introduce a symmetry-based method to boost quantum operation fidelity by matching hardware errors in symmetric subroutine implementations, supported by numerical and analytical results.

Findings

Fidelity boost factor of up to 10 observed in Shor's algorithm

Analytical scaling predicts a minimum boost factor of about 3 for large qubit numbers

Symmetry boost persists across different qubit sizes and algorithms

Abstract

Frequently, subroutines in quantum computers have the structure $\mathcal{F}\mathcal{U}\mathcal{F}^{-1}$, where $\mathcal{F}$ is some unitary transform and $\mathcal{U}$ is performing a quantum computation. In this paper we suggest that if, in analogy to spin echoes, $\mathcal{F}$ and $\mathcal{F}^{-1}$ can be implemented symmetrically such that $\mathcal{F}$ and $\mathcal{F}^{-1}$ have the same hardware errors, a symmetry boost in the fidelity of the combined $\mathcal{F}\mathcal{U}\mathcal{F}^{-1}$ quantum operation results. Running the complete gate--by--gate implemented Shor algorithm, we show that the fidelity boost can be as large as a factor 10. Corroborating and extending our numerical results, we present analytical scaling calculations that show that a symmetry boost persists in the practically interesting case of a large number of qubits. Our analytical calculations predict a minimum boost factor of about 3, valid for all qubit numbers, which includes the boost factor 10 observed in our low-qubit-number simulations. While we find and document this symmetry boost here in the case of Shor's algorithm, we suggest that other quantum algorithms might profit from similar symmetry-based performance boosts whenever $\mathcal{F}\mathcal{U}\mathcal{F}^{-1}$ sub-units of the corresponding quantum algorithm can be identified.