Logical shadow tomography: Efficient estimation of error-mitigated observables

TL;DR

This paper presents a new method called logical shadow tomography for efficiently estimating error-mitigated observables on noisy quantum computers, reducing resource overhead compared to existing techniques.

Contribution

The authors introduce a framework that generalizes subspace expansion and virtual distillation, enabling more resource-efficient error mitigation through shadow tomography on logical states.

Findings

Requires fewer samples than subspace expansion for logical Pauli observables.

Can compute powers of the density matrix without extra quantum states.

Demonstrates fast convergence to error-free values with limited samples under noise.

Abstract

We introduce a technique to estimate error-mitigated expectation values on noisy quantum computers. Our technique performs shadow tomography on a logical state to produce a memory-efficient classical reconstruction of the noisy density matrix. Using efficient classical post-processing, one can mitigate errors by projecting a general nonlinear function of the noisy density matrix into the codespace. The subspace expansion and virtual distillation can be viewed as special cases of the new framekwork. We show our method is favorable in the quantum and classical resources overhead. Relative to subspace expansion which requires $O\left(2^{N} \right)$ samples to estimate a logical Pauli observable with $[[N, k]]$ error correction code, our technique requires only $O\left(4^{k} \right)$ samples. Relative to virtual distillation, our technique can compute powers of the density matrix without additional copies of quantum states or quantum memory. We present numerical evidence using logical states encoded with up to sixty physical qubits and show fast convergence to error-free expectation values with only $10^5$ samples under 1% depolarizing noise.