A framework of partial error correction for intermediate-scale quantum computers

TL;DR

This paper proposes a framework for partial error correction in intermediate-scale quantum computers, demonstrating that selectively error-correcting some qubits can slow decoherence and improve computational robustness under certain conditions.

Contribution

It introduces a concrete construction of logical operations combining noisy and error-corrected qubits, and provides analytical and numerical evidence of benefits in decoherence slowdown.

Findings

Slower convergence to uniform distribution with more error-corrected qubits

Decoherence is reduced when the number of error-corrected qubits exceeds a certain threshold

Advantages depend on the coupling between error-corrected and noisy qubits

Abstract

As quantum computing hardware steadily increases in qubit count and quality, one important question is how to allocate these resources to mitigate the effects of hardware noise. In a transitional era between noisy small-scale and fully fault-tolerant systems, we envisage a scenario in which we are only able to error correct a small fraction of the qubits required to perform an interesting computation. In this work, we develop concrete constructions of logical operations on a joint system of a collection of noisy and a collection of error-corrected logical qubits. Within this setting and under Pauli noise assumptions, we provide analytical evidence that brick-layered circuits display on average slower concentration to the "useless" uniform distribution with increasing circuit depth compared to fully noisy circuits. We corroborate these findings by numerical demonstration of slower decoherence with an increasing fraction of error-corrected qubits under a noise model inspired by a real device. We find that this advantage only comes when the number of error-corrected qubits passes a specified threshold which depends on the number of couplings between error-corrected and noisy registers.