Fault-Resilience of Dissipative Processes for Quantum Computing

TL;DR

This paper investigates the error-resilience of dissipative quantum algorithms, showing that while dissipative ground state preparation can exponentially suppress errors, dissipative quantum computation does not outperform standard quantum circuits in noise robustness.

Contribution

It proves that dissipative ground state preparation can enhance fault-tolerance, whereas dissipative quantum computation offers no additional noise resilience compared to traditional methods.

Findings

Dissipative ground state preparation suppresses errors exponentially with code distance.

Dissipative quantum computation is not more robust to noise than standard quantum circuits.

The results apply to geometrically local, stabilizer-encoded Hamiltonians.

Abstract

Dissipative processes have long been proposed as a means of performing computational tasks on quantum computers that may be intrinsically more robust to noise. In this work, we prove two main results concerning the error-resilience capabilities of two types of dissipative algorithms: dissipative ground state preparation in the form of the dissipative quantum eigensolver (DQE), and dissipative quantum computation (DQC). The first result is that under circuit-level depolarizing noise, a version of the DQE algorithm applied to the geometrically local, stabilizer-encoded Hamiltonians that arise naturally when fermionic Hamiltonians are represented in qubits, can suppress the additive error in the ground space overlap of the final output state exponentially in the code distance. This enables us to get closer to fault-tolerance for this task without the associated overhead. In contrast, for computation as opposed to ground state preparation, the second result proves that DQC is no more robust to noise than the standard quantum circuit model.