Exploring Noisy Quantum Thermodynamical Processes via the Depolarizing-Channel Approximation

TL;DR

This paper introduces a depolarizing-channel approximation framework to analyze the effects of noise on quantum thermodynamical cooling protocols, providing analytical insights into their performance limits under realistic noisy conditions.

Contribution

The paper presents a novel approximation method for modeling gate-dependent noise in quantum thermodynamics, specifically applied to the TSAC cooling protocol, revealing fundamental bounds and optimal qubit numbers.

Findings

The approximation reliably describes noisy quantum dynamics in certain regimes.

Analytical derivation of the asymptotic cooling limit under noise.

Identification of optimal qubit number for maximum cooling performance.

Abstract

Noise and errors are unavoidable in any realistic quantum process, including processes designed to reduce noise and errors in the first place. In particular, quantum thermodynamical protocols for cooling can be significantly affected, potentially altering both their performance and efficiency. Analytically characterizing the impact of such errors becomes increasingly challenging as the system size grows, particularly in deep quantum circuits where noise can accumulate in complex ways. To address this, we introduce a general framework for approximating the cumulative effect of gate-dependent noise using a global depolarizing channel. We specify the regime in which this approximation provides a reliable description of the noisy dynamics. Applying our framework to the thermodynamical two-sort algorithmic cooling (TSAC) protocol, we analytically derive its asymptotic cooling limit in the presence of noise. Using the cooling limit, the optimal cooling performance is achieved by a finite number of qubits--distinguished from the conventional noiseless TSAC protocol by an infinite number of qubits--and fundamental bounds on the achievable ground-state population are derived. This approach opens new avenues for exploring noisy quantum thermodynamical processes.