Thermodynamic Recycling in Quantum Computing: Demonstration Using the Harrow-Hassidim-Lloyd Algorithm and Information Erasure

TL;DR

A generic framework that reuses failure branches as thermodynamic resources and achieves erasure with heat dissipation below the Landauer limit is proposed, establishing a practical connection between quantum computing and quantum thermodynamics and suggesting a route toward reducing thermodynamic costs in future large-scale quantum computers.

Abstract

Branch selection, including postselection, is a standard method for implementing nonunitary transformations in quantum algorithms. Conventionally, states associated with unsuccessful branches are discarded and treated as useless. Here we propose a generic framework that reuses these failure branches as thermodynamic resources. The central element is an athermal bath that is naturally generated during the reset of a failure branch. By coupling this bath to a target system prior to relaxation, useful thermodynamic tasks can be performed, enabling performance beyond conventional thermodynamic limits. As an application, we analyze information erasure and derive the resulting gain analytically. We further demonstrate the framework by implementing the Harrow-Hassidim-Lloyd algorithm on IBM's superconducting quantum processor. Despite substantial noise and errors in current hardware, our method achieves erasure with heat dissipation below the Landauer limit. These results establish a practical connection between quantum computing and quantum thermodynamics and suggest a route toward reducing thermodynamic costs in future large-scale quantum computers.

Figures (6)

• Figure 1: Illustration of thermodynamic recycling. During the reset of a failure branch state after running an algorithm, the bath $B$ can transition to an athermal state $\rho_B^{\mathrm{ath}}$. Before relaxation, we couple it to the target system $S$ and perform a thermodynamic task (information erasure in this work).
• Figure 2: Circuit sketch of the demonstration protocol. The success/failure of HHL is determined by mid-circuit measurement, and only upon failure, we reset the failure branch by a SWAP with $B$ via feedforward. Before $B$ relaxes, we implement the erasure operation by another SWAP. Full state tomography is performed on $S$ before and after erasure.
• Figure 3: Fidelity $F(\theta_b)$ of the output state in the success branch of the HHL algorithm. Each point corresponds to a single trial, and the curve connects the medians over multiple trials.
• Figure 4: Information-erasure results on ibm_kawasaki. (a) Erasure using an equilibrium bath. (b) Experimental results for erasure using thermodynamic recycling. (c) Theoretical prediction for erasure using thermodynamic recycling. The horizontal axis is the parameter $\theta_b$, and the vertical axis is the heat dissipation $\Delta Q_B$ and the theoretical bounds $Q_{\rm ath}$, $Q_{\rm tight}$, and $Q_{\rm Landauer}$. Each point corresponds to a single trial, and the curve connects the medians over multiple trials.
• Figure 5: Dependence of heat dissipation $\Delta Q_B$ on the initial mixedness $p_x$ of the target system. (a) Empirical heat dissipation $\Delta Q_B$ and the theoretical bounds $Q_{\rm ath}$, $Q_{\rm tight}$, and $Q_{\rm Landauer}$ for $\theta_b=0$. (b) Results for the dissipation ratio $(\Delta Q_B - Q_{\rm tight})/Q_{\rm tight}$ for all $\theta_b$. The list of $\theta_b$ is the same as in Fig. \ref{['fig:results']}. In both (a) and (b), we plot only the regime where $\Delta S_S>0$. Each point corresponds to a single trial, and the curves connect the medians over multiple trials.