CaRBM: A Fixed-Depth Quantum Algorithm with Partial Correction for Thermal State Preparation

TL;DR

The paper presents CaRBM, a fixed-depth quantum algorithm for thermal state preparation that uses partial correction to extend its effective temperature range, demonstrated on complex quantum models.

Contribution

Introduces CaRBM, a novel fixed-depth quantum algorithm employing partial correction for thermal state preparation, improving temperature range coverage.

Findings

Effective at high temperatures with success probability decreasing at lower temperatures.

Partial correction scheme extends the temperature range for reliable thermal state preparation.

Successfully applied to compute partition function zeros and phase diagrams of complex models.

Abstract

We introduce the CaRBM algorithm for fixed-depth thermal state preparation. Our algorithm is based on thermal state purification and uses the Restricted Boltzmann Machine (RBM) block-encoding scheme to implement the imaginary-time propagator $e^{-\beta H}$, which is implemented in the quantum circuit in a fixed-depth manner via Cartan decomposition. Our algorithm performs best at high temperatures, with the success probability of the block encoding decreasing as the temperature decreases. To increase the success probability, we have devised a correction scheme for the block-encoding that increases the temperature range our algorithm reliably probes. We demonstrate our algorithm by calculating the partition function zeros of the XXZ model and the phase diagram of the Gross-Neveu model, which is a model of strongly interacting relativistic fermions.