Classical simulation of circuits with realistic odd-dimensional Gottesman-Kitaev-Preskill states

TL;DR

This paper introduces an efficient classical simulation algorithm for circuits with odd-dimensional GKP states, enabling the simulation of large-scale bosonic quantum circuits with high squeezing levels, which was previously computationally prohibitive.

Contribution

The authors develop a novel simulation method leveraging the Zak-Gross Wigner function, specifically tailored for high-squeezing GKP states, allowing scalable simulation of complex bosonic quantum circuits.

Findings

Simulates up to 1,000 modes with 12 dB squeezing efficiently.

Runtime scales with Wigner function negativity, enabling targeted simulations.

Potential for benchmarking early bosonic quantum computing implementations.

Abstract

Classically simulating circuits with bosonic codes is challenging due to the prohibitive cost of simulating quantum systems with many, possibly infinite, energy levels. We propose an algorithm to simulate circuits with encoded Gottesman-Kitaev-Preskill (GKP) states, specifically for odd-dimensional encoded qudits. Our approach is tailored to be especially effective in the most challenging but practically relevant regime, where the codeword states exhibit high (but finite) squeezing. Our algorithm leverages the Zak-Gross Wigner function introduced by J. Davis et al. [arXiv:2407.18394], which represents infinitely squeezed encoded stabilizer states positively. The runtime of the algorithm scales with the negativity of the Wigner function, allowing for efficient simulation of certain large-scale circuits - namely, input stabilizer GKP states undergoing generalized GKP-encoded Clifford operations followed by modular measurements - with a high degree of squeezing. For stabilizer GKP states exhibiting 12 dB of squeezing, our algorithm can simulate circuits with up to 1,000 modes with less than double the number of samples required for a single input mode, in stark contrast to existing simulators. Therefore, this approach holds significant potential for benchmarking early implementations of quantum computing architectures utilizing bosonic codes.