Scalable Emulation of Sign-Problem$-$Free Hamiltonians with Room Temperature p-bits

TL;DR

This paper demonstrates that a room-temperature probabilistic p-bit based coprocessor can efficiently emulate sign-problem-free quantum Hamiltonians, significantly accelerating quantum Monte Carlo simulations on classical hardware.

Contribution

It introduces a novel hardware approach using p-bits to emulate stoquastic quantum systems, enabling room-temperature, high-speed quantum simulations.

Findings

P-bit coprocessor accelerates QMC algorithms by several orders of magnitude.

Realistic device simulations confirm correct quantum correlations at room temperature.

The approach overcomes limitations of physical quantum annealers for certain quantum systems.

Abstract

The growing field of quantum computing is based on the concept of a q-bit which is a delicate superposition of 0 and 1, requiring cryogenic temperatures for its physical realization along with challenging coherent coupling techniques for entangling them. By contrast, a probabilistic bit or a p-bit is a robust classical entity that fluctuates between 0 and 1, and can be implemented at room temperature using present-day technology. Here, we show that a probabilistic coprocessor built out of room temperature p-bits can be used to accelerate simulations of a special class of quantum many-body systems that are sign-problem$-$free or stoquastic, leveraging the well-known Suzuki-Trotter decomposition that maps a $d$-dimensional quantum many body Hamiltonian to a $d$+1-dimensional classical Hamiltonian. This mapping allows an efficient emulation of a quantum system by classical computers and is commonly used in software to perform Quantum Monte Carlo (QMC) algorithms. By contrast, we show that a compact, embedded MTJ-based coprocessor can serve as a highly efficient hardware-accelerator for such QMC algorithms providing several orders of magnitude improvement in speed compared to optimized CPU implementations. Using realistic device-level SPICE simulations we demonstrate that the correct quantum correlations can be obtained using a classical p-circuit built with existing technology and operating at room temperature. The proposed coprocessor can serve as a tool to study stoquastic quantum many-body systems, overcoming challenges associated with physical quantum annealers.