Classical Chaos in Quantum Computers

TL;DR

This paper demonstrates that classical simulations can effectively diagnose stability and chaos in large quantum processors, providing a scalable tool to understand and mitigate issues in quantum computing hardware development.

Contribution

It introduces the use of classical chaos diagnostics as a scalable method to analyze and predict stability in large quantum computing systems, including current and future transmon chips.

Findings

Classical and quantum stability metrics align in small systems.

Classical simulations can handle systems with thousands of qubits.

Lyapunov exponents increase with system size, indicating higher chaos in larger devices.

Abstract

The development of quantum computing hardware is facing the challenge that current-day quantum processors, comprising 50-100 qubits, already operate outside the range of quantum simulation on classical computers. In this paper we demonstrate that the simulation of classical limits can be a potent diagnostic tool potentially mitigating this problem. As a testbed for our approach we consider the transmon qubit processor, a computing platform in which the coupling of large numbers of nonlinear quantum oscillators may trigger destabilizing chaotic resonances. We find that classical and quantum simulations lead to similar stability metrics (classical Lyapunov exponents vs. quantum wave function participation ratios) in systems with $\mathcal{O}(10)$ transmons. However, the big advantage of classical simulation is that it can be pushed to large systems comprising up to thousands of qubits. We exhibit the utility of this classical toolbox by simulating all current IBM transmon chips, including the recently announced 433-qubit processor of the Osprey generation, as well as future devices with 1,121 qubits (Condor generation). For realistic system parameters, we find a systematic increase of Lyapunov exponents with system size, suggesting that larger layouts require added efforts in information protection.