Classical Chaos in Quantum Computers

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.

11 pages, 17 figures, Appendix (3 pages, 3 figures)

References in corpus (15)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Charge insensitive qubit design derived from the Cooper pair box
• Anderson Transitions
• Circuit Quantum Electrodynamics
• Suppressing quantum errors by scaling a surface code logical qubit
• Phenomenology of fully many-body-localized systems
• Laser-annealing Josephson junctions for yielding scaled-up superconducting quantum processors
• High-fidelity, high-scalability two-qubit gate scheme for superconducting qubits
• Microwave-induced coupling of superconducting qubits
• Fluxonium: an alternative qubit platform for high-fidelity operations
• Operation and intrinsic error budget of a two-qubit cross-resonance gate
• Transmon platform for quantum computing challenged by chaotic fluctuations
• Observation of Josephson Harmonics in Tunnel Junctions
• Photon blockade and the quantum-to-classical transition in the driven-dissipative Josephson pendulum coupled to a resonator
• Beyond hard-core bosons in transmon arrays

Cited by in corpus (10)

• Stabilizer entropy in non-integrable quantum evolutions
• Quantum computer error structure probed by quantum error correction syndrome measurements
• How to seed ergodic dynamics of interacting bosons under conditions of many-body quantum chaos
• Arresting Quantum Chaos Dynamically in Transmon Arrays
• Suppressing chaos with mixed superconducting qubit devices
• Frozonium: Freezing Anharmonicity in Floquet Superconducting Circuits
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• Propagation of two-particle correlations across the chaotic phase for interacting bosons
• Characterization of the chaotic phase in the tilted Bose-Hubbard model
• Fundamental Limits to Cat-Code Qubits from Chaos-Assisted Tunneling