Free Mode Removal and Mode Decoupling for Simulating General Superconducting Quantum Circuits

TL;DR

This paper introduces a formal method using linear canonical transformations to remove free modes and decouple modes in superconducting quantum circuits, enabling more efficient simulation of complex, strongly coupled multimode circuits beyond traditional approaches.

Contribution

It provides a provably correct algorithm for removing free modes and a series of transformations to reduce intermode couplings, improving simulation efficiency for general superconducting circuits.

Findings

Achieved several orders of magnitude reduction in Hilbert space size for fluxonium qubits

Demonstrated effective decoupling of free modes in complex circuits

Enhanced simulation capability for strongly coupled multimode circuits

Abstract

Superconducting quantum circuits is one of the leading candidates for a universal quantum computer. Designing novel qubit and multiqubit superconducting circuits requires the ability to simulate and analyze the properties of a general circuit. In particular, going outside the transmon approach, we cannot make assumptions on anharmonicity, thus precluding blackbox quantization approaches and necessitating the formal circuit quantization approach. We consider and solve two issues involved in simulating general superconducting circuits. One of the issues is the handling of free modes in the circuit, that is, circuit modes with no potential term in the Hamiltonian. Another issue is circuit size, namely the challenge of simulating strongly coupled multimode circuits. The main mathematical tool we use to address these issues is the linear canonical transformation in the setting of quantum mechanics. We address the first issue by giving a provably correct algorithm for removing free modes by performing a linear canonical transformation to completely decouple the free modes from other circuit modes. We address the second by giving a series of different linear canonical transformations to reduce intermode couplings, thereby reducing the problem to the weakly coupled case and greatly mitigating the overhead for classical simulation. We benchmark our decoupling methods by applying them to the circuit of two inductively coupled fluxonium qubits, obtaining several orders of magnitude reduction in the size of the Hilbert space that needs to be simulated.