Quantum adiabatic theorem for unbounded Hamiltonians with a cutoff and its application to superconducting circuits

• URL: http://arxiv.org/abs/2011.08116v2
• Date: Mon, 5 Dec 2022 23:34:19 GMT
• Title: Quantum adiabatic theorem for unbounded Hamiltonians with a cutoff and its application to superconducting circuits
• Authors: Evgeny Mozgunov, Daniel A. Lidar
• Abstract summary: We present a new quantum adiabatic theorem that allows one to rigorously bound the adiabatic timescale for a variety of systems. Our bound is geared towards the qubit approximation of superconducting circuits.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a new quantum adiabatic theorem that allows one to rigorously bound the adiabatic timescale for a variety of systems, including those described by unbounded Hamiltonians. Our bound is geared towards the qubit approximation of superconducting circuits, and presents a sufficient condition for remaining within the $2^n$-dimensional qubit subspace of a circuit model of $n$ qubits. The novelty of this adiabatic theorem is that unlike previous rigorous results, it does not contain $2^n$ as a factor in the adiabatic timescale, and it allows one to obtain an expression for the adiabatic timescale independent of the cutoff of the infinite-dimensional Hilbert space of the circuit Hamiltonian. As an application, we present an explicit dependence of this timescale on circuit parameters for a superconducting flux qubit, and demonstrate that leakage out of the qubit subspace is inevitable as the tunnelling barrier is raised towards the end of a quantum anneal. We also discuss a method of obtaining a $2^n\times 2^n$ effective Hamiltonian that best approximates the true dynamics induced by slowly changing circuit control parameters.

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