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arXiv · 2011.08116

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

Evgeny Mozgunov·Daniel A. Lidar
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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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Evgeny Mozgunov, Daniel A. Lidar. 2020-11-16. Quantum adiabatic theorem for unbounded Hamiltonians with a cutoff and its application to superconducting circuits. https://doi.org/10.1098/rsta.2021.0407

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