Quantum adiabatic theorem for unbounded Hamiltonians with a cutoff and its application to superconducting circuits
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866911757007585280 |
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| author | Mozgunov, Evgeny Lidar, Daniel A. |
| author_facet | Mozgunov, Evgeny Lidar, Daniel A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_08116 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Quantum adiabatic theorem for unbounded Hamiltonians with a cutoff and its application to superconducting circuits Mozgunov, Evgeny Lidar, Daniel A. Quantum Physics 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. |
| title | Quantum adiabatic theorem for unbounded Hamiltonians with a cutoff and its application to superconducting circuits |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2011.08116 |