Constructing Qudits from Infinite Dimensional Oscillators by Coupling to Qubits

• URL: http://arxiv.org/abs/2105.02896v4
• Date: Fri, 10 Sep 2021 02:13:36 GMT
• Title: Constructing Qudits from Infinite Dimensional Oscillators by Coupling to Qubits
• Authors: Yuan Liu, Jasmine Sinanan-Singh, Matthew T. Kearney, Gabriel Mintzer, and Isaac L. Chuang
• Abstract summary: We show how a Hilbert space can be analytically constructed from the lowest energy states of a qubit-oscillator system. This work suggests that the combination of a qubit and a bosonic system may serve as hardware-efficient quantum resources for quantum information processing.
• Score: 3.161454999079499
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: An infinite dimensional system such as a quantum harmonic oscillator offers a potentially unbounded Hilbert space for computation, but accessing and manipulating the entire state space requires a physically unrealistic amount of energy. When such a quantum harmonic oscillator is coupled to a qubit, for example via a Jaynes-Cummings interaction, it is well known that the total Hilbert space can be separated into independently accessible subspaces of constant energy, but the number of subspaces is still infinite. Nevertheless, a closed four-dimensional Hilbert space can be analytically constructed from the lowest energy states of the qubit-oscillator system. We extend this idea and show how a $d$-dimensional Hilbert space can be analytically constructed, which is closed under a finite set of unitary operations resulting solely from manipulating standard Jaynes-Cummings Hamiltonian terms. Moreover, we prove that the first-order sideband pulses and carrier pulses comprise a universal set for quantum operations on the qubit-oscillator qudit. This work suggests that the combination of a qubit and a bosonic system may serve as hardware-efficient quantum resources for quantum information processing.

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