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arXiv:quant-ph/0011080

Quantum Computation with Harmonic Oscillators

Stephen D. Bartlett, Barry C. Sanders, Benjamin T. H. Varcoe, Hubert de Guise

Published Nov 20, 2000• 4 citations
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Abstract

By encoding a qudit in a harmonic oscillator and investigating the infinite limit, we give an entirely new realization of continuous-variable quantum computation. The generalized Pauli group is generated by number and phase operators for harmonic oscillators. We describe a physical realization in terms of modes in a microwave cavity, coupled via a standard Kerr nonlinearity.

DOI
10.48550/arxiv.quant-ph/0011080

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By encoding a qudit in a harmonic oscillator and investigating the infinite limit, we give an entirely new realization of continuous-variable quantum computation. The generalized Pauli group is generated by number and phase operators for harmonic oscillators. We describe a physical realization in terms of modes in a microwave cavity, coupled via a standard Kerr nonlinearity.
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Quantum harmonic oscillators are promising resources for quantum computation and quantum error correction, owing to the infinite number of available states and their ubiquitous presence in nature in various realizations, but accessing and manipulating the entire state space requires an infinite amount of energy. In this paper, the authors provide a fully analytical construction to systematically close off any finite-dimensional subspace of an oscillator and further achieve universal control on it, by coupling to a qubit.
Quantum simulation enables one to mimic the evolution of other quantum systems using a controllable quantum system. Quantum harmonic oscillator (QHO) is one of the most important model systems in quantum physics. To observe the transient dynamics of a QHO with high oscillation frequency directly is difficult. We experimentally simulate the transient behaviors of QHO in an open system during time evolution with an optical mode and a logical operation system of continuous variable quantum computation. The time evolution of an atomic ensemble in the collective spontaneous emission is analytically simulated by mapping the atomic ensemble onto a QHO. The measured fidelity, which is used for quantifying the quality of the simulation, is higher than its classical limit. The presented simulation scheme provides a new tool for studying the dynamic behaviors of QHO.