Holonomic quantum control with continuous variable systems

Abstract

Universal computation of a quantum system consisting of superpositions of well-separated coherent states of multiple harmonic oscillators can be achieved by three families of adiabatic holonomic gates. The first gate consists of moving a coherent state around a closed path in phase space, resulting in a relative Berry phase between that state and the other states. The second gate consists of "colliding" two coherent states of the same oscillator, resulting in coherent population transfer between them. The third gate is an effective controlled-phase gate on coherent states of two different oscillators. Such gates should be realizable via reservoir engineering of systems which support tunable nonlinearities, such as trapped ions and circuit QED.

6 pages, 3 figures + 4 page supplement; (v3 scheme now universal; v4 title changed to match published version); gate animations available at http://dancingblobs.krastanov.org/

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• Fast binomial-code holonomic quantum computation with ultrastrong light-matter coupling
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• Shortcuts to Adiabaticity for Open Systems in Circuit Quantum Electrodynamics
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• Stabilization of cat-state manifolds using nonlinear reservoir engineering
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• Generalized Parity Measurements and Efficient Large Multi-component Cat State Preparation with Quantum Signal Processing
• On-chip microwave coherent source with in-situ control of the photon number distribution
• Geometric and holonomic quantum computation