Optimal Control Theory for Continuous Variable Quantum Gates

Abstract

We apply the methodology of optimal control theory to the problem of implementing quantum gates in continuous variable systems with quadratic Hamiltonians. We demonstrate that it is possible to define a fidelity measure for continuous variable (CV) gate optimization that is devoid of traps, such that the search for optimal control fields using local algorithms will not be hindered. The optimal control of several quantum computing gates, as well as that of algorithms composed of these primitives, is investigated using several typical physical models and compared for discrete and continuous quantum systems. Numerical simulations indicate that the optimization of generic CV quantum gates is inherently more expensive than that of generic discrete variable quantum gates, and that the exact-time controllability of CV systems plays an important role in determining the maximum achievable gate fidelity. The resulting optimal control fields typically display more complicated Fourier spectra that suggest a richer variety of possible control mechanisms. Moreover, the ability to control interactions between qunits is important for delimiting the total control fluence. The comparative ability of current experimental protocols to implement such time-dependent controls may help determine which physical incarnations of CV quantum information processing will be the easiest to implement with optimal fidelity.

39 pages, 11 figures

References in corpus (14)

• Quantum information with continuous variables
• Encoding a qubit in an oscillator
• Quantum computation over continuous variables
• Time Optimal Control in Spin Systems
• Squeezing as an irreducible resource
• Efficient Classical Simulation of Continuous Variable Quantum Information Processes
• Molecular Quantum Computing by an Optimal Control Algorithm for Unitary Transformations
• Analog quantum error correction
• Quantum Control Landscapes
• Unconditional two-mode squeezing of separated atomic ensembles
• Optimal control of quantum gates and suppression of decoherence in a system of interacting two-level particles
• Entanglement generation and Hamiltonian simulation in Continuous-Variable Systems
• Vibrational coherent quantum computation
• Unitary Gate Synthesis for Continuous Variable Systems

Cited by in corpus (15)

• Control of quantum phenomena: Past, present, and future
• Singularities of Quantum Control Landscapes
• Riemannian Optimization on the Symplectic Stiefel Manifold
• Diverging quantum speed limits: a herald of classicality
• Optimal State Manipulation for a Two-Qubit System Driven by Coherent and Incoherent Controls
• Robust population inversion in three-level systems by composite pulses
• Amplification of quadratic Hamiltonians
• Fast Quantum Communication in Linear Networks
• Dynamical recurrence and the quantum control of coupled oscillators
• Critical Topology for Optimization on the Symplectic Group
• Quantum Control of Infinite Dimensional Many-Body Systems
• The reachable set of single-mode unstable quadratic Hamiltonians
• Optimization on the symplectic group
• Locally optimal symplectic control of multimode Gaussian states
• Geometry of the symplectic Stiefel manifold endowed with the Euclidean metric