On the practicality of time-optimal two-qubit Hamiltonian simulation

Abstract

What is the time-optimal way of using a set of control Hamiltonians to obtain a desired interaction? Vidal, Hammerer and Cirac [Phys. Rev. Lett. 88 (2002) 237902] have obtained a set of powerful results characterizing the time-optimal simulation of a two-qubit quantum gate using a fixed interaction Hamiltonian and fast local control over the individual qubits. How practically useful are these results? We prove that there are two-qubit Hamiltonians such that time-optimal simulation requires infinitely many steps of evolution, each infinitesimally small, and thus is physically impractical. A procedure is given to determine which two-qubit Hamiltonians have this property, and we show that almost all Hamiltonians do. Finally, we determine some bounds on the penalty that must be paid in the simulation time if the number of steps is fixed at a finite number, and show that the cost in simulation time is not too great.

9 pages, 2 figures

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Cited by in corpus (8)

• Using Quantum Computers for Quantum Simulation
• Time Optimal Control of Coupled Qubits Under Non-Stationary Interactions
• Conditions for optimal construction of two-qubit non-local gates
• Quantum simulation of interacting high-dimensional systems: the influence of noise
• Gate simulation and lower bounds on the simulation time
• Simulating Hamiltonian dynamics using many-qudit Hamiltonians and local unitary control
• Entanglement magnification induced by local manipulations
• Optimal generation of entanglement under local control