Efficient implementation of unitary transformations

Abstract

Quantum computation and quantum control operate by building unitary transformations out of sequences of elementary quantum logic operations or applications of control fields. This paper puts upper bounds on the minimum time required to implement a desired unitary transformation on a d-dimensional Hilbert space when applying sequences of Hamiltonian transformations. We show that strategies of building up a desired unitary out of non-infinitesimal and infinitesimal unitaries, or equivalently, using power and band limited controls, can yield the best possible scaling in time $O(d^2)$.

14 pages plus appendices, 4 figures

References in corpus (6)

• Simulating Hamiltonian dynamics with a truncated Taylor series
• Synthesis of Quantum Logic Circuits
• Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
• Measurement of many-body chaos using a quantum clock
• Quantum control by von Neumann measurements
• Simulating sparse Hamiltonians with star decompositions

Cited by in corpus (1)

• Learning Unitaries by Gradient Descent