Quantum Gate Design Metric

Abstract

What is the time-optimal way of realizing quantum operations? Here, we show how important instances of this problem can be related to the study of shortest paths on the surface of a sphere under a special metric. Specifically, we provide an efficient synthesis of a controlled NOT (CNOT) gate between qubits coupled indirectly via Ising-type couplings to a third spin. Our implementation of the CNOT gate is more than twice as fast as conventional approaches. The pulse sequences for efficient manipulation of our coupled spin system are obtained by explicit computation of geodesics on a sphere under the special metric. These methods are also used for the efficient synthesis of indirect couplings and of the Toffoli gate. We provide experimental realizations of the presented methods on a linear three-spin chain with Ising couplings.

Cited by in corpus (4)

• The quantum brachistochrone problem for an arbitrary spin in a magnetic field
• Quantum state geometry and entanglement of two spins with anisotropic interaction in evolution
• Geometry of quantum state manifolds generated by the Lie algebra operators
• Measuring distance between quantum states on a quantum computer