Geodesics for Efficient Creation and Propagation of Order along Ising Spin Chains

Abstract

Experiments in coherent nuclear and electron magnetic resonance, and optical spectroscopy correspond to control of quantum mechanical ensembles, guiding them from initial to final target states by unitary transformations. The control inputs (pulse sequences) that accomplish these unitary transformations should take as little time as possible so as to minimize the effects of relaxation and decoherence and to optimize the sensitivity of the experiments. Here we give efficient syntheses of various unitary transformations on Ising spin chains of arbitrary length. The efficient realization of the unitary transformations presented here is obtained by computing geodesics on a sphere under a special metric. We show that contrary to the conventional belief, it is possible to propagate a spin order along an Ising spin chain with coupling strength J (in units of Hz), significantly faster than 1/(2J) per step. The methods presented here are expected to be useful for immediate and future applications involving control of spin dynamics in coherent spectroscopy and quantum information processing.

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Cited by in corpus (14)

• Training Schrödinger's cat: quantum optimal control
• Symmetry Principles in Quantum Systems Theory
• Elliptic functions and efficient control of Ising spin chains with unequal couplings
• Optimal control of circuit quantum electrodynamics in one and two dimensions
• Time-Optimal Transfer of Coherence
• Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain
• Time-optimal synthesis of unitary transformations in coupled fast and slow qubit system
• Multiple-spin coherence transfer in linear Ising spin chains and beyond: numerically-optimized pulses and experiments
• Time-optimal Unitary Operations in Ising Chains II: Unequal Couplings and Fixed Fidelity
• Time-Optimal Generation of Cluster States
• Efficient synthesis of quantum gates on indirectly coupled spins
• Time-optimal polarization transfer from an electron spin to a nuclear spin
• Characterization of majorization monotone quantum dynamics
• Brachistochrone of Entanglement for Spin Chains