Fidelity of optimally controlled quantum gates with randomly coupled multiparticle environments

Abstract

This work studies the feasibility of optimal control of high-fidelity quantum gates in a model of interacting two-level particles. One particle (the qubit) serves as the quantum information processor, whose evolution is controlled by a time-dependent external field. The other particles are not directly controlled and serve as an effective environment, coupling to which is the source of decoherence. The control objective is to generate target one-qubit gates in the presence of strong environmentally-induced decoherence and under physically motivated restrictions on the control field. It is found that interactions among the environmental particles have a negligible effect on the gate fidelity and require no additional adjustment of the control field. Another interesting result is that optimally controlled quantum gates are remarkably robust to random variations in qubit-environment and inter-environment coupling strengths. These findings demonstrate the utility of optimal control for management of quantum-information systems in a very precise and specific manner, especially when the dynamics complexity is exacerbated by inherently uncertain environmental coupling.

Optimal control of fast and high-fidelity quantum gates with electron and nuclear spins of a nitrogen-vacancy center in diamond

“…We will consider first the case where the quantum gate operations of the system qubits are influenced by the interactions with nearby noise qubits with a low number of degrees of freedom [50,82,83]. In this case, the most general approach is to describe the dynamics of both the system and noise qubits and their interactions in Hamiltonian unitary approach and then perform the QOC calculations for the quantum gate operations.…”

“…The noise qubits are regarded as an effective small environment interacting with the system qubits that serve as a register for quantum information processing. The implementation of quantum gates in the presence of only a few noise qubits using the Hamiltonian unitary approach for QOC calculations has been investigated [82,83]. Here besides a few noise qubits, the leakage state and the spin bath are also considered.…”

“…Here besides a few noise qubits, the leakage state and the spin bath are also considered. We thus define the error function K as the distance measure between the associated propagator P U (T ) at the final time T of the composite system and the target gate G in the column vector representation as follows [82,83]:…”

Optimized pulses for the control of uncertain qubits

“…[54], which is applicable to studies involving composite systems where only the qubit/system dynamics are directly of interest [55,56]. Concerning mathematical notation, because the unitary time-evolution operator is a function of time and a functional of the control, it will be expressed more generally as U (t; C) for all time t and a control C, compared to U (t); the final-time unitary operator will be expressed more generally as U t f (C), compared to U (t f ).…”

Incoherent Quantum Control

“…In particular, in conventional models of quantum computation the target transformation P target is a unitary gate (e.g., a phase U φ or Hadamard U H gate, and for these examples P target = U φ or P target = U H , respectively) [27,28]. More general non-unitary target transformations can arise [e.g., in quantum computing with mixed states [29] or for generating controls robust to variations of the initial system's state [30] (see also Sec.…”