Optimized pulses for the control of uncertain qubits

Abstract

Constructing high-fidelity control fields that are robust to control, system, and/or surrounding environment uncertainties is a crucial objective for quantum information processing. Using the two-state Landau-Zener model for illustrative simulations of a controlled qubit, we generate optimal controls for π/2- and π-pulses, and investigate their inherent robustness to uncertainty in the magnitude of the drift Hamiltonian. Next, we construct a quantum-control protocol to improve system-drift robustness by combining environment-decoupling pulse criteria and optimal control theory for unitary operations. By perturbatively expanding the unitary time-evolution operator for an open quantum system, previous analysis of environment-decoupling control pulses has calculated explicit control-field criteria to suppress environment-induced errors up to (but not including) third order from π/2- and π-pulses. We systematically integrate this criteria with optimal control theory, incorporating an estimate of the uncertain parameter, to produce improvements in gate fidelity and robustness, demonstrated via a numerical example based on double quantum dot qubits. For the qubit model used in this work, post facto analysis of the resulting controls suggests that realistic control-field fluctuations and noise may contribute just as significantly to gate errors as system and environment fluctuations.

38 pages, 15 figures, RevTeX 4.1, minor modifications to the previous version

References in corpus (24)

• Non-Abelian Anyons and Topological Quantum Computation
• Quantum Computing
• Fault-Tolerant Quantum Dynamical Decoupling
• Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization
• Theory of electron spin decoherence by interacting nuclear spins in a quantum dot
• Dynamically Error-Corrected Gates for Universal Quantum Computation
• Tackling Systematic Errors in Quantum Logic Gates with Composite Rotations
• Arbitrarily accurate composite pulses
• Performance of Deterministic Dynamical Decoupling Schemes: Concatenated and Periodic Pulse Sequences
• Quantum Computing with NMR
• Exact Results on Dynamical Decoupling by $\pi$-Pulses in Quantum Information Processes
• Electron spin decoherence in isotope-enriched silicon
• Dynamic Nuclear Polarization with Single Electron Spins
• Dangling-bond spin relaxation and magnetic 1/f noise from the amorphous-semiconductor/oxide interface: Theory
• Dynamical Quantum Error Correction of Unitary Operations with Bounded Controls
• Sliding mode control of quantum systems
• Application of Optimal Control to CPMG Refocusing Pulse Design
• Decoherence induced by anisotropic hyperfine interaction in Si spin qubits
• Optimization of Short Coherent Control Pulses
• Arbitrary precision composite pulses for NMR quantum computing
• Optimal Control for Open Quantum Systems: Qubits and Quantum Gates
• Generalization of short coherent control pulses: extension to arbitrary rotations
• Numerical Analysis of Optimized Coherent Control Pulses
• Implications of Electronics Constraints for Solid-State Quantum Error Correction and Quantum Circuit Failure Probability

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