Universally Robust Quantum Control

Abstract

We study the robustness of the evolution of a quantum system against small uncontrolled variations in parameters in the Hamiltonian. We show that the fidelity susceptibility, which quantifies the perturbative error to leading order, can be expressed in superoperator form and use this to derive control pulses which are robust to any class of systematic unknown errors. The proposed optimal control protocol is equivalent to searching for a sequence of unitaries that mimics the first-order moments of the Haar distribution, i.e. it constitutes a 1-design. We highlight the power of our results for error resistant single- and two-qubit gates.

18 pages, 9 figures

References in corpus (28)

• Quantum Computing in the NISQ era and beyond
• Shortcuts to adiabaticity: concepts, methods, and applications
• Quantum Fisher information matrix and multiparameter estimation
• Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
• Noise tailoring for scalable quantum computation via randomized compiling
• Optimal Control at the Quantum Speed Limit
• Chaos and complexity by design
• Evenly distributed unitaries: on the structure of unitary designs
• Optimally robust shortcuts to population inversion in two-level quantum systems
• Symmetrizing Evolutions
• Dynamically Error-Corrected Gates for Universal Quantum Computation
• Review of Decoherence Free Subspaces, Noiseless Subsystems, and Dynamical Decoupling
• Leakage reduction in fast superconducting qubit gates via optimal control
• Arbitrary quantum control of qubits in the presence of universal noise
• Correction of Arbitrary Errors in Population Inversion of Quantum Systems by Universal Composite Pulses
• Dynamical Quantum Error Correction of Unitary Operations with Bounded Controls
• Convergence rates for arbitrary statistical moments of random quantum circuits
• Automated Synthesis of Dynamically Corrected Quantum Gates
• Time-optimal synthesis of SU(2) transformations for a spin-1/2 system
• Operator fidelity susceptibility, decoherence and quantum criticality
• Inhibiting unwanted transitions in population transfer in two- and three-level quantum systems
• Quantum circuits for exact unitary $t$-designs and applications to higher-order randomized benchmarking
• Geometrical Formalism for Dynamically Corrected Gates in Multiqubit Systems
• Geometric quantum speed limits and short-time accessibility to unitary operations
• Quantum Pareto Optimal Control
• Small, Highly Accurate Quantum Processor for Intermediate-Depth Quantum Simulations
• Quantum chaos and operator fidelity metric
• Optimal Control in Disordered Quantum Systems

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