Exploring adiabatic quantum trajectories via optimal control

Abstract

Adiabatic quantum computation employs a slow change of a time-dependent control function (or functions) to interpolate between an initial and final Hamiltonian, which helps to keep the system in the instantaneous ground state. When the evolution time is finite, the degree of adiabaticity (quantified in this work as the average ground-state population during evolution) depends on the particulars of a dynamic trajectory associated with a given set of control functions. We use quantum optimal control theory with a composite objective functional to numerically search for controls that achieve the target final state with a high fidelity while simultaneously maximizing the degree of adiabaticity. Exploring properties of optimal adiabatic trajectories in model systems elucidates the dynamic mechanisms that suppress unwanted excitations from the ground state. Specifically, we discover that the use of multiple control functions makes it possible to access a rich set of dynamic trajectories, some of which attain a significantly improved performance (in terms of both fidelity and adiabaticity) through the increase of the energy gap during most of the evolution time.

The final version accepted by New J. Phys., 20 pages, 2 figures

References in corpus (9)

• Optimized Dynamical Decoupling in a Model Quantum Memory
• Bounds for the adiabatic approximation with applications to quantum computation
• Towards Fault Tolerant Adiabatic Quantum Computation
• The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
• Error suppression and error correction in adiabatic quantum computation I: techniques and challenges
• Hamiltonian Oracles
• Validity of the Adiabatic Approximation
• Quantum Pareto Optimal Control
• Quantum Multiobservable Control

Cited by in corpus (19)

• Optimizing Variational Quantum Algorithms using Pontryagin's Minimum Principle
• Counterdiabaticity and the quantum approximate optimization algorithm
• Lyapunov control-inspired strategies for quantum combinatorial optimization
• Ultrafast Variational Simulation of Non-trivial Quantum States with Long Range Interactions
• Schedule path optimization for quantum annealing and adiabatic quantum computing
• Searching for quantum optimal controls under severe constraints
• Designing Quantum Annealing Schedules using Bayesian Optimization
• Robust Quantum Control for Adiabatic Quantum Computation
• Optimizing adiabatic quantum pathways via a learning algorithm
• Second order phase dispersion by optimised rotation pulses
• Superadiabatic Control of Quantum Operations
• Exploring the complexity of quantum control optimization trajectories
• Numerical Engineering of Robust Adiabatic Operations
• Speeding up quantum adiabatic processes with dynamical quantum geometric tensor
• Bounds on quantum adiabaticity in driven many-body systems from generalized orthogonality catastrophe and quantum speed limit
• Inertial geometric quantum logic gates
• Physical consequences of Lindbladian invariance transformations
• Using optimal control to guide neural-network interpolation of continuously-parameterized gates
• Exact solutions for the time-evolution of quantum spin systems under arbitrary waveforms using algebraic graph theory