An algorithm for solving unconstrained unitary quantum brachistochrone problems
arXiv:1906.02934 · doi:10.1103/PhysRevA.100.062328
Abstract
We introduce an iterative method to search for time-optimal Hamiltonians that drive a quantum system between two arbitrary, and in general mixed, quantum states. The method is based on the idea of progressively improving the efficiency of an initial, randomly chosen, Hamiltonian, by reducing its components that do not actively contribute to driving the system. We show that our method converges rapidly even for large dimensional systems, and that its solutions saturate any attainable bound for the minimal time of evolution. We provide a rigorous geometric interpretation of the iterative method by exploiting an isomorphism between geometric phases acquired by the system along a path and the Hamiltonian that generates it, and discuss resulting similarities with Grover's quantum search algorithm. Our method is directly applicable as a powerful tool for state preparation and gate design problems.
arXiv commentMain: 6 pages, 2 figures. Appendix: 2 pages, 3 figures
References in corpus (49)
- Quantum Mechanics helps in searching for a needle in a haystack
- Quantum-enhanced measurements: beating the standard quantum limit
- NMR Techniques for Quantum Control and Computation
- Observation of entanglement propagation in a quantum many-body system
- Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
- Shortcuts to adiabaticity by counter-diabatic driving
- Enhancing the charging power of quantum batteries
- Optimal Control at the Quantum Speed Limit
- Quantum speed limits in open system dynamics
- Quantacell: Powerful charging of quantum batteries
- Faster than Hermitian Quantum Mechanics
- Onset of a Quantum Phase Transition with a Trapped Ion Quantum Simulator
- Quantum Equivalence and Quantum Signatures in Heat Engines
- Quantum Brachistochrone
- The fundamental limit on the rate of quantum dynamics: the unified bound is tight
- Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
- Improved quantum metrology using quantum error-correction
- Quantum Error Correction for Metrology
- Trade-off between speed and cost in shortcuts to adiabaticity
- Experimental realization of stimulated Raman shortcut-to-adiabatic passage with cold atoms
- Monotonically convergent optimization in quantum control using Krotov's method
- Energy-time uncertainty relation for driven quantum systems
- Shortcuts to adiabaticity by counterdiabatic driving for trapped-ion displacement in phase space
- Quantum Adiabatic Brachistochrone
- Optimal Control-Based Efficient Synthesis of Building Blocks of Quantum Algorithms Seen in Perspective from Network Complexity towards Time Complexity
- Tightening Quantum Speed Limits for Almost All States
- Optimal control of complex atomic quantum systems
- Time Optimal Unitary Operations
- Experimental Realization of a Quantum Integer-Spin Chain with Controllable Interactions
- Quantum brachistochrone curves as geodesics: obtaining accurate control protocols for time-optimal quantum gates
- Pulsed Laser Cooling for Cavity-Optomechanical Resonators
- Ultra-Efficient Cooling of Resonators: Beating Sideband Cooling with Quantum Control
- Quantum Brachistochrone Problem and the Geometry of the State Space in Pseudo-Hermitian Quantum Mechanics
- Shortcuts to adiabaticity for trapped ultracold gases
- Physical Optimization of Quantum Error Correction Circuits
- Tight, robust, and feasible quantum speed limits for open dynamics
- Shortcut to adiabatic gate teleportation
- Optimal quantum control of Bose-Einstein condensates in magnetic microtraps: Comparison of GRAPE and Krotov optimization schemes
- Experimental time-optimal universal control of spin qubits in solids
- Time-dependent Hamiltonians with 100% evolution speed efficiency
- Time-optimal navigation through quantum wind
- Quantum Brachistochrone for Mixed States
- Beating the limits with initial correlations
- Entanglement and the Quantum Brachistochrone Problem
- Time-Optimal Transfer of Coherence
- Optimal control for fast and high-fidelity quantum gates in coupled superconducting flux qubits
- Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain
- The quantum brachistochrone problem for non-Hermitian Hamiltonians
- Time-optimal Unitary Operations in Ising Chains II: Unequal Couplings and Fixed Fidelity
Cited by in corpus (9)
- Colloquium: Quantum Batteries
- Action quantum speed limits
- Resource speed limits: Maximal rate of resource variation
- Minimal time required to charge a quantum system
- Qubit Geodesics on the Bloch Sphere from Optimal-Speed Hamiltonian Evolutions
- Complexity of Pure and Mixed Qubit Geodesic Paths on Curved Manifolds
- Quantum Speed Limit under Brachistochrone Evolution
- Relaxation Control of Open Quantum Systems
- Optimal-speed unitary quantum time evolutions and propagation of light with maximal degree of coherence