Optimal Bounds on State Transfer Under Quantum Channels with Application to Spin System Engineering
arXiv:1903.03569 · doi:10.1103/PhysRevA.100.022313
Abstract
Modern applications of quantum control in quantum information science and technology require the precise characterization of quantum states and quantum channels. In particular, high-performance quantum state engineering often demands that quantum states are transferred with optimal efficiency via realizable controlled evolution, the latter often modeled by quantum channels. When an appropriate quantum control model for an interested system is constructed, the exploration of optimal bounds on state transfer for the underlying quantum channel is then an important task. In this work, we analyze the state transfer efficiency problem for different class of quantum channels, including unitary, mixed unitary and Markovian. We then apply the theory to nuclear magnetic resonance (NMR) experiments. We show that two most commonly used control techniques in NMR, namely gradient field control and phase cycling, can be described by mixed unitary channels. Then we show that employing mixed unitary channels does not extend the unitarily accessible region of states. Also, we present a strategy of optimal experiment design, which incorporates coherent radio-frequency field control, gradient field control and phase cycling, aiming at maximizing state transfer efficiency and meanwhile minimizing the number of experiments required. Finally, we perform pseudopure state preparation experiments on two- and three-spin systems, in order to test the bound theory and to demonstrate the usefulness of non-unitary control means.
arXiv comment11 pages, 8 figures
References in corpus (38)
- NMR Techniques for Quantum Control and Computation
- Control of quantum phenomena: Past, present, and future
- Open Quantum Systems. An Introduction
- Quantum Thermodynamics
- Training Schrödinger's cat: quantum optimal control
- Quantum control theory and applications: A survey
- Nuclear magnetic resonance spectroscopy: An experimentally accessible paradigm for quantum computing
- Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator
- Hybrid Quantum-Classical Approach to Quantum Optimal Control
- Controlling open quantum systems: Tools, achievements, and limitations
- Quantum feedback: theory, experiments, and applications
- Modeling and Control of Quantum Systems: An Introduction
- Effective Pure States for Bulk Quantum Computation
- Benchmarking quantum control methods on a 12-qubit system
- Optimal adaptive control for quantum metrology with time-dependent Hamiltonians
- Stabilizing Open Quantum Systems by Markovian Reservoir Engineering
- Quantum Measurement Cooling
- Controllability properties for finite dimensional quantum Markovian master equations
- Optimizing Variational Quantum Algorithms using Pontryagin's Minimum Principle
- Thermodynamics of quantum systems under dynamical control
- Quantum control by von Neumann measurements
- Quantum state engineering of a Hubbard system with ultracold fermions
- Simulation of a Heisenberg XY- chain and realization of a perfect state transfer algorithm using liquid nuclear magnetic resonance
- Ultra-Efficient Cooling of Resonators: Beating Sideband Cooling with Quantum Control
- Boundary of Quantum Evolution under Decoherence
- A spin based heat engine: demonstration of multiple rounds of algorithmic cooling
- Coherent Control of Bond Making
- Optimal control for one-qubit quantum sensing
- Preparation of pseudo-pure states by line-selective pulses in Nuclear Magnetic Resonance
- Control-free control: manipulating a quantum system using only a limited set of measurements
- High-dimensional quantum state transfer through a quantum spin chain
- Measurement driven quantum evolution
- Multi-photon quantum communication in quantum networks
- Quantum Information and Computation for Chemistry
- Approximation of Reachable Set for Coherently Controlled Open Quantum Systems: Application to Quantum State Engineering
- Non-conservative Forces via Quantum Reservoir Engineering
- Preparing pseudo-pure states with controlled-transfer gates
- Control of Ultracold Photodissociation with Magnetic Fields