Source-linked AI summary
Hybrid Quantum-Classical Approach to Quantum Optimal Control
Jun Li, Xiaodong Yang, Xinhua Peng, Chang-Pu Sun
TL;DR
The paper develops a hybrid quantum-classical framework for gradient-based optimal control. Quantum-simulator evolution and measurement support the iterative procedure, while classical computation handles other optimization steps; an experiment prepares a target state with fidelity f = 0.9824.
Problem
The paper addresses developing a hybrid quantum-classical framework for gradient-based optimal control.
Method
The scheme uses a quantum simulator for evolution and measurement while a classical computer performs one-dimensional search and updates control parameters iteratively.
Results
f = 0.9824 was achieved for the final state generated by the experimental preparation circuit under the real Hamiltonian.
Takeaways & Limitations
The hybrid setup supports experimental quantum optimal-control preparation using repeated sample queries and classical optimization steps.
Takeaways & Limitations
The analysis does not consider initialization and detection errors or relaxation effects during preparation.
Abstract
from arXiv · showhide
A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantum-classical scheme to tackle the quantum optimal control problem. We show that the most computationally demanding part of gradient-based algorithms, namely computing the fitness function and its gradient for a control input, can be accomplished by the process of evolution and measurement on a quantum simulator. By posing queries to and receiving messages from the quantum simulator, classical computing devices update the control parameters until an optimal control solution is found. To demonstrate the quantum-classical scheme in experiment, we use a nine-spin nuclear magnetic resonance system, on which we have succeeded in preparing a seven-correlated quantum state without involving classical computation of the large Hilbert space evolution.
GRADIENT-BASED METHODS
The paper frames gradient-based optimal control as iterative line searches that use fitness and gradient information to update controls. It discusses gradient ascent, nonlinear conjugate gradient, and quasi-Newton strategies for choosing search directions.
- GRADIENT-BASED METHODS: Each iteration determines a gradient-related search direction, finds an optimal step size, and updates u(q+1) = u(q) + α(q)p(q).
- GRADIENT-BASED METHODS: Gradient ascent chooses search directions directly from the fitness gradient.
- GRADIENT-BASED METHODS: Nonlinear conjugate gradient determines the search direction using the current gradient and a coefficient β(q) computed from the Fletcher-Reeves formula.
- GRADIENT-BASED METHODS: Quasi-Newton methods use gradient information and an updated Hessian approximation to achieve superlinear convergence.
- GRADIENT-BASED METHODS: In the hybrid implementation, the classical computer records iterative information about f and ∇f to compute subsequent search directions.
EXPERIMENT
The experiment demonstrates the hybrid algorithm on fully 13C-labeled crotonic acid by repeatedly querying the sample through initialization, preparation, and detection stages.
- EXPERIMENT: The experiment uses fully 13C-labeled crotonic acid to demonstrate a sample computing its own optimal control pulse.
- EXPERIMENT: Each query consists of initialization, preparation, and detection, with the final target-state detection made by observing the C2 spectrum.
Initialization
Initialization creates the desired initial state from equilibrium using a non-unitary steady-state hetero-nuclear Overhauser effect procedure. The method improves polarization and reduces reset time for the sample.
- Initialization: Initialization creates ρi from the equilibrium state through a non-unitary process based on the steady-state hetero-nuclear Overhauser effect.
- Initialization: The procedure produces the desired initial state by retaining the C2 signal after saturating proton polarization and removing other carbon signals.
- Initialization: The NOE-based reset provides higher initial polarization and a reset time about six times faster for the sample.
Preparation
The preparation stage constructs an approximate state-transfer circuit from a simplified coupling network, then compiles it into selective pulses for the real Hamiltonian. The resulting sequence prepares a seven-correlated state with high fidelity.
- Preparation: The approximate circuit is built from a simplified Hamiltonian that ignores small couplings and differences among large couplings.
- Preparation: The two circuit sub-steps generate three-correlated and seven-correlated operators through selected coupled evolutions with unwanted couplings refocused.
- Preparation: f = 0.9824 is obtained when the approximate circuit is applied to the real Hamiltonian.
- Preparation: The circuit is compiled into selective pulses that implement multiple-spin rotations while minimizing excitation of spins outside the targeted frequency region.
- Preparation: The pulse sequence lasts 16.36 ms, is discretized into 818 time slices, and contains 108 nonzero slices, yielding 2 × 108 nonzero pulse parameters.
- Preparation: The oracle's experimental time cost includes initialization, a 16.36 ms circuit, and 1∼2 seconds of detection, while the reset procedure reduces the total cost to 5 hours.