Quantum Optimal Control via Semi-Automatic Differentiation
arXiv:2205.15044 · doi:10.22331/q-2022-12-07-871
Abstract
We develop a framework of "semi-automatic differentiation" that combines existing gradient-based methods of quantum optimal control with automatic differentiation. The approach allows to optimize practically any computable functional and is implemented in two open source Julia packages, GRAPE.jl and Krotov.jl, part of the QuantumControl.jl framework. Our method is based on formally rewriting the optimization functional in terms of propagated states, overlaps with target states, or quantum gates. An analytical application of the chain rule then allows to separate the time propagation and the evaluation of the functional when calculating the gradient. The former can be evaluated with great efficiency via a modified GRAPE scheme. The latter is evaluated with automatic differentiation, but with a profoundly reduced complexity compared to the time propagation. Thus, our approach eliminates the prohibitive memory and runtime overhead normally associated with automatic differentiation and facilitates further advancement in quantum control by enabling the direct optimization of non-analytic functionals for quantum information and quantum metrology, especially in open quantum systems. We illustrate and benchmark the use of semi-automatic differentiation for the optimization of perfectly entangling quantum gates on superconducting qubits coupled via a shared transmission line. This includes the first direct optimization of the non-analytic gate concurrence.
arXiv comment30 pages, 2 figures, 2 tables. Accepted in Quantum
References in corpus (59)
- SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
- Quantum sensing
- Charge insensitive qubit design derived from the Cooper pair box
- Quantum Simulation
- QuTiP 2: A Python framework for the dynamics of open quantum systems
- Circuit Quantum Electrodynamics
- Superconducting Qubits: Current State of Play
- Control of quantum phenomena: Past, present, and future
- Entanglement, Non-linear Dynamics, and the Heisenberg Limit
- Quantum spin squeezing
- Quantum information processing with circuit quantum electrodynamics
- Vibrations, Quanta and Biology
- Optimal Creation of Entanglement Using a Two--Qubit Gate
- Optimal control technique for Many Body Quantum Systems dynamics
- A geometric theory of non-local two-qubit operations
- Chopped random-basis quantum optimization
- Nonlocal properties of two-qubit gates and mixed states and optimization of quantum computations
- A Review of automatic differentiation and its efficient implementation
- Optimal control theory for unitary transformations
- Second order gradient ascent pulse engineering
- Controlling open quantum systems: Tools, achievements, and limitations
- Comparing, Optimising and Benchmarking Quantum Control Algorithms in a Unifying Programming Framework
- Monotonically convergent optimization in quantum control using Krotov's method
- Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control
- Gradient optimization of analytic controls: the route to high accuracy quantum optimal control
- Entanglement of two superconducting qubits in a waveguide cavity via monochromatic two-photon excitation
- Dressing the chopped-random-basis optimization: a bandwidth-limited access to the trap-free landscape
- Speedup for quantum optimal control from automatic differentiation based on graphics processing units
- Quantum metrology with full and fast quantum control
- Quantum control of bosonic modes with superconducting circuits
- Krotov: A Python implementation of Krotov's method for quantum optimal control
- Robustness of high-fidelity Rydberg gates with single-site addressability
- Gradient-based optimal control of open quantum systems using quantum trajectories and automatic differentiation
- Optimal control theory for a unitary operation under dissipative evolution
- Integrated tool-set for Control, Calibration and Characterization of quantum devices applied to superconducting qubits
- Recent Advances in Programmable Photonic-Assisted Ultrabroadband Radio-Frequency Arbitrary Waveform Generation
- Protecting coherence in Optimal Control Theory: State dependent constraint approach
- Charting the circuit QED design landscape using optimal control theory
- Quantum Optimal Control in a Chopped Basis: Applications in Control of Bose-Einstein Condensates
- Modified Newton-Raphson GRAPE methods for optimal control of spin systems
- Auxiliary matrix formalism for interaction representation transformations, optimal control and spin relaxation theories
- Optimizing for an arbitrary perfect entangler: I. Functionals
- Efficient Algorithms for Optimal Control of Quantum Dynamics: The "Krotov'' Method unencumbered
- Quantum optimal control via gradient ascent in function space and the time-bandwidth quantum speed limit
- Universal gates for protected superconducting qubits using optimal control
- Krotov Method for Optimal Control in Closed Quantum Systems
- A differentiable programming method for quantum control
- Optimal dynamical control of many-body entanglement
- Optimizing for an arbitrary perfect entangler. II. Application
- Lower bounds on the complexity of simulating quantum gates
- Metric Structure of the Space of Two-Qubit Gates, Perfect Entanglers and Quantum Control
- A Chebychev propagator for inhomogeneous Schrödinger equations
- Optimal Control for Quantum Metrology via Pontryagin's principle
- Entanglement Storage Units
- Control of Stochastic Quantum Dynamics by Differentiable Programming
- Efficient optimization of state preparation in quantum networks using quantum trajectories
- Principles of tractor atom interferometry
- Tractor Atom Interferometry
- Reducing Memory Requirements of Quantum Optimal Control
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- Optimal entanglement generation in optomechanical systems via Krotov control of covariance matrix dynamics
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- Quantum superpositions of current states in Rydberg-atom networks
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- Comparing planar quantum computing platforms at the quantum speed limit
- Extractable energy from quantum superposition of current states
- Exponentiation of Parametric Hamiltonians via Unitary interpolation
- Monte Carlo approach for finding optimally controlled quantum gates with differential geometry
- Quantum Zeno Dynamics of Two Interacting Particles
- High-Order Hermite Optimization: Fast and Exact Gradient Computation in Open-Loop Quantum Optimal Control using a Discrete Adjoint Approach
- Dipolar optimal control of entangled current states
- GRAPE.jl: Gradient Ascent Pulse Engineering in Julia
- Optimal transfer of entanglement in oscillator chains in non-Markovian open systems