QGOpt: Riemannian optimization for quantum technologies

Abstract

Many theoretical problems in quantum technology can be formulated and addressed as constrained optimization problems. The most common quantum mechanical constraints such as, e.g., orthogonality of isometric and unitary matrices, CPTP property of quantum channels, and conditions on density matrices, can be seen as quotient or embedded Riemannian manifolds. This allows to use Riemannian optimization techniques for solving quantum-mechanical constrained optimization problems. In the present work, we introduce QGOpt, the library for constrained optimization in quantum technology. QGOpt relies on the underlying Riemannian structure of quantum-mechanical constraints and permits application of standard gradient based optimization methods while preserving quantum mechanical constraints. Moreover, QGOpt is written on top of TensorFlow, which enables automatic differentiation to calculate necessary gradients for optimization. We show two application examples: quantum gate decomposition and quantum tomography.

28 pages, 7 figures, 4 tables, a note on relevant research is added

References in corpus (9)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• The iTEBD algorithm beyond unitary evolution
• Quantum Process Tomography: Resource Analysis of Different Strategies
• Tensor Networks in a Nutshell
• Riemannian optimization of isometric tensor networks
• Control landscapes for two-level open quantum systems
• Optimization search effort over the control landscapes for open quantum systems with Kraus-map evolution
• Variational autoencoder reconstruction of complex many-body physics

Cited by in corpus (20)

• TensorCircuit: a Quantum Software Framework for the NISQ Era
• Riemannian geometry and automatic differentiation for optimization problems of quantum physics and quantum technologies
• Scaling of neural-network quantum states for time evolution
• Tensor networks for quantum computing
• Multipartite correlations in quantum collision models
• Robustly learning the Hamiltonian dynamics of a superconducting quantum processor
• Efficient MPS representations and quantum circuits from the Fourier modes of classical image data
• Efficient Quantum Circuit Compilation for Near-Term Quantum Advantage
• Gradient-descent methods for fast quantum state tomography
• Finite-depth scaling of infinite quantum circuits for quantum critical points
• Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
• Exploring postselection-induced quantum phenomena with time-bidirectional state formalism
• Riemannian quantum circuit optimization based on matrix product operators
• Efficient Quantum Circuits based on the Quantum Natural Gradient
• Controlling quantum many-body systems using reduced-order modelling
• Two Dimensional Isometric Tensor Networks on an Infinite Strip
• Automatic Structural Search of Tensor Network States including Entanglement Renormalization
• Simulating quantum circuits using the multi-scale entanglement renormalization ansatz
• Continuous monitoring for noisy intermediate-scale quantum processors
• A Riemannian Approach to the Lindbladian Dynamics of a Locally Purified Tensor Network