Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems

• URL: http://arxiv.org/abs/2204.07284v2
• Date: Mon, 18 Apr 2022 06:17:54 GMT
• Title: Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems
• Authors: Jin-Min Liang, Shi-Jie Wei, Shao-Ming Fei
• Abstract summary: gradient descent is a key ingredient in variational quantum algorithms and machine learning tasks. We present approaches to simulate the nonequilibrium steady states of Markovian open quantum many-body systems. We adapt the quantum gradient descent algorithm to solve linear algebra problems including linear systems of equations and matrix-vector multiplications.
• Score: 0.17188280334580192
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks, which is an optimization algorithm for finding a local minimum of an objective function. The quantum versions of gradient descent have been investigated and implemented in calculating molecular ground states and optimizing polynomial functions. Based on the quantum gradient descent algorithm and Choi-Jamiolkowski isomorphism, we present approaches to simulate efficiently the nonequilibrium steady states of Markovian open quantum many-body systems. Two strategies are developed to evaluate the expectation values of physical observables on the nonequilibrium steady states. Moreover, we adapt the quantum gradient descent algorithm to solve linear algebra problems including linear systems of equations and matrix-vector multiplications, by converting these algebraic problems into the simulations of closed quantum systems with well-defined Hamiltonians. Detailed examples are given to test numerically the effectiveness of the proposed algorithms for the dissipative quantum transverse Ising models and matrix-vector multiplications.

Related papers

• Hybrid algorithm simulating non-equilibrium steady states of an open quantum system [10.752869788647802]
  Non-equilibrium steady states are a focal point of research in the study of open quantum systems. Previous variational algorithms for searching these steady states have suffered from resource-intensive implementations. We present a novel variational quantum algorithm that efficiently searches for non-equilibrium steady states by simulating the operator-sum form of the Lindblad equation.
  arXiv  Detail & Related papers  (2023-09-13T01:57:27Z)
• GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls [77.34726150561087]
  The GRadient Ascent Pulse Engineering (GRAPE) method is widely used for optimization in quantum control. We adopt GRAPE method for optimizing objective functionals for open quantum systems driven by both coherent and incoherent controls. The efficiency of the algorithm is demonstrated through numerical simulations for the state-to-state transition problem.
  arXiv  Detail & Related papers  (2023-07-17T13:37:18Z)
• Pure Quantum Gradient Descent Algorithm and Full Quantum Variational Eigensolver [0.7149735232319818]
  gradient-based gradient descent algorithm is a widely adopted optimization method. We propose a novel quantum-based gradient calculation method that requires only a single oracle calculation. We successfully implemented the quantum gradient descent algorithm and applied it to the Variational Quantum Eigensolver (VQE)
  arXiv  Detail & Related papers  (2023-05-07T05:52:41Z)
• A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules [62.997667081978825]
  We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix. We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
  arXiv  Detail & Related papers  (2023-04-12T18:10:47Z)
• Implicit differentiation of variational quantum algorithms [0.8594140167290096]
  We show how to leverage implicit differentiation for computation through variational quantum algorithms. We explore applications in condensed matter physics, quantum machine learning, and quantum information.
  arXiv  Detail & Related papers  (2022-11-24T19:00:19Z)
• Quadratic Unconstrained Binary Optimisation via Quantum-Inspired Annealing [58.720142291102135]
  We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. We benchmark our approach for large scale problem instances with tuneable hardness and planted solutions.
  arXiv  Detail & Related papers  (2021-08-18T09:26:17Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Variational Quantum Linear Solver with Dynamic Ansatz [0.0]
  Variational quantum algorithms have found success in the NISQ era owing to their hybrid quantum-classical approach. We introduce the dynamic ansatz in the Variational Quantum Linear Solver for a system of linear algebraic equations. We demonstrate the algorithm advantage in comparison to the standard, static ansatz by utilizing fewer quantum resources.
  arXiv  Detail & Related papers  (2021-07-19T03:42:25Z)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• An efficient adaptive variational quantum solver of the Schrodinger equation based on reduced density matrices [8.24048506727803]
  We present an efficient adaptive variational quantum solver of the Schrodinger equation based on ADAPT-VQE. This new algorithm is quite suitable for quantum simulations of chemical systems on near-term noisy intermediate-scale hardware.
  arXiv  Detail & Related papers  (2020-12-13T12:22:41Z)
• Quantum-Inspired Algorithms from Randomized Numerical Linear Algebra [53.46106569419296]
  We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression. We argue that the previous quantum-inspired algorithms for these problems are doing leverage or ridge-leverage score sampling in disguise.
  arXiv  Detail & Related papers  (2020-11-09T01:13:07Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.