Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA Hybrid Quantum-Classical Hamiltonian Learning Algorithm
67
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Hamiltonian learning is crucial to the certification of quantum devices and quantum simulators. In this paper, we propose a hybrid quantum-classical Hamiltonian learning algorithm to find the coefficients of the Pauli operator components of the Hamiltonian. Its main subroutine is the practical log-partition function estimation algorithm, which is based on the minimization of the free energy of the system. Concretely, we devise a stochastic variational quantum eigensolver (SVQE) to diagonalize the Hamiltonians and then exploit the obtained eigenvalues to compute the free energys global minimum using convex optimization. Our approach not only avoids the challenge of estimating von Neumann entropy in free energy minimization, but also reduces the quantum resources via importance sampling in Hamiltonian diagonalization, facilitating the implementation of our method on near-term quantum devices. Finally, we demonstrate our approachs validity by conducting numerical experiments with Hamiltonians of interest in quantum many-body physics.
rate research
Read More
General statistical ensembles in the Hamiltonian formulation of hybrid quantum-classical systems are analyzed. It is argued that arbitrary probability densities on the hybrid phase space must be considered as the class of possible physically distinguishable statistical ensembles of hybrid systems. Nevertheless, statistical operators associated with the hybrid system and with the quantum subsystem can be consistently defined. Dynamical equations for the statistical operators representing the mixed states of the hybrid system and its quantum subsystem are derived and analyzed. In particular, these equations irreducibly depend on the total probability density on the hybrid phase space.
Variational quantum eigensolver~(VQE) typically optimizes variational parameters in a quantum circuit to prepare eigenstates for a quantum system. Its applications to many problems may involve a group of Hamiltonians, e.g., Hamiltonian of a molecule is a function of nuclear configurations. In this paper, we incorporate derivatives of Hamiltonian into VQE and develop some hybrid quantum-classical algorithms, which explores both Hamiltonian and wavefunction spaces for optimization. Aiming for solving quantum chemistry problems more efficiently, we first propose mutual gradient descent algorithm for geometry optimization by updating parameters of Hamiltonian and wavefunction alternatively, which shows a rapid convergence towards equilibrium structures of molecules. We then establish differential equations that governs how optimized variational parameters of wavefunction change with intrinsic parameters of the Hamiltonian, which can speed up calculation of energy potential surface. Our studies suggest a direction of hybrid quantum-classical algorithm for solving quantum systems more efficiently by considering spaces of both Hamiltonian and wavefunction.
Deep neural network powered artificial intelligence has rapidly changed our daily life with various applications. However, as one of the essential steps of deep neural networks, training a heavily weighted network requires a tremendous amount of computing resources. Especially in the post-Moores Law era, the limit of semiconductor fabrication technology has restricted the development of learning algorithms to cope with the increasing high-intensity training data. Meanwhile, quantum computing has demonstrated its significant potential in terms of speeding up the traditionally compute-intensive workloads. For example, Google illustrated quantum supremacy by completing a sampling calculation task in 200 seconds, which is otherwise impracticable on the worlds largest supercomputers. To this end, quantum-based learning has become an area of interest, with the potential of a quantum speedup. In this paper, we propose GenQu, a hybrid and general-purpose quantum framework for learning classical data through quantum states. We evaluate GenQu with real datasets and conduct experiments on both simulations and real quantum computer IBM-Q. Our evaluation demonstrates that, compared with classical solutions, the proposed models running on GenQu framework achieve similar accuracy with a much smaller number of qubits, while significantly reducing the parameter size by up to 95.86% and converging speedup by 33.33% faster.
Despite the successes of recent works in quantum reinforcement learning, there are still severe limitations on its applications due to the challenge of encoding large observation spaces into quantum systems. To address this challenge, we propose using a neural network as a data encoder, with the Atari games as our testbed. Specifically, the neural network converts the pixel input from the games to quantum data for a Quantum Variational Circuit (QVC); this hybrid model is then used as a function approximator in the Double Deep Q Networks algorithm. We explore a number of variations of this algorithm and find that our proposed hybrid models do not achieve meaningful results on two Atari games - Breakout and Pong. We suspect this is due to the significantly reduced sizes of the hybrid quantum-classical systems.
The Klein-Kramers equation, governing the Brownian motion of a classical particle in quantum environment under the action of an arbitrary external potential, is derived. Quantum temperature and friction operators are introduced and at large friction the corresponding Smoluchowski equation is obtained. Introducing the Bohm quantum potential, this Smoluchowski equation is extended to describe the Brownian motion of a quantum particle in quantum environment.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
