Unitary-coupled restricted Boltzmann machine ansatz for quantum simulations

Abstract

Neural-network quantum state (NQS) has attracted significant interests as a powerful wave-function ansatz to model quantum phenomena. In particular, a variant of NQS based on the restricted Boltzmann machine (RBM) has been adapted to model the ground state of spin lattices and the electronic structures of small molecules in quantum devices. Despite these progresses, significant challenges remain with the RBM-NQS-based quantum simulations. In this work, we present a state-preparation protocol to generate a specific set of complex-valued RBM-NQS, which we name the unitary-coupled RBM-NQS, in quantum circuits. Our proposal expands the applicability of NQS as prior works deal exclusively with real-valued RBM-NQS for quantum algorithms. With this scheme, we achieve (1) modeling complex-valued wave functions, (2) using as few as one ancilla qubit to simulate M hidden spins in an RBM architecture, and (3) avoiding post-selections to improve scalability.

Simulation of Condensed-Phase Spectroscopy with Near-term Digital Quantum Computer

“…In recent years there have been a large number of works developing NISQ algorithms to compute the ground or low-energy states of static and isolated quantum systems. [41][42][43][44][45][46][47][48][49] However, chemical systems are typically immersed in condensed phases and many phenomena like chemical reactions and spectroscopy are heavily influenced by the interactions with these condensed-phase environments. Computational modelling of these phenomena is challenging as it requires simulating the time evolution of quantum dynamics, a computational task that is far more difficult than the ground state simulation as quantum dynamics typically involve the participation of many eigenstates.…”

Variational Quantum Simulation of Chemical Dynamics with Quantum Computers

“…Additionally, a large body of works have been developed to find the ground or low-energy excited states of a Hamiltonian [14], these methods can be easily adopted into our subspace approach. Furthermore the quality of the ground or excited state computation can generally be systematically improved by increasing the circuit depth in the ansatz or via the use of extra ancillary qubits [52].…”

Neural Predictor based Quantum Architecture Search

“…Various VQA have been designed for problems in a vast array of fields. Some typical examples include determining the ground and low excited states of a quantum Hamiltonian [4,[6][7][8][94][95][96][97], simulating quantum dynamics [98][99][100][101][102][103][104][105][106][107], preparing Gibbs thermal states [108][109][110], supervised and unsupervised machine learning [15][16][17][18][19][20][21][22][23][24][25][26][27], compiling quantum circuits [111][112][113], solving classical combinatorial optimizations [10][11][12][13][14], factoring integers [114][115][116], and solving linear or differential equations [117][118]…”