10 research outputs found
Variational Quantum Gibbs State Preparation with a Truncated Taylor Series
The preparation of quantum Gibbs state is an essential part of quantum
computation and has wide-ranging applications in various areas, including
quantum simulation, quantum optimization, and quantum machine learning. In this
paper, we propose variational hybrid quantum-classical algorithms for quantum
Gibbs state preparation. We first utilize a truncated Taylor series to evaluate
the free energy and choose the truncated free energy as the loss function. Our
protocol then trains the parameterized quantum circuits to learn the desired
quantum Gibbs state. Notably, this algorithm can be implemented on near-term
quantum computers equipped with parameterized quantum circuits. By performing
numerical experiments, we show that shallow parameterized circuits with only
one additional qubit can be trained to prepare the Ising chain and spin chain
Gibbs states with a fidelity higher than 95%. In particular, for the Ising
chain model, we find that a simplified circuit ansatz with only one parameter
and one additional qubit can be trained to realize a 99% fidelity in Gibbs
state preparation at inverse temperatures larger than 2.Comment: v2 accepted in Phys. Rev. Applie
Simulating Z 2 lattice gauge theory with the variational quantum thermalizer
The properties of strongly-coupled lattice gauge theories at finite density as well as in real time have largely eluded first-principles studies on the lattice. This is due to the failure of importance sampling for systems with a complex action. An alternative to evade the sign problem is quantum simulation. Although still in its infancy, a lot of progress has been made in devising algorithms to address these problems. In particular, recent efforts have addressed the question of how to produce thermal Gibbs states on a quantum computer. In this study, we apply a variational quantum algorithm to a low-dimensional model which has a local abelian gauge symmetry. We demonstrate how this approach can be applied to obtain information regarding the phase diagram as well as unequal-time correlation functions at non-zero temperature
Variational Quantum Singular Value Decomposition
Singular value decomposition is central to many problems in engineering and
scientific fields. Several quantum algorithms have been proposed to determine
the singular values and their associated singular vectors of a given matrix.
Although these algorithms are promising, the required quantum subroutines and
resources are too costly on near-term quantum devices. In this work, we propose
a variational quantum algorithm for singular value decomposition (VQSVD). By
exploiting the variational principles for singular values and the Ky Fan
Theorem, we design a novel loss function such that two quantum neural networks
(or parameterized quantum circuits) could be trained to learn the singular
vectors and output the corresponding singular values. Furthermore, we conduct
numerical simulations of VQSVD for random matrices as well as its applications
in image compression of handwritten digits. Finally, we discuss the
applications of our algorithm in recommendation systems and polar
decomposition. Our work explores new avenues for quantum information processing
beyond the conventional protocols that only works for Hermitian data, and
reveals the capability of matrix decomposition on near-term quantum devices.Comment: 23 pages, v3 accepted by Quantu
Quantum Computation of Finite-Temperature Static and Dynamical Properties of Spin Systems Using Quantum Imaginary Time Evolution
Developing scalable quantum algorithms to study finite-temperature physics of quantum many-body systems has attracted considerable interest due to recent advancements in quantum hardware. However, such algorithms in their present form require resources that exceed the capabilities of current quantum computers except for a limited range of system sizes and observables. Here, we report calculations of finite-temperature properties including energies, static and dynamical correlation functions, and excitation spectra of spin Hamiltonians with up to four sites on five-qubit IBM Quantum devices. These calculations are performed using the quantum imaginary time evolution (QITE) algorithm and made possible by several algorithmic improvements, including a method to exploit symmetries that reduces the quantum resources required by QITE, circuit optimization procedures to reduce circuit depth, and error mitigation techniques to improve the quality of raw hardware data. Our work demonstrates that the ansatz-independent QITE algorithm is capable of computing diverse finite-temperature observables on near-term quantum devices
Quantum Computation of Finite-Temperature Static and Dynamical Properties of Spin Systems Using Quantum Imaginary Time Evolution
Developing scalable quantum algorithms to study finite-temperature physics of quantum many-body systems has attracted considerable interest due to recent advancements in quantum hardware. However, such algorithms in their present form require resources that exceed the capabilities of current quantum computers except for a limited range of system sizes and observables. Here, we report calculations of finite-temperature properties, including energy, static and dynamical correlation functions, and excitation spectra of spin systems with up to four sites on five-qubit IBM Quantum devices. These calculations are performed using the quantum imaginary time evolution (QITE) algorithm and made possible by several algorithmic improvements, including a method to exploit symmetries that reduces the quantum resources required by QITE, circuit optimization procedures to reduce circuit depth, and error-mitigation techniques to improve the quality of raw hardware data. Our work demonstrates that the ansatz-independent QITE algorithm is capable of computing diverse finite-temperature observables on near-term quantum devices