A resource-efficient quantum-classical hybrid algorithm for energy gap
evaluation
- URL: http://arxiv.org/abs/2305.07382v2
- Date: Fri, 19 May 2023 07:35:28 GMT
- Title: A resource-efficient quantum-classical hybrid algorithm for energy gap
evaluation
- Authors: Yongdan Yang, Ying Li, Xiaosi Xu, Xiao Yuan
- Abstract summary: Estimating the eigenvalue or energy gap of a Hamiltonian H is vital for studying quantum many-body systems.
We propose a hybrid non-variational quantum algorithm that uses the Monte Carlo method and real-time Hamiltonian simulation.
- Score: 4.925443385819888
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Estimating the eigenvalue or energy gap of a Hamiltonian H is vital for
studying quantum many-body systems. Particularly, many of the problems in
quantum chemistry, condensed matter physics, and nuclear physics investigate
the energy gap between two eigenstates. Hence, how to efficiently solve the
energy gap becomes an important motive for researching new quantum algorithms.
In this work, we propose a hybrid non-variational quantum algorithm that uses
the Monte Carlo method and real-time Hamiltonian simulation to evaluate the
energy gap of a general quantum many-body system. Compared to conventional
approaches, our algorithm does not require controlled real-time evolution, thus
making its implementation much more experimental-friendly. Since our algorithm
is non-variational, it is also free from the "barren plateaus" problem. To
verify the efficiency of our algorithm, we conduct numerical simulations for
the Heisenberg model and molecule systems on a classical emulator.
Related papers
- Hybrid Quantum-Classical Clustering for Preparing a Prior Distribution of Eigenspectrum [10.950807972899575]
We consider preparing the prior distribution and circuits for the eigenspectrum of time-independent Hamiltonians.
The proposed algorithm unfolds in three strategic steps: Hamiltonian transformation, parameter representation, and classical clustering.
The algorithm is showcased through applications to the 1D Heisenberg system and the LiH molecular system.
arXiv Detail & Related papers (2024-06-29T14:21:55Z) - Ground state energy and magnetization curve of a frustrated magnetic
system from real-time evolution on a digital quantum processor [0.47191037525744733]
We show how to construct efficient quantum circuits to implement time evolution for the Heisenberg model.
We also give an empirical demonstration on small systems that the hybrid algorithms can efficiently find the ground state energy and the magnetization curve.
arXiv Detail & Related papers (2024-01-05T18:57:34Z) - 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) - Quantum Thermal State Preparation [39.91303506884272]
We introduce simple continuous-time quantum Gibbs samplers for simulating quantum master equations.
We construct the first provably accurate and efficient algorithm for preparing certain purified Gibbs states.
Our algorithms' costs have a provable dependence on temperature, accuracy, and the mixing time.
arXiv Detail & Related papers (2023-03-31T17:29:56Z) - Perturbation theory with quantum signal processing [0.0]
We provide a quantum algorithm to obtain perturbative energies on quantum computers.
The proposed algorithm uses quantum signal processing (QSP) to achieve this goal.
This work is a first step towards explainable'' quantum simulation on fault-tolerant quantum computers.
arXiv Detail & Related papers (2022-10-03T05:20:26Z) - A full circuit-based quantum algorithm for excited-states in quantum
chemistry [6.973166066636441]
We propose a non-variational full circuit-based quantum algorithm for obtaining the excited-state spectrum of a quantum chemistry Hamiltonian.
Compared with previous classical-quantum hybrid variational algorithms, our method eliminates the classical optimization process.
The algorithm can be widely applied to various Hamiltonian spectrum determination problems on the fault-tolerant quantum computers.
arXiv Detail & Related papers (2021-12-28T15:48:09Z) - 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) - Quantum-Classical Hybrid Algorithm for the Simulation of All-Electron
Correlation [58.720142291102135]
We present a novel hybrid-classical algorithm that computes a molecule's all-electron energy and properties on the classical computer.
We demonstrate the ability of the quantum-classical hybrid algorithms to achieve chemically relevant results and accuracy on currently available quantum computers.
arXiv Detail & Related papers (2021-06-22T18:00:00Z) - 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) - A Hybrid Quantum-Classical Hamiltonian Learning Algorithm [6.90132007891849]
Hamiltonian learning is crucial to the certification of quantum devices and quantum simulators.
We propose a hybrid quantum-classical Hamiltonian learning algorithm to find the coefficients of the Pauli operator of the Hamiltonian.
arXiv Detail & Related papers (2021-03-01T15:15:58Z) - Imaginary Time Propagation on a Quantum Chip [50.591267188664666]
Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems.
We propose an algorithm to implement imaginary time propagation on a quantum computer.
arXiv Detail & Related papers (2021-02-24T12:48:00Z)
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.