Strategies for simulating time evolution of Hamiltonian lattice field theories
- URL: http://arxiv.org/abs/2312.11637v2
- Date: Sat, 8 Jun 2024 19:04:20 GMT
- Title: Strategies for simulating time evolution of Hamiltonian lattice field theories
- Authors: Siddharth Hariprakash, Neel S. Modi, Michael Kreshchuk, Christopher F. Kane, Christian W Bauer,
- Abstract summary: Simulating the time evolution of quantum field theories given some Hamiltonian $H$ requires developing algorithms for implementing the unitary operator e-iHt.
Some techniques exist that promise better scaling in certain parameters of the theory being simulated, the most efficient of which are based on the concept of block encoding.
We derive and compare the gate complexities of several commonly used simulation techniques in application to Hamiltonian Lattice Field Theories.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Simulating the time evolution of quantum field theories given some Hamiltonian $H$ requires developing algorithms for implementing the unitary operator e^{-iHt}. A variety of techniques exist that accomplish this task, with the most common technique used so far being Trotterization, which is a special case of the application of a product formula. However, other techniques exist that promise better asymptotic scaling in certain parameters of the theory being simulated, the most efficient of which are based on the concept of block encoding. In this work we study the performance of such algorithms in simulating lattice field theories. We derive and compare the asymptotic gate complexities of several commonly used simulation techniques in application to Hamiltonian Lattice Field Theories. Using the scalar \phi^4 theory as a test, we also perform numerical studies and compare the gate costs required by Product Formulas and Signal Processing based techniques to simulate time evolution. For the latter, we use the the Linear Combination of Unitaries construction augmented with the Quantum Fourier Transform circuit to switch between the field and momentum eigenbases, which leads to immediate order-of-magnitude improvement in the cost of preparing the block encoding. The paper also includes a pedagogical review of utilized techniques, in particular Product Formulas, LCU, Qubitization, QSP, as well as a technique we call HHKL based on its inventors' names.
Related papers
- Efficient and practical Hamiltonian simulation from time-dependent product formulas [1.2534672170380357]
We propose an approach for implementing time-evolution of a quantum system using product formulas.
Our algorithms generate a decomposition of the evolution operator into a product of simple unitaries that are directly implementable on a quantum computer.
Although the theoretical scaling is suboptimal compared with state-of-the-art algorithms, the performance of the algorithms we propose is highly competitive in practice.
arXiv Detail & Related papers (2024-03-13T17:29:05Z) - Nearly-optimal state preparation for quantum simulations of lattice
gauge theories [0.0]
We present several improvements to the recently developed ground state preparation algorithm based on the Quantum Eigenvalue Transformation for Unitary Matrices (QETU)
We use QETU to prepare the ground state of a U(1) lattice gauge theory in 2 spatial dimensions.
We also propose a novel application of QETU, a highly efficient preparation of Gaussian distributions.
arXiv Detail & Related papers (2023-10-20T18:35:06Z) - Hamiltonian Encoding for Quantum Approximate Time Evolution of Kinetic
Energy Operator [2.184775414778289]
The time evolution operator plays a crucial role in the precise computation of chemical experiments on quantum computers.
We have proposed a new encoding method, namely quantum approximate time evolution (QATE) for the quantum implementation of the kinetic energy operator.
arXiv Detail & Related papers (2023-10-05T05:25:38Z) - GloptiNets: Scalable Non-Convex Optimization with Certificates [61.50835040805378]
We present a novel approach to non-cube optimization with certificates, which handles smooth functions on the hypercube or on the torus.
By exploiting the regularity of the target function intrinsic in the decay of its spectrum, we allow at the same time to obtain precise certificates and leverage the advanced and powerful neural networks.
arXiv Detail & Related papers (2023-06-26T09:42:59Z) - Semantic embedding for quantum algorithms [0.0]
A need has developed for an assurance of the correctness of high-level quantum algorithmic reasoning.
Many quantum algorithms have been unified and improved using quantum signal processing (QSP) and quantum singular value transformation (QSVT)
We show that QSP/QSVT can be treated and combined modularly, purely in terms of the functional transforms they embed.
We also identify existing quantum algorithms whose use of semantic embedding is implicit, spanning from distributed search to soundness in quantum cryptography.
arXiv Detail & Related papers (2023-04-27T17:55:40Z) - Riemannian quantum circuit optimization for Hamiltonian simulation [2.1227079314039057]
Hamiltonian simulation is a natural application of quantum computing.
For translation invariant systems, the gates in such circuit topologies can be further optimized on classical computers.
For the Ising and Heisenberg models on a one-dimensional lattice, we achieve orders of magnitude accuracy improvements.
arXiv Detail & Related papers (2022-12-15T00:00:17Z) - Variational Adiabatic Gauge Transformation on real quantum hardware for
effective low-energy Hamiltonians and accurate diagonalization [68.8204255655161]
We introduce the Variational Adiabatic Gauge Transformation (VAGT)
VAGT is a non-perturbative hybrid quantum algorithm that can use nowadays quantum computers to learn the variational parameters of the unitary circuit.
The accuracy of VAGT is tested trough numerical simulations, as well as simulations on Rigetti and IonQ quantum computers.
arXiv Detail & Related papers (2021-11-16T20:50:08Z) - Hybridized Methods for Quantum Simulation in the Interaction Picture [69.02115180674885]
We provide a framework that allows different simulation methods to be hybridized and thereby improve performance for interaction picture simulations.
Physical applications of these hybridized methods yield a gate complexity scaling as $log2 Lambda$ in the electric cutoff.
For the general problem of Hamiltonian simulation subject to dynamical constraints, these methods yield a query complexity independent of the penalty parameter $lambda$ used to impose an energy cost.
arXiv Detail & Related papers (2021-09-07T20:01:22Z) - Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware.
We present an algorithm that compresses the Trotter steps into a single block of quantum gates.
This results in a fixed depth time evolution for certain classes of Hamiltonians.
arXiv Detail & Related papers (2021-08-06T19:38:01Z) - 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) - Simulating nonnative cubic interactions on noisy quantum machines [65.38483184536494]
We show that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware.
On noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates.
arXiv Detail & Related papers (2020-04-15T05:16:24Z)
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.