Quantum Algorithms for Simulating the Lattice Schwinger Model

• URL: http://arxiv.org/abs/2002.11146v3
• Date: Wed, 5 Aug 2020 15:26:11 GMT
• Title: Quantum Algorithms for Simulating the Lattice Schwinger Model
• Authors: Alexander F. Shaw, Pavel Lougovski, Jesse R. Stryker, Nathan Wiebe
• Abstract summary: We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$. We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
• Score: 63.18141027763459
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Schwinger model (quantum electrodynamics in 1+1 dimensions) is a testbed for the study of quantum gauge field theories. We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In particular, we perform a tight analysis of low-order Trotter formula simulations of the Schwinger model, using recently derived commutator bounds, and give upper bounds on the resources needed for simulations in both scenarios. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x^{-1/2}$ and electric field cutoff $x^{-1/2}\Lambda$ can be simulated on a quantum computer for time $2xT$ using a number of $T$-gates or CNOTs in $\widetilde{O}( N^{3/2} T^{3/2} \sqrt{x} \Lambda )$ for fixed operator error. This scaling with the truncation $\Lambda$ is better than that expected from algorithms such as qubitization or QDRIFT. Furthermore, we give scalable measurement schemes and algorithms to estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density. Finally, we bound the root-mean-square error in estimating this observable via simulation as a function of the diamond distance between the ideal and actual CNOT channels. This work provides a rigorous analysis of simulating the Schwinger model, while also providing benchmarks against which subsequent simulation algorithms can be tested.

Related papers

• Slow Mixing of Quantum Gibbs Samplers [47.373245682678515]
  We present a quantum generalization of these tools through a generic bottleneck lemma. This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles. Even with sublinear barriers, we use Feynman-Kac techniques to lift classical to quantum ones establishing tight lower bound $T_mathrmmix = 2Omega(nalpha)$.
  arXiv  Detail & Related papers  (2024-11-06T22:51:27Z)
• Optimized Quantum Simulation Algorithms for Scalar Quantum Field Theories [0.3394351835510634]
  We provide practical simulation methods for scalar field theories on a quantum computer that yield improveds. We implement our approach using a series of different fault-tolerant simulation algorithms for Hamiltonians. We find in both cases that the bounds suggest physically meaningful simulations can be performed using on the order of $4times 106$ physical qubits and $1012$ $T$-gates.
  arXiv  Detail & Related papers  (2024-07-18T18:00:01Z)
• Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks [54.177130905659155]
  Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks. In this paper, we study a suitable function space for over- parameterized two-layer neural networks with bounded norms.
  arXiv  Detail & Related papers  (2024-04-29T15:04:07Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Stochastic Approach For Simulating Quantum Noise Using Tensor Networks [0.8258451067861933]
  We show that our simulation error is relatively low, even for large numbers of qubits. By using the slicing technique, we can simulate up to 100 qubitOA circuits with high depth using supercomputers.
  arXiv  Detail & Related papers  (2022-10-28T03:44:59Z)
• Minimax Optimal Quantization of Linear Models: Information-Theoretic Limits and Efficient Algorithms [59.724977092582535]
  We consider the problem of quantizing a linear model learned from measurements. We derive an information-theoretic lower bound for the minimax risk under this setting. We show that our method and upper-bounds can be extended for two-layer ReLU neural networks.
  arXiv  Detail & Related papers  (2022-02-23T02:39:04Z)
• Inverting brain grey matter models with likelihood-free inference: a tool for trustable cytoarchitecture measurements [62.997667081978825]
  characterisation of the brain grey matter cytoarchitecture with quantitative sensitivity to soma density and volume remains an unsolved challenge in dMRI. We propose a new forward model, specifically a new system of equations, requiring a few relatively sparse b-shells. We then apply modern tools from Bayesian analysis known as likelihood-free inference (LFI) to invert our proposed model.
  arXiv  Detail & Related papers  (2021-11-15T09:08:27Z)
• Provably accurate simulation of gauge theories and bosonic systems [2.406160895492247]
  We develop methods for bounding the rate of growth of local quantum numbers. For the Hubbard-Holstein model, we compute a bound on $Lambda$ that achieves accuracy $epsilon$. We also establish a criterion for truncating the Hamiltonian with a provable guarantee on the accuracy of time evolution.
  arXiv  Detail & Related papers  (2021-10-13T18:00:02Z)
• Simulating Effective QED on Quantum Computers [0.2007262412327553]
  We show that effective quantum electrodynamics, which is equivalent to QED to second order in perturbation theory, can be simulated on a quantum computer in time. We find that the number of $T$-gates needed to perform such simulations on a $3D$ lattice of $n_s$ sites scales at worst as $O(n_s3/epsilon)1+o(1)$ in the thermodynamic limit. We also estimate the planewave cutoffs needed to accurately simulate heavy elements such as gold.
  arXiv  Detail & Related papers  (2020-12-31T23:55:06Z)
• Even more efficient quantum computations of chemistry through tensor hypercontraction [0.6234350105794442]
  We describe quantum circuits with only $widetildecal O(N)$ Toffoli complexity that block encode the spectra of quantum chemistry Hamiltonians in a basis of $N$ arbitrary orbitals. This is the lowest complexity that has been shown for quantum computations of chemistry within an arbitrary basis.
  arXiv  Detail & Related papers  (2020-11-06T18:03:29Z)

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.