Measurement-based quantum simulation of Abelian lattice gauge theories
- URL: http://arxiv.org/abs/2210.10908v1
- Date: Wed, 19 Oct 2022 22:14:45 GMT
- Title: Measurement-based quantum simulation of Abelian lattice gauge theories
- Authors: Hiroki Sukeno and Takuya Okuda
- Abstract summary: We show that sequential single-qubit measurements with the bases adapted according to the former measurement outcomes induce a deterministic Hamiltonian quantum simulation of the gauge theory on the boundary.
We demonstrate that the generalized cluster state has a symmetry-protected topological order with respect to generalized global symmetries.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Numerical simulation of lattice gauge theories is an indispensable tool in
high energy physics, and their quantum simulation is expected to become a major
application of quantum computers in the future. In this work, for an Abelian
lattice gauge theory in $d$ spacetime dimensions, we define an entangled
resource state (generalized cluster state) that reflects the spacetime
structure of the gauge theory. We show that sequential single-qubit
measurements with the bases adapted according to the former measurement
outcomes induce a deterministic Hamiltonian quantum simulation of the gauge
theory on the boundary. Our construction includes the $(2+1)$-dimensional
Abelian lattice gauge theory simulated on three-dimensional cluster state as an
example, and generalizes to the simulation of Wegner's lattice models
$M_{(d,n)}$ that involve higher-form Abelian gauge fields. We demonstrate that
the generalized cluster state has a symmetry-protected topological order with
respect to generalized global symmetries that are related to the symmetries of
the simulated gauge theories on the boundary. Our procedure can be generalized
to the simulation of Kitaev's Majorana chain on a fermionic resource state. We
also study the imaginary-time quantum simulation with two-qubit measurements
and post-selections, and a classical-quantum correspondence, where the
statistical partition function of the model $M_{(d,n)}$ is written as the
overlap between the product of two-qubit measurement bases and the wave
function of the generalized cluster state.
Related papers
- Anomaly inflow, dualities, and quantum simulation of abelian lattice gauge theories induced by measurements [0.0]
Previous work has demonstrated that quantum simulation of abelian lattice gauge theories can be achieved by local adaptive measurements.
In this work, we explicitly demonstrate the anomaly inflow mechanism between the deconfining phase of the simulated gauge theory on the boundary and the SPT state in the bulk.
We construct the resource state and the measurement pattern for the measurement-based quantum simulation of a lattice gauge theory with a matter field.
arXiv Detail & Related papers (2024-02-13T19:00:04Z) - Gaussian Entanglement Measure: Applications to Multipartite Entanglement
of Graph States and Bosonic Field Theory [50.24983453990065]
An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers.
We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states.
By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
arXiv Detail & Related papers (2024-01-31T15:50:50Z) - A new basis for Hamiltonian SU(2) simulations [0.0]
We develop a new basis suitable for the simulation of an SU(2) lattice gauge theory in the maximal tree gauge.
We show how to perform a Hamiltonian truncation so that the eigenvalues of both the magnetic and electric gauge-fixed Hamiltonian are mostly preserved.
arXiv Detail & Related papers (2023-07-21T18:03:26Z) - Normalizing flows for lattice gauge theory in arbitrary space-time
dimension [135.04925500053622]
Applications of normalizing flows to the sampling of field configurations in lattice gauge theory have so far been explored almost exclusively in two space-time dimensions.
We discuss masked autoregressive with tractable and unbiased Jacobian determinants, a key ingredient for scalable and exact flow-based sampling algorithms.
For concreteness, results from a proof-of-principle application to SU(3) gauge theory in four space-time dimensions are reported.
arXiv Detail & Related papers (2023-05-03T19:54:04Z) - General quantum algorithms for Hamiltonian simulation with applications
to a non-Abelian lattice gauge theory [44.99833362998488]
We introduce quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple quantum numbers.
The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions.
The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories.
arXiv Detail & Related papers (2022-12-28T18:56:25Z) - Electric-magnetic duality and $\mathbb{Z}_2$ symmetry enriched Abelian lattice gauge theory [2.206623168926072]
Kitaev's quantum double model is a lattice gauge theoretic realization of Dijkgraaf-Witten topological quantum field theory (TQFT)
Topologically protected ground state space has broad applications for topological quantum computation and topological quantum memory.
arXiv Detail & Related papers (2022-01-28T14:13:38Z) - Boundary theories of critical matchgate tensor networks [59.433172590351234]
Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices.
For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states.
We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model.
arXiv Detail & Related papers (2021-10-06T18:00:03Z) - Quantum simulation of gauge theory via orbifold lattice [47.28069960496992]
We propose a new framework for simulating $textU(k)$ Yang-Mills theory on a universal quantum computer.
We discuss the application of our constructions to computing static properties and real-time dynamics of Yang-Mills theories.
arXiv Detail & Related papers (2020-11-12T18:49:11Z) - Cold Atom Quantum Simulator for String and Hadron Dynamics in
Non-Abelian Lattice Gauge Theory [0.0]
Scheme calls for the realization of a two-state ultracold fermionic system in a 1-dimensional bipartite lattice.
Being based on novel loop string hadron formalism of SU(2) lattice gauge theory, this simulation technique is completely SU(2) invariant.
arXiv Detail & Related papers (2020-09-29T12:39:14Z) - State preparation and measurement in a quantum simulation of the O(3)
sigma model [65.01359242860215]
We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site.
We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes.
We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
arXiv Detail & Related papers (2020-06-28T23:44:12Z)
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.