Automated detection of symmetry-protected subspaces in quantum simulations

• URL: http://arxiv.org/abs/2302.08586v3
• Date: Mon, 27 Mar 2023 21:17:02 GMT
• Title: Automated detection of symmetry-protected subspaces in quantum simulations
• Authors: Caleb Rotello, Eric B. Jones, Peter Graf, Eliot Kapit
• Abstract summary: We introduce two classical algorithms, which efficiently compute and elucidate features of symmetry-protected subspaces. These algorithms lend themselves to the post-selection of quantum computer data, optimized classical simulation of quantum systems, and the discovery of previously hidden symmetries in quantum mechanical systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The analysis of symmetry in quantum systems is of utmost theoretical importance, useful in a variety of applications and experimental settings, and is difficult to accomplish in general. Symmetries imply conservation laws, which partition Hilbert space into invariant subspaces of the time-evolution operator, each of which is demarcated according to its conserved quantity. We show that, starting from a chosen basis, any invariant, symmetry-protected subspaces which are diagonal in that basis are discoverable using transitive closure on graphs representing state-to-state transitions under $k$-local unitary operations. Importantly, the discovery of these subspaces relies neither upon the explicit identification of a symmetry operator or its eigenvalues nor upon the construction of matrices of the full Hilbert space dimension. We introduce two classical algorithms, which efficiently compute and elucidate features of these subspaces. The first algorithm explores the entire symmetry-protected subspace of an initial state in time complexity linear to the size of the subspace by closing local basis state-to-basis state transitions. The second algorithm determines, with bounded error, if a given measurement outcome of a dynamically-generated state is within the symmetry-protected subspace of the state in which the dynamical system is initialized. We demonstrate the applicability of these algorithms by performing post-selection on data generated from emulated noisy quantum simulations of three different dynamical systems: the Heisenberg-XXX model and the $T_6$ and $F_4$ quantum cellular automata. Due to their efficient computability and indifference to identifying the underlying symmetry, these algorithms lend themselves to the post-selection of quantum computer data, optimized classical simulation of quantum systems, and the discovery of previously hidden symmetries in quantum mechanical systems.

Related papers

• The signaling dimension of two-dimensional and polytopic systems [2.4554686192257424]
  The signaling dimension of any given physical system represents its classical simulation cost. We propose a branch and bound division-free algorithm for the exact computation of the symmetries of any given polytope. We apply our algorithm to compute the exact value of the signaling dimension for all rational Platonic, Archimedean, and Catalan solids.
  arXiv  Detail & Related papers  (2024-07-25T02:54:21Z)
• Solving the homogeneous Bethe-Salpeter equation with a quantum annealer [34.173566188833156]
  The homogeneous Bethe-Salpeter equation (hBSE) was solved for the first time by using a D-Wave quantum annealer. A broad numerical analysis of the proposed algorithms was carried out using both the proprietary simulated-anneaing package and the D-Wave Advantage 4.1 system.
  arXiv  Detail & Related papers  (2024-06-26T18:12:53Z)
• Variational quantum simulation using non-Gaussian continuous-variable systems [39.58317527488534]
  We present a continuous-variable variational quantum eigensolver compatible with state-of-the-art photonic technology. The framework we introduce allows us to compare discrete and continuous variable systems without introducing a truncation of the Hilbert space.
  arXiv  Detail & Related papers  (2023-10-24T15:20:07Z)
• Dilation theorem via Schr\"odingerisation, with applications to the quantum simulation of differential equations [29.171574903651283]
  Nagy's unitary dilation theorem in operator theory asserts the possibility of dilating a contraction into a unitary operator. In this study, we demonstrate the viability of the recently devised Schr"odingerisation approach.
  arXiv  Detail & Related papers  (2023-09-28T08:55:43Z)
• 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)
• Quantum Mechanics for Closure of Dynamical Systems [0.6445605125467572]
  We propose a scheme for data-driven parameterization of unresolved dimensions of dynamical systems. Given a system in which some components of the state are unknown, this method involves defining a surrogate system. We analyze the results of two different modalities of this methodology applied to the Lorenz 63 and Lorenz 96 multiscale systems.
  arXiv  Detail & Related papers  (2022-08-05T21:18:44Z)
• Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
  We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity. For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
  arXiv  Detail & Related papers  (2021-12-22T15:27:30Z)
• Experimental characterization of quantum processes: a selective and efficient method in arbitrary finite dimension [0.0]
  We show how to implement an algorithm to selectively and efficiently estimate any parameter characterizing a quantum process in a non-prime power dimension. We conducted for the first time an experimental verification of the algorithm in a Hilbert space of dimension $d=6$.
  arXiv  Detail & Related papers  (2020-11-16T19:14:56Z)
• Preparing symmetry broken ground states with variational quantum algorithms [0.559239450391449]
  In solid state physics, finding the correct symmetry broken ground state of an interacting electron system is one of the central challenges. In this work, we discuss three variations of the Variational Hamiltonian Ansatz (VHA) designed to find the correct broken symmetry states. For the calculation we simulate a gate-based quantum computer and also consider the effects of dephasing noise on the algorithms.
  arXiv  Detail & Related papers  (2020-07-03T09:51:02Z)
• Faster Digital Quantum Simulation by Symmetry Protection [0.6554326244334866]
  We show that by introducing quantum gates implementing unitary transformations one can induce destructive interference between the errors from different steps of the simulation. In particular, when the symmetry transformations are chosen as powers of a unitary, the error of the algorithm is approximately projected to the so-called quantum Zeno subspaces. We apply the symmetry protection technique to the simulations of the XXZ Heisenberg interactions with local disorder and the Schwinger model in quantum field theory.
  arXiv  Detail & Related papers  (2020-06-29T18:00:00Z)
• 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.