Restoring broken symmetries using oracles
- URL: http://arxiv.org/abs/2210.11181v1
- Date: Thu, 20 Oct 2022 11:54:31 GMT
- Title: Restoring broken symmetries using oracles
- Authors: Edgar Andres Ruiz Guzman and Denis Lacroix
- Abstract summary: We show how to construct the oracle and the projector associated with a symmetry operator.
The procedure is illustrated for the parity, particle number, and total spin symmetries.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We present a new method to perform variation after projection in many-body
systems on quantum computers that does not require performing explicit
projection. The technique employs the notion of ``oracle'', generally used in
quantum search algorithms. We show how to construct the oracle and the
projector associated with a symmetry operator. The procedure is illustrated for
the parity, particle number, and total spin symmetries. The oracle is used to
restore symmetry by indirect measurements using a single ancillary qubit. An
Illustration of the technique is made to obtain the approximate ground state
energy for the pairing model Hamiltonian.
Related papers
- Quantum Algorithms for Realizing Symmetric, Asymmetric, and Antisymmetric Projectors [3.481985817302898]
Knowing the symmetries of a given system or state obeys or disobeys is often useful in quantum computing.
We present a collection of quantum algorithms that realize projections onto the symmetric subspace.
We show how projectors can be combined in a systematic way to effectively measure various projections in a single quantum circuit.
arXiv Detail & Related papers (2024-07-24T18:00:07Z) - Restoring symmetries in quantum computing using Classical Shadows [0.0]
We introduce a method to enforce some symmetries starting from a trial wave-function prepared on quantum computers that might not respect these symmetries.
We show that the present scheme can be competitive to predict observables on symmetry-restored states once optimization through derandomization is employed.
arXiv Detail & Related papers (2023-11-08T10:11:01Z) - Identifying the Group-Theoretic Structure of Machine-Learned Symmetries [41.56233403862961]
We propose methods for examining and identifying the group-theoretic structure of such machine-learned symmetries.
As an application to particle physics, we demonstrate the identification of the residual symmetries after the spontaneous breaking of non-Abelian gauge symmetries.
arXiv Detail & Related papers (2023-09-14T17:03:50Z) - Third quantization of open quantum systems: new dissipative symmetries
and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
We reformulate the technique of third quantization in a way that explicitly connects all three methods.
We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians.
For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
arXiv Detail & Related papers (2023-02-27T18:56:40Z) - Oracle-Preserving Latent Flows [58.720142291102135]
We develop a methodology for the simultaneous discovery of multiple nontrivial continuous symmetries across an entire labelled dataset.
The symmetry transformations and the corresponding generators are modeled with fully connected neural networks trained with a specially constructed loss function.
The two new elements in this work are the use of a reduced-dimensionality latent space and the generalization to transformations invariant with respect to high-dimensional oracles.
arXiv Detail & Related papers (2023-02-02T00:13:32Z) - Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras
from First Principles [55.41644538483948]
We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset.
We use fully connected neural networks to model the transformations symmetry and the corresponding generators.
Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.
arXiv Detail & Related papers (2023-01-13T16:25:25Z) - Learning quantum symmetries with interactive quantum-classical
variational algorithms [0.0]
A symmetry of a state $vert psi rangle$ is a unitary operator of which $vert psi rangle$ is an eigenvector.
symmetries provide key physical insight into the quantum system.
We develop a variational hybrid quantum-classical learning scheme to systematically probe for symmetries of $vert psi rangle$.
arXiv Detail & Related papers (2022-06-23T20:41:26Z) - Finite resolution ancilla-assisted measurements of quantum work
distributions [77.34726150561087]
We consider an ancilla-assisted protocol measuring the work done on a quantum system driven by a time-dependent Hamiltonian.
We consider system Hamiltonians which both commute and do not commute at different times, finding corrections to fluctuation relations like the Jarzynski equality and the Crooks relation.
arXiv Detail & Related papers (2021-11-30T15:08:25Z) - 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) - Symmetry assisted preparation of entangled many-body states on a quantum
computer [0.0]
A method is proposed to construct entangled states that describe correlated many-body systems on quantum computers.
Using operators for which the discrete set of eigenvalues is known, the QPE approach is followed by measurements that serve as projectors on the entangled states.
These states can then be used as inputs for further quantum or hybrid quantum-classical processing.
arXiv Detail & Related papers (2020-06-11T14:59:22Z)
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.