Quantum Algorithms for Realizing Symmetric, Asymmetric, and Antisymmetric Projectors

• URL: http://arxiv.org/abs/2407.17563v1
• Date: Wed, 24 Jul 2024 18:00:07 GMT
• Title: Quantum Algorithms for Realizing Symmetric, Asymmetric, and Antisymmetric Projectors
• Authors: Margarite L. LaBorde, Soorya Rethinasamy, Mark M. Wilde,
• Abstract summary: 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.
• Score: 3.481985817302898
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning applications, and certain asymmetric quantum states are known to be resourceful in various applications. Symmetry testing algorithms provide a means to identify and quantify these properties with respect to a representation of a group. In this paper, we present a collection of quantum algorithms that realize projections onto the symmetric subspace, as well as the asymmetric subspace, of quantum systems. We describe how this can be modified to realize an antisymmetric projection as well, and we show how projectors can be combined in a systematic way to effectively measure various projections in a single quantum circuit. Using these constructions, we demonstrate applications such as testing for Werner-state symmetry and estimating Schmidt ranks of bipartite states, supported by experimental data from IBM Quantum systems. This work underscores the pivotal role of symmetry in simplifying quantum calculations and advancing quantum information tasks.

Related papers

• Group-invariant estimation of symmetric states generated by noisy quantum computers [0.0]
  We analyze the density matrices of symmetric quantum states generated by a quantum processor. We take advantage of an estimation technique that results to be equivalent to the quantum Maximum Entropy (MaxEnt) estimation. The smart use of prior knowledge of the quantum state symmetries allows for a reduction in both, the number of measurements that need to be made on the system, and the size of the computational problem to store and process the data.
  arXiv  Detail & Related papers  (2024-08-17T12:20:43Z)
• Physical consequences of gauge optimization in quantum open systems evolutions [44.99833362998488]
  We show that gauge transformations can be exploited, on their own, to optimize practical physical tasks. First, we describe the inherent structure of the underlying symmetries in quantum Markovian dynamics. We then analyze examples of optimization in quantum thermodynamics.
  arXiv  Detail & Related papers  (2024-07-02T18:22:11Z)
• A universal scheme to self-test any quantum state and extremal measurement [41.94295877935867]
  quantum network considered in this work is the simple star network, which is implementable using current technologies. For our purposes, we also construct a scheme that can be used to self-test the two-dimensional tomographically complete set of measurements with an arbitrary number of parties.
  arXiv  Detail & Related papers  (2023-12-07T16:20:28Z)
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [46.99825956909532]
  Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system. This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
  arXiv  Detail & Related papers  (2023-10-04T09:51:00Z)
• Efficient quantum algorithms for testing symmetries of open quantum systems [17.55887357254701]
  In quantum mechanics, it is possible to eliminate degrees of freedom by leveraging symmetry to identify the possible physical transitions. Previous works have focused on devising quantum algorithms to ascertain symmetries by means of fidelity-based symmetry measures. We develop alternative symmetry testing quantum algorithms that are efficiently implementable on quantum computers.
  arXiv  Detail & Related papers  (2023-09-05T18:05:26Z)
• Symmetric Pruning in Quantum Neural Networks [111.438286016951]
  Quantum neural networks (QNNs) exert the power of modern quantum machines. QNNs with handcraft symmetric ansatzes generally experience better trainability than those with asymmetric ansatzes. We propose the effective quantum neural tangent kernel (EQNTK) to quantify the convergence of QNNs towards the global optima.
  arXiv  Detail & Related papers  (2022-08-30T08:17:55Z)
• An Introduction to Quantum Machine Learning for Engineers [36.18344598412261]
  Quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers. This book provides a self-contained introduction to quantum machine learning for an audience of engineers with a background in probability and linear algebra.
  arXiv  Detail & Related papers  (2022-05-11T12:10:52Z)
• Quantum Algorithms for Testing Hamiltonian Symmetry [4.62316736194615]
  We show that familiar expressions of Hamiltonian symmetry in quantum mechanics correspond directly with the acceptance of our algorithms. We execute one of our symmetry-testing algorithms on existing quantum computers for simple examples of both symmetric and asymmetric cases.
  arXiv  Detail & Related papers  (2022-03-18T15:30:50Z)
• Circuit Symmetry Verification Mitigates Quantum-Domain Impairments [69.33243249411113]
  We propose circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state. In particular, we propose the Fourier-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain formalism to circuit-oriented stabilizers.
  arXiv  Detail & Related papers  (2021-12-27T21:15:35Z)
• Testing symmetry on quantum computers [3.481985817302898]
  In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks. This paper details several quantum algorithms that test the symmetry of quantum states and channels.
  arXiv  Detail & Related papers  (2021-05-26T18:01:54Z)
• 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.