Symmetry assisted preparation of entangled many-body states on a quantum computer

• URL: http://arxiv.org/abs/2006.06491v2
• Date: Mon, 16 Nov 2020 17:10:14 GMT
• Title: Symmetry assisted preparation of entangled many-body states on a quantum computer
• Authors: D. Lacroix
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Starting from the Quantum-Phase-Estimate (QPE) algorithm, 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. When the operator is associated to a symmetry of the Hamiltonian, the approach can be seen as a quantum--computer formulation of symmetry breaking followed by symmetry restoration. The method proposed in this work, called Discrete Spectra Assisted (DSA), is applied to superfluid systems. By using the blocking technique adapted to qubits, the full spectra of a pairing Hamiltonian is obtained.

Related papers

• Simulating NMR Spectra with a Quantum Computer [49.1574468325115]
  This paper provides a formalization of the complete procedure of the simulation of a spin system's NMR spectrum. We also explain how to diagonalize the Hamiltonian matrix with a quantum computer, thus enhancing the overall process's performance.
  arXiv  Detail & Related papers  (2024-10-28T08:43:40Z)
• 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)
• A quantum implementation of high-order power method for estimating geometric entanglement of pure states [39.58317527488534]
  This work presents a quantum adaptation of the iterative higher-order power method for estimating the geometric measure of entanglement of multi-qubit pure states. It is executable on current (hybrid) quantum hardware and does not depend on quantum memory. We study the effect of noise on the algorithm using a simple theoretical model based on the standard depolarising channel.
  arXiv  Detail & Related papers  (2024-05-29T14:40:24Z)
• 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)
• Symmetry breaking and restoration for many-body problems treated on quantum computers [0.0]
  This thesis explores the application of the Symmetry-Breaking/Symmetry-Restoration methodology on quantum computers. It involves intentionally breaking and restoring the symmetries of the wave function ansatz at different stages of the variational search for the ground state. In the final part, hybrid quantum-classical techniques were introduced to extract an approximation of the low-lying spectrum of a Hamiltonian.
  arXiv  Detail & Related papers  (2023-10-27T09:12:38Z)
• Quantum tensor networks algorithms for evaluation of spectral functions on quantum computers [0.0]
  We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. We demonstrate algorithms to prepare ground and excited states on a quantum computer and apply them to molecular nanomagnets (MNMs) as a paradigmatic example.
  arXiv  Detail & Related papers  (2023-09-26T18:01:42Z)
• 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)
• Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry [51.827942608832025]
  Near-term quantum computers can calculate the ground-state properties of small molecules. We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
  arXiv  Detail & Related papers  (2021-12-31T16:33:10Z)
• 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)
• Accessing ground state and excited states energies in many-body system after symmetry restoration using quantum computers [0.0]
  We explore the possibility to perform symmetry restoration with the variation after projection technique on a quantum computer. The final goal is to develop configuration interaction techniques based on many-body trial states pre-optimized on a quantum computer.
  arXiv  Detail & Related papers  (2021-11-25T13:42:27Z)
• From geometry to coherent dissipative dynamics in quantum mechanics [68.8204255655161]
  We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation. We describe quantum decays in a 2-level system as coherent and continuous processes.
  arXiv  Detail & Related papers  (2021-07-29T18:27:38Z)

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.