Efficient Eigenstate Preparation in an Integrable Model with Hilbert Space Fragmentation

• URL: http://arxiv.org/abs/2411.15132v1
• Date: Fri, 22 Nov 2024 18:57:08 GMT
• Title: Efficient Eigenstate Preparation in an Integrable Model with Hilbert Space Fragmentation
• Authors: Roberto Ruiz, Alejandro Sopena, Balázs Pozsgay, Esperanza López,
• Abstract summary: We consider the preparation of all the eigenstates of spin chains using quantum circuits. We showivities of the growth is also achievable for interacting models where the interaction between the particles is sufficiently simple.
• Score: 42.408991654684876
• License:
• Abstract: We consider the preparation of all the eigenstates of spin chains using quantum circuits. It is known that generic eigenstates of free-fermionic spin chains can be prepared with circuits whose depth grows only polynomially with the length of the chain and the number of particles. We show that the polynomial growth is also achievable for selected interacting models where the interaction between the particles is sufficiently simple. Our working example is the folded XXZ model, an integrable spin chain that exhibits Hilbert space fragmentation. We present the explicit quantum circuits that prepare arbitrary eigenstates of this model on an open chain efficiently. We perform error-mitigated noisy simulations with circuits of up to 13 qubits and different connectivities between qubits, achieving a relative error below 5%. As a byproduct, we extend a recent reformulation of the Bethe ansatz as a quantum circuit from closed to open boundary conditions.

Related papers

• Observing quantum many-body scars in random quantum circuits [0.0]
  We devise quantum simulations to investigate the dynamics of the Schwinger model in its low dimensional form. We apply trotterization to write quantum circuits that effectively generate the evolution under the Schwinger model Hamiltonian. Our comparison of sequential and randomized circuit dynamics shows that the non-thermal sector of the Hilbert space, including the scars, are more sensitive to randomization.
  arXiv  Detail & Related papers  (2024-02-09T15:46:21Z)
• Strong zero modes in integrable quantum circuits [0.0]
  We show that an exact SZM operator can be constructed for certain integrable quantum circuits. Our predictions are corroborated by numerical simulations of infinite-temperature autocorrelation functions.
  arXiv  Detail & Related papers  (2024-01-22T19:02:33Z)
• Quantum emulation of the transient dynamics in the multistate Landau-Zener model [50.591267188664666]
  We study the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity. Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.
  arXiv  Detail & Related papers  (2022-11-26T15:04:11Z)
• Transition to chaos in extended systems and their quantum impurity models [0.0]
  Chaos sets a fundamental limit to quantum-information processing schemes. We study the onset of chaos in spatially extended quantum many-body systems that are relevant to quantum optical devices.
  arXiv  Detail & Related papers  (2022-05-02T18:01:09Z)
• 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)
• Exact thermal properties of free-fermionic spin chains [68.8204255655161]
  We focus on spin chain models that admit a description in terms of free fermions. Errors stemming from the ubiquitous approximation are identified in the neighborhood of the critical point at low temperatures.
  arXiv  Detail & Related papers  (2021-03-30T13:15:44Z)
• Hilbert Space Fragmentation and Exact Scars of Generalized Fredkin Spin Chains [0.0]
  We introduce a family of spin-$1/2$ many-body Hamiltonians with a three-site interaction. The interplay between fragmentation and scarring leads to rich tunable non-ergodic dynamics.
  arXiv  Detail & Related papers  (2021-02-11T16:45:17Z)
• Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature [62.997667081978825]
  We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
  arXiv  Detail & Related papers  (2021-01-21T14:33:34Z)
• Qubit regularization of asymptotic freedom [35.37983668316551]
  Heisenberg-comb acts on a Hilbert space with only two qubits per spatial lattice site. We show that the model reproduces the universal step-scaling function of the traditional model up to correlation lengths of 200,000 in lattice units. We argue that near-term quantum computers may suffice to demonstrate freedom.
  arXiv  Detail & Related papers  (2020-12-03T18:41:07Z)
• From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics [68.8204255655161]
  We introduce the asymmetric extension of the Quantum Symmetric Simple Exclusion Process. We show that the time-integrated current of fermions defines a height field which exhibits a quantum non-linear dynamics.
  arXiv  Detail & Related papers  (2020-01-13T14:30:36Z)

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.