Does causal dynamics imply local interactions?

• URL: http://arxiv.org/abs/2006.10707v5
• Date: Mon, 27 Jun 2022 09:19:25 GMT
• Title: Does causal dynamics imply local interactions?
• Authors: Zolt\'an Zimbor\'as, Terry Farrelly, Szil\'ard Farkas, Lluis Masanes
• Abstract summary: We consider quantum systems with causal dynamics in discrete spacetimes, also known as quantum cellular automata (QCA) We ask if any of the Hamiltonians generating a QCA unitary is local in some sense, and we obtain two very different answers.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider quantum systems with causal dynamics in discrete spacetimes, also known as quantum cellular automata (QCA). Due to time-discreteness this type of dynamics is not characterized by a Hamiltonian but by a one-time-step unitary. This can be written as the exponential of a Hamiltonian but in a highly non-unique way. We ask if any of the Hamiltonians generating a QCA unitary is local in some sense, and we obtain two very different answers. On one hand, we present an example of QCA for which all generating Hamiltonians are fully non-local, in the sense that interactions do not decay with the distance. We expect this result to have relevant consequences for the classification of topological phases in Floquet systems, given that this relies on the effective Hamiltonian. On the other hand, we show that all one-dimensional quasi-free fermionic QCAs have quasi-local generating Hamiltonians, with interactions decaying exponentially in the massive case and algebraically in the critical case. We also prove that some integrable systems do not have local, quasi-local nor low-weight constants of motion; a result that challenges the standard definition of integrability.

Related papers

• Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement [42.896772730859645]
  We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations. We apply this approach to the classic logistic and Lorenz systems in both integrable and chaotic regimes.
  arXiv  Detail & Related papers  (2024-10-04T18:06:12Z)
• Learning Generalized Hamiltonians using fully Symplectic Mappings [0.32985979395737786]
  Hamiltonian systems have the important property of being conservative, that is, energy is conserved throughout the evolution. In particular Hamiltonian Neural Networks have emerged as a mechanism to incorporate structural inductive bias into the NN model. We show that symplectic schemes are robust to noise and provide a good approximation of the system Hamiltonian when the state variables are sampled from a noisy observation.
  arXiv  Detail & Related papers  (2024-09-17T12:45:49Z)
• Coherence generation with Hamiltonians [44.99833362998488]
  We explore methods to generate quantum coherence through unitary evolutions. This quantity is defined as the maximum derivative of coherence that can be achieved by a Hamiltonian. We identify the quantum states that lead to the largest coherence derivative induced by the Hamiltonian.
  arXiv  Detail & Related papers  (2024-02-27T15:06:40Z)
• Quantized Thouless pumps protected by interactions in dimerized Rydberg tweezer arrays [41.94295877935867]
  In the noninteracting case, quantized Thouless pumps can only occur when a topological singularity is encircled adiabatically. In the presence of interactions, such topological transport can even persist for exotic paths in which the system gets arbitrarily close to the noninteracting singularity.
  arXiv  Detail & Related papers  (2024-02-14T16:58:21Z)
• Quantum simulation for time-dependent Hamiltonians -- with applications to non-autonomous ordinary and partial differential equations [31.223649540164928]
  We propose an alternative formalism that turns any non-autonomous unitary dynamical system into an autonomous unitary system. This makes the simulation with time-dependent Hamiltonians not much more difficult than that of time-independent Hamiltonians. We show how our new quantum protocol for time-dependent Hamiltonians can be performed in a resource-efficient way and without measurements.
  arXiv  Detail & Related papers  (2023-12-05T14:59:23Z)
• Recovery of a generic local Hamiltonian from a degenerate steady state [11.567029926262476]
  Hamiltonian Learning (HL) is essential for validating quantum systems in quantum computing. HL success depends on the Hamiltonian model and steady state. We analyze HL for a specific type of steady state composed of eigenstates with degenerate mixing weight.
  arXiv  Detail & Related papers  (2023-09-01T08:40:50Z)
• Spectral form factor in a minimal bosonic model of many-body quantum chaos [1.3793594968500609]
  We study spectral form factor in periodically-kicked bosonic chains. We numerically find a nontrivial systematic system-size dependence of the Thouless time.
  arXiv  Detail & Related papers  (2022-03-10T15:56:24Z)
• Simultaneous Stoquasticity [0.0]
  Stoquastic Hamiltonians play a role in the computational complexity of the local Hamiltonian problem. We address the question of whether two or more Hamiltonians may be made simultaneously stoquastic via a unitary transformation.
  arXiv  Detail & Related papers  (2022-02-17T19:08:30Z)
• A simple approach to characterizing band topology in bosonic pairing Hamiltonians [0.0]
  We revisit the problem of characterizing band topology in dynamically-stable quadratic bosonic Hamiltonians that do not conserve particle number. We show this problem can be rigorously addressed by a smooth and local adiabatic mapping procedure to a particle number conserving Hamiltonian. Our approach shows that particle non-conserving bosonic Hamiltonians can be classified using known approaches for fermionic models.
  arXiv  Detail & Related papers  (2021-04-13T04:40:19Z)
• Stoquasticity in circuit QED [78.980148137396]
  We show that scalable sign-problem free path integral Monte Carlo simulations can typically be performed for such systems. We corroborate the recent finding that an effective, non-stoquastic qubit Hamiltonian can emerge in a system of capacitively coupled flux qubits.
  arXiv  Detail & Related papers  (2020-11-02T16:41:28Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)

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.