Trotter errors from dynamical structural instabilities of Floquet maps in quantum simulation

• URL: http://arxiv.org/abs/2110.03568v2
• Date: Fri, 8 Apr 2022 14:30:31 GMT
• Title: Trotter errors from dynamical structural instabilities of Floquet maps in quantum simulation
• Authors: Karthik Chinni, Manuel H. Mu\~noz-Arias, Ivan H. Deutsch, Pablo M. Poggi
• Abstract summary: We study the behavior of errors in the quantum simulation of spin systems with long-range multi-body interactions. We identify a regime where the Floquet operator underlying the Trotter decomposition undergoes sharp changes even for small variations in the simulation step size.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the behavior of errors in the quantum simulation of spin systems with long-range multi-body interactions resulting from the Trotter-Suzuki decomposition of the time-evolution operator. We identify a regime where the Floquet operator underlying the Trotter decomposition undergoes sharp changes even for small variations in the simulation step size. This results in a time evolution operator that is very different from the dynamics generated by the targeted Hamiltonian, which leads to a proliferation of errors in the quantum simulation. These regions of sharp change in the Floquet operator, referred to as structural instability regions, appear typically at intermediate Trotter step sizes and in the weakly-interacting regime, and are thus complementary to recently revealed quantum chaotic regimes of the Trotterized evolution (Sieberer et al., npj Quantum Information 5, 1 (2019)). We characterize these structural instability regimes in $p$-spin models, transverse-field Ising models with all-to-all $p$-body interactions, and analytically predict their occurrence based on unitary perturbation theory. We further show that the effective Hamiltonian associated with the Trotter decomposition of the unitary time-evolution operator, when the Trotter-step size is chosen to be in the structural instability region, is very different from the target Hamiltonian, which explains the large errors that can occur in the simulation in the regions of instability. These results have implications for the reliability of near-term gate-based quantum simulators, and reveal an important interplay between errors and the physical properties of the system being simulated.

Related papers

• Simulating spin biology using a digital quantum computer: Prospects on a near-term quantum hardware emulator [0.0]
  We leverage Trotterization to map coherent radical pair spin dynamics onto a digital gate-based quantum simulation. We identify approximately 15 Trotter steps to be sufficient for faithfully reproducing the coupled spin dynamics of a prototypical system.
  arXiv  Detail & Related papers  (2024-06-18T18:09:31Z)
• Optimal-order Trotter-Suzuki decomposition for quantum simulation on noisy quantum computers [0.05343200742664294]
  We show that when the gate error is decreased by approximately an order of magnitude relative to typical modern values, higher-order Trotterization becomes advantageous. This form of Trotterization yields a global minimum of the overall simulation error.
  arXiv  Detail & Related papers  (2024-05-02T09:48:52Z)
• A Floquet-Rydberg quantum simulator for confinement in $\mathbb{Z}_2$ gauge theories [44.99833362998488]
  Recent advances in the field of quantum technologies have opened up the road for the realization of small-scale quantum simulators. We present a scalable Floquet scheme for the quantum simulation of the real-time dynamics in a $mathbbZ$ LGT. We show that an observation of gauge-invariant confinement dynamics in the Floquet-Rydberg setup is at reach of current experimental techniques.
  arXiv  Detail & Related papers  (2023-11-28T13:01:24Z)
• Krylov complexity and Trotter transitions in unitary circuit dynamics [0.0]
  Floquet circuits arising as the Trotter decomposition of Hamiltonian dynamics are studied. We find that local maximally ergodic operators appear at a critical Trotter step.
  arXiv  Detail & Related papers  (2023-08-07T18:01:29Z)
• Trapped-Ion Quantum Simulation of Collective Neutrino Oscillations [55.41644538483948]
  We study strategies to simulate the coherent collective oscillations of a system of N neutrinos in the two-flavor approximation using quantum computation. We find that the gate complexity using second order Trotter- Suzuki formulae scales better with system size than with other decomposition methods such as Quantum Signal Processing.
  arXiv  Detail & Related papers  (2022-07-07T09:39:40Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• Dynamical quantum phase transitions in the one-dimensional extended Fermi-Hubbard model [0.0]
  We study the emergence of dynamical quantum phase transitions (DQPTs) in a half-filled one-dimensional lattice. We identify several types of sudden interaction quenches which lead to DQPTs. State-of-the-art cold-atom quantum simulators constitute ideal platforms to implement several reported DQPTs experimentally.
  arXiv  Detail & Related papers  (2021-09-16T04:12:50Z)
• Rotating Majorana Zero Modes in a disk geometry [75.34254292381189]
  We study the manipulation of Majorana zero modes in a thin disk made from a $p$-wave superconductor. We analyze the second-order topological corner modes that arise when an in-plane magnetic field is applied. We show that oscillations persist even in the adiabatic phase because of a frequency independent coupling between zero modes and excited states.
  arXiv  Detail & Related papers  (2021-09-08T11:18:50Z)
• The effect of chaos on the simulation of quantum critical phenomena in analog quantum simulators [0.0]
  We study how chaos, introduced by a weak perturbation, affects the reliability of the output of analog quantum simulation. Inspired by the semiclassical behavior of the order parameter in the thermodynamic limit, we propose a protocol to measure the quantum phase transition in the ground state.
  arXiv  Detail & Related papers  (2021-03-03T22:03:43Z)
• Neural-Swarm2: Planning and Control of Heterogeneous Multirotor Swarms using Learned Interactions [38.881310154473205]
  We present Neural-Swarm2, a learning-based method for motion planning and control that allows heterogeneous multirotors in a swarm to safely fly in close proximity. Our approach combines a physics-based nominal dynamics model with learned Deep Neural Networks (DNNs) with strong Lipschitz properties.
  arXiv  Detail & Related papers  (2020-12-10T05:08:31Z)
• Bulk detection of time-dependent topological transitions in quenched chiral models [48.7576911714538]
  We show that the winding number of the Hamiltonian eigenstates can be read-out by measuring the mean chiral displacement of a single-particle wavefunction. This implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases.
  arXiv  Detail & Related papers  (2020-01-16T17:44:52Z)

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.