scholarly journals Digital quantum simulation, Trotter errors, and quantum chaos of the kicked top

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Lukas M. Sieberer ◽  
Tobias Olsacher ◽  
Andreas Elben ◽  
Markus Heyl ◽  
Philipp Hauke ◽  
...  
Keyword(s):  
Time Evolution ◽  
Quantum Chaos ◽  
Threshold Value ◽  
Quantum Simulation ◽  
Spin Systems ◽  
Step Size ◽  
Sharp Threshold ◽  
Trapped Ion ◽  
Quantum Simulators ◽  
Atomic Spins

Abstract This work aims at giving Trotter errors in digital quantum simulation (DQS) of collective spin systems an interpretation in terms of quantum chaos of the kicked top. In particular, for DQS of such systems, regular dynamics of the kicked top ensures convergence of the Trotterized time evolution, while chaos in the top, which sets in above a sharp threshold value of the Trotter step size, corresponds to the proliferation of Trotter errors. We show the possibility to analyze this phenomenology in a wide variety of experimental realizations of the kicked top, ranging from single atomic spins to trapped-ion quantum simulators which implement DQS of all-to-all interacting spin-1/2 systems. These platforms thus enable in-depth studies of Trotter errors and their relation to signatures of quantum chaos, including the growth of out-of-time-ordered correlators.

scholarly journals Practical verification protocols for analog quantum simulators

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Ryan Shaffer ◽  
Eli Megidish ◽  
Joseph Broz ◽  
Wei-Ting Chen ◽  
Hartmut Häffner
Keyword(s):  
System Size ◽  
Quantum Simulation ◽  
Quantum Devices ◽  
Error Sources ◽  
Trapped Ion ◽  
Quantum Simulators ◽  
Simulation Results ◽  
Quantum Simulator ◽  
Near Term ◽  
Significant Application

AbstractAnalog quantum simulation is expected to be a significant application of near-term quantum devices. Verification of these devices without comparison to known simulation results will be an important task as the system size grows beyond the regime that can be simulated classically. We introduce a set of experimentally-motivated verification protocols for analog quantum simulators, discussing their sensitivity to a variety of error sources and their scalability to larger system sizes. We demonstrate these protocols experimentally using a two-qubit trapped-ion analog quantum simulator and numerically using models of up to five qubits.

scholarly journals Quantum localization bounds Trotter errors in digital quantum simulation

2019 ◽  
Vol 5 (4) ◽  
pp. eaau8342 ◽  
Author(s):  
Markus Heyl ◽  
Philipp Hauke ◽  
Peter Zoller
Keyword(s):  
Time Evolution ◽  
Quantum Interference ◽  
Body Wave ◽  
System Size ◽  
Quantum Simulation ◽  
Chaotic Regime ◽  
Many Body ◽  
Step Size ◽  
Local Observables ◽  
Quantum Localization

A fundamental challenge in digital quantum simulation (DQS) is the control of an inherent error, which appears when discretizing the time evolution of a quantum many-body system as a sequence of quantum gates, called Trotterization. Here, we show that quantum localization-by constraining the time evolution through quantum interference-strongly bounds these errors for local observables, leading to an error independent of system size and simulation time. DQS is thus intrinsically much more robust than suggested by known error bounds on the global many-body wave function. This robustness is characterized by a sharp threshold as a function of the Trotter step size, which separates a localized region with controllable Trotter errors from a quantum chaotic regime. Our findings show that DQS with comparatively large Trotter steps can retain controlled errors for local observables. It is thus possible to reduce the number of gate operations required to represent the desired time evolution faithfully.

Quantum Chaos and Universal Trotterisation Performance Behaviours in Digital Quantum Simulation

2021 ◽  
Author(s):  
Cahit Kargi ◽  
Juan Pablo Dehollain ◽  
Fabio Henriques ◽  
Lukas M. Sieberer ◽  
Tobias Olsacher ◽  
...  
Keyword(s):  
Quantum Chaos ◽  
Quantum Simulation

scholarly journals Nature of quantum chaos in spin systems

1986 ◽  
Vol 34 (4) ◽  
pp. 3345-3355 ◽  
Author(s):  
Gerhard Müller
Keyword(s):  
Quantum Chaos ◽  
Spin Systems

scholarly journals Cryogenic trapped-ion system for large scale quantum simulation

2018 ◽  
Vol 4 (1) ◽  
pp. 014004 ◽  
Author(s):  
G Pagano ◽  
P W Hess ◽  
H B Kaplan ◽  
W L Tan ◽  
P Richerme ◽  
...  
Keyword(s):  
Large Scale ◽  
Quantum Simulation ◽  
Trapped Ion

Augmented Time-Stepping by Step-Size Adjustment and Extrapolation

2007 ◽  
Author(s):  
Christian Studer ◽  
Christoph Glocker
Keyword(s):  
Time Evolution ◽  
Integration Method ◽  
Switching Time ◽  
Mechanical Systems ◽  
Unilateral Contact ◽  
Step Size ◽  
Frictional Contacts ◽  
Time Stepping ◽  
Size Adjustment ◽  
Integration Order

Time-stepping schemes are widely used when integrating non-smooth systems. In this paper we discuss an augmented time-stepping scheme which uses step-size adjustment and extrapolation. The time evolution of non-smooth systems can be divided in different smooth parts, which are separated by switching points. We deduce the time-stepping method of Moreau, which is a common order-one integration method for non-smooth systems. We formulate the method using contact inclusions, and show how these inclusions can be solved by a projection. We show how time-steps which contain a switching point can be detected by observing the projection behaviour, and propose a step-size adjustment, which treats these switching time-steps with a minimal step-size Δtmin. Time-steps in smooth parts of the motion are run with a larger step-size, and an extrapolation method, which is based on the time-stepping scheme, is used to increase the integration order. The presented method is suitable for mechanical systems with unilateral and frictional contacts. For simplicity, we deduce the method considering solely mechanical systems with one unilateral contact.

scholarly journals Initialization of quantum simulators by sympathetic cooling

2020 ◽  
Vol 6 (10) ◽  
pp. eaaw9268 ◽  
Author(s):  
Meghana Raghunandan ◽  
Fabian Wolf ◽  
Christian Ospelkaus ◽  
Piet O. Schmidt ◽  
Hendrik Weimer
Keyword(s):  
Energy State ◽  
Hamiltonian Dynamics ◽  
Many Body ◽  
Sympathetic Cooling ◽  
Trapped Ion ◽  
Physical Chemical ◽  
Quantum Simulators ◽  
Auxiliary Particle ◽  
Quantum Simulator ◽  
Chemical And Biological Systems

Simulating computationally intractable many-body problems on a quantum simulator holds great potential to deliver insights into physical, chemical, and biological systems. While the implementation of Hamiltonian dynamics within a quantum simulator has already been demonstrated in many experiments, the problem of initialization of quantum simulators to a suitable quantum state has hitherto remained mostly unsolved. Here, we show that already a single dissipatively driven auxiliary particle can efficiently prepare the quantum simulator in a low-energy state of largely arbitrary Hamiltonians. We demonstrate the scalability of our approach and show that it is robust against unwanted sources of decoherence. While our initialization protocol is largely independent of the physical realization of the simulation device, we provide an implementation example for a trapped ion quantum simulator.

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