Exploring quantum chaos with a single nuclear spin

Mourik, Vincent; Asaad, Serwan; Firgau, Hannes R.; Pla, Jarryd; Holmes, C. A.; Milburn, G. J.; McCallum, Jeffrey C.; Morello, Andrea

doi:10.1103/physreve.98.042206

Cited by 27 publications

(35 citation statements)

References 91 publications

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“…That is, for ↵ ! 0 the Trotterized dynamics of the spin chain as 26) and (27). c Growth rate λ for the range of times in a during which the OTOC grows exponentially.…”

Section: Resultsmentioning

confidence: 99%

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

et al. 2019

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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.

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“…That is, for ↵ ! 0 the Trotterized dynamics of the spin chain as 26) and (27). c Growth rate λ for the range of times in a during which the OTOC grows exponentially.…”

Section: Resultsmentioning

confidence: 99%

“…Figure 3 shows that the RMT expression C COE of the OTOC agrees with the temporal average obtained from Eq. (27) in the chaotic regime and beyond the Ehrenfest time t E .…”

Section: Methodsmentioning

confidence: 99%

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

et al. 2019

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“…We have theoretically proposed, and quantitatively analyzed, the embodiment of a periodically driven top (a more experimentally feasible variant of the kicked top, where the system is subjected to a sinusoidal drive instead of a train of δ‐functions) using a the nuclear spin of a group‐V donor in silicon. [ 33 ]…”

Section: High‐spin Nuclei: Quadrupole Interactions and Its Applicationsmentioning

confidence: 99%

Donor Spins in Silicon for Quantum Technologies

et al. 2020

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Dopant atoms are ubiquitous in semiconductor technologies, providing the tailored electronic properties that underpin the modern digital information era. Harnessing the quantum nature of these atomic‐scale objects represents a new and exciting technological revolution. In this article, the use of ion‐implanted donor spins in silicon for quantum technologies is described. It is reviewed how to fabricate and operate single‐atom spin qubits in silicon, obtaining some of the most coherent solid‐state qubits, and pathways to scale up these qubits to build large quantum processors are discussed. Heavier group‐V donors with large nuclear spins display electric quadrupole couplings that enable nuclear electric resonance, quantum chaos, and strain sensing. Donor ensembles can be coupled to microwave cavities to develop hybrid quantum Turing machines. Counted, deterministic implantation of single donors, combined with novel methods for precision placement, will allow the integration of individual donor spins with industry‐standard silicon fabrication processes, making implanted donors a prime physical platform for the second quantum revolution.

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“…2 are the collective angular momentum operators. While originally studied in the context of nuclear physics [30], the LMG model has applications in a wide variety of contexts, including the dynamics of twomode Bose Einstein condensates for applications of quantum metrology [31][32][33], studies of quantum chaos [34,35], and quantum simulation [11,36,37]. For the remainder of this manuscript, we scale the energy and parametrize the LMG Hamiltonian with a single parameter s according to…”

Section: Quantum Phase Transitions In the Lmg Modelmentioning

confidence: 99%

The effect of chaos on the simulation of quantum critical phenomena in analog quantum simulators

Chinni,

Poggi,

Deutsch

2021

Preprint

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We study how chaos, introduced by a weak perturbation, affects the reliability of the output of analog quantum simulation. As a toy model, we consider the Lipkin-Meshkov-Glick (LMG) model. 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 and the dynamical quantum phase transition associated with quench dynamics. We show that the presence of a small time-dependent perturbation can render the dynamics of the system chaotic. We then show that the estimates of the critical points of these quantum phase transitions, obtained from the quantum simulation of its dynamics, are robust to the presence of this chaotic perturbation, while other aspects of the system, such as the mean magnetization are fragile, and therefore cannot be reliably extracted from this simulator. This can be understood in terms of the simulated quantities that depend on the global structure of phase space vs. those that depend on local trajectories.

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Exploring quantum chaos with a single nuclear spin

Cited by 27 publications

References 91 publications

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

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

Donor Spins in Silicon for Quantum Technologies

The effect of chaos on the simulation of quantum critical phenomena in analog quantum simulators

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