Quantifying the sensitivity to errors in analog quantum simulation

 

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P. M. Poggi¹, N. K. Lysne², K. W. Kuper², I. H. Deutsch¹, and P. S. Jessen²

1. Center for Quantum Information and Control (CQuIC), Department of Physics and Astronomy,
University of New Mexico, Albuquerque, New Mexico 87131, USA
2. Center for Quantum Information and Control (CQuIC), Wyant College of Optical Sciences,
University of Arizona, Tucson, Arizona 85721, USA
 

Quantum simulators are widely seen as one of the most promising near-term applications of quantum technologies. However, it remains unclear to what extent a noisy device can output reliable results in the presence of unavoidable imperfections. Here we propose a framework to characterize the performance of quantum simulators by linking robustness of quantum expectation values to the spectral properties of the output observable, which in turn can be associated with its macroscopic or microscopic character. We show that, under general assumptions and on average over all states, imperfect devices are able to reproduce the dynamics of macroscopic observables accurately, while the relative error in the expectation value of microscopic observables is much larger on average. We experimentally demonstrate the universality of these features in a state-of-the-art quantum simulator and show that the predicted behavior is generic for a highly accurate device, without assuming any knowledge about the nature of the imperfections.
 

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Simulation of complex dynamics of mean-field p-spin models using measurement-based quantum feedback control

 

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M. H. Muñoz-Arias¹, I. H. Deutsch¹, P. S. Jessen², and P. M. Poggi¹

1. Center for Quantum Information and Control, CQuIC, Department of Physics and Astronomy,
University of New Mexico, Albuquerque, New Mexico 87131, USA
2. Center for Quantum Information and Control, CQuIC, College of Optical Sciences and
Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
 

We study the application of a new method for simulating nonlinear dynamics of many-body spin systems using quantum measurement and feedback [Munoz-Arias et al., Phys. Rev. Lett. 124, 110503 (2020)] to a broad class of many-body models known as p-spin Hamiltonians, which describe Ising-like models on a completely connected graph with p-body interactions. The method simulates the desired mean field dynamics in the thermodynamic limit by combining nonprojective measurements of a component of the collective spin with a global rotation conditioned on the measurement outcome. We apply this protocol to simulate the dynamics of the p-spin Hamiltonians and demonstrate how different aspects of criticality in the mean-field regime are readily accessible with our protocol. We study applications including properties of dynamical phase transitions and the emergence of spontaneous symmetry breaking in the adiabatic dynamics of the collective spin for different values of the parameter p. We also demonstrate how this method can be employed to study the quantum-to-classical transition in the dynamics continuously as a function of system size.
 

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A small, highly accurate quantum processor for intermediate-depth quantum simulations

 

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N. K. Lysne¹, K. W. Kuper¹, P. M. Poggi², I. H. Deutsch², and P. S. Jessen¹

1. Center for Quantum Information and Control, Wyant College of Optical Sciences,
University of Arizona, Tucson, Arizona 85721, USA
2. Center for Quantum Information and Control, Department of Physics and Astronomy,
University of New Mexico, Albuquerque, New Mexico 87131, USA
 

Analog quantum simulation is widely considered a step on the path to fault tolerant quantum computation. With current noisy hardware, the accuracy of an analog simulator will degrade after just a few time steps, especially when simulating complex systems likely to exhibit quantum chaos. Here we describe a quantum simulator based on the combined electron-nuclear spins of individual Cs atoms, and its use to run high fidelity simulations of three different model Hamiltonians for >100 time steps. While not scalable to exponentially large Hilbert spaces, it provides the accuracy and programmability required to explore the interplay between dynamics, imperfections, and accuracy in quantum simulation.
 

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Simulating nonlinear dynamics of collective spins via quantum measurement and feedback

 

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M. H. Muñoz¹, P. M. Poggi¹, P. S. Jessen², and I. H. Deutsch¹

1. Center for Quantum Information and Control, University of New Mexico,
Albuquerque, New Mexico 87131, USA
2. Center for Quantum Information and Control, University of Arizona,
Tucson, Arizona 85721, USA
 

We study a method to simulate quantum many-body dynamics of spin ensembles using measurement- based feedback. By performing a weak collective measurement on a large ensemble of two-level quantum systems and applying global rotations conditioned on the measurement outcome, one can simulate the dynamics of a mean-field quantum kicked top, a standard paradigm of quantum chaos. We analytically show that there exists a regime in which individual quantum trajectories adequately recover the classical limit, and show the transition between noisy quantum dynamics to full deterministic chaos described by classical Lyapunov exponents. We also analyze the effects of decoherence, and show that the proposed scheme represents a robust method to explore the emergence of chaos from complex quantum dynamics in a realistic experimental platform based on an atom-light interface.
 

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