Randomized measurement protocols for lattice gauge theories

Jacob Bringewatt1,2, Jonathan Kunjummen1,2, and Niklas Mueller3

1Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
2Joint Quantum Institute/NIST, University of Maryland, College Park, Maryland 20742, USA
3InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, Seattle, WA 98195, USA.

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Abstract

Randomized measurement protocols, including classical shadows, entanglement tomography, and randomized benchmarking are powerful techniques to estimate observables, perform state tomography, or extract the entanglement properties of quantum states. While unraveling the intricate structure of quantum states is generally difficult and resource-intensive, quantum systems in nature are often tightly constrained by symmetries. This can be leveraged by the symmetry-conscious randomized measurement schemes we propose, yielding clear advantages over symmetry-blind randomization such as reducing measurement costs, enabling symmetry-based error mitigation in experiments, allowing differentiated measurement of (lattice) gauge theory entanglement structure, and, potentially, the verification of topologically ordered states in existing and near-term experiments. Crucially, unlike symmetry-blind randomized measurement protocols, these latter tasks can be performed without relearning symmetries via full reconstruction of the density matrix.

A quantum state may encode exponential information. Only a minuscule amount of this information is typically revealed by a single measurement. Randomized measurement protocols offer a promising avenue to overcome this limitation, allowing access to many quantities of interest while requiring relatively few measurements. In this work, we suggest enhancing the randomized measurement toolbox by making use of an ubiquitous situation in engineered and natural quantum systems, the presence of symmetries. Our symmetry-conscious approach yields a direct method to extract the entanglement structure of quantum many body systems without the need for full tomography. One prime application is the study and verification of topologically ordered phases in synthetic quantum materials, a step towards enabling fault-tolerant quantum information processing, or measurement of the entanglement structure of gauge theories in quantum simulation experiments.

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[2] Andrea Bulgarelli and Marco Panero, "Entanglement entropy from non-equilibrium Monte Carlo simulations", Journal of High Energy Physics 2023 6, 30 (2023).

[3] Yongtao Zhan, Andreas Elben, Hsin-Yuan Huang, and Yu Tong, "Learning Conservation Laws in Unknown Quantum Dynamics", PRX Quantum 5 1, 010350 (2024).

[4] Edison M. Murairi and Michael J. Cervia, "Reducing circuit depth with qubitwise diagonalization", Physical Review A 108 6, 062414 (2023).

[5] Dongjin Lee and Beni Yoshida, "Randomly Monitored Quantum Codes", arXiv:2402.00145, (2024).

[6] Jesús Cobos, David F. Locher, Alejandro Bermudez, Markus Müller, and Enrique Rico, "Noise-aware variational eigensolvers: a dissipative route for lattice gauge theories", arXiv:2308.03618, (2023).

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[8] Zohreh Davoudi, Christopher Jarzynski, Niklas Mueller, Greeshma Oruganti, Connor Powers, and Nicole Yunger Halpern, "Quantum thermodynamics of nonequilibrium processes in lattice gauge theories", arXiv:2404.02965, (2024).

The above citations are from SAO/NASA ADS (last updated successfully 2024-04-12 14:40:50). The list may be incomplete as not all publishers provide suitable and complete citation data.

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