@article {3490, title = {Efficiently verifiable quantum advantage on near-term analog quantum simulators}, year = {2024}, month = {3/13/2024}, abstract = {

Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog quantum simulators have been realized in many experiments to study novel physics. In this work, we propose a quantum advantage protocol based on single-step Feynman-Kitaev verification of an analog quantum simulation, in which the verifier need only run an O(λ2)-time classical computation, and the prover need only prepare O(1) samples of a history state and perform O(λ2) single-qubit measurements, for a security parameter λ. We also propose a near-term feasible strategy for honest provers and discuss potential experimental realizations.

}, url = {https://arxiv.org/abs/2403.08195}, author = {Zhenning Liu and Dhruv Devulapalli and Dominik Hangleiter and Yi-Kai Liu and Alicia J. Koll{\'a}r and Alexey V. Gorshkov and Andrew M. Childs} } @article {3462, title = {Estimation of Hamiltonian parameters from thermal states}, year = {2024}, month = {1/18/2024}, abstract = {

We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term that contains the parameter and on the term\&$\#$39;s degree of noncommutativity with the full Hamiltonian: higher uncertainty and commuting operators lead to better precision. We apply the bounds to show that there exist entangled thermal states such that the parameter can be estimated with an error that decreases faster than 1/n\−\−\√, beating the standard quantum limit. This result governs Hamiltonians where an unknown scalar parameter (e.g. a component of a magnetic field) is coupled locally and identically to n qubit sensors. In the high-temperature regime, our bounds allow for pinpointing the optimal estimation error, up to a constant prefactor. Our bounds generalize to joint estimations of multiple parameters. In this setting, we recover the high-temperature sample scaling derived previously via techniques based on quantum state discrimination and coding theory. In an application, we show that noncommuting conserved quantities hinder the estimation of chemical potentials.

}, url = {https://arxiv.org/abs/2401.10343}, author = {Luis Pedro Garc{\'\i}a-Pintos and Kishor Bharti and Jacob Bringewatt and Hossein Dehghani and Adam Ehrenberg and Nicole Yunger Halpern and Alexey V. Gorshkov} } @article {3498, title = {Experimental roadmap for optimal state transfer and entanglement generation in power-law systems}, year = {2024}, month = {2/12/2024}, abstract = {

Experimental systems with power-law interactions have recently garnered interest as promising platforms for quantum information processing. Such systems are capable of spreading entanglement superballistically and achieving an asymptotic speed-up over locally interacting systems. Recently, protocols developed by Eldredge et al. [Phys. Rev. Lett. 119, 170503 (2017)] and Tran et al. [Phys. Rev. X 11, 031016 (2021)] for the task of transferring a quantum state between distant particles quickly were shown to be optimal and saturate theoretical bounds. However, the implementation of these protocols in physical systems with long-range interactions remains to be fully realized. In this work, we provide an experimental roadmap towards realizing fast state-transfer protocols in three classes of atomic and molecular systems with dipolar interactions: polar molecules composed of alkali-metal dimers, neutral atoms in excited Rydberg states, and atoms with strong magnetic moments (e.g. dysprosium). As a guide to near-term experimental implementation, we numerically evaluate the tradeoffs between the two protocols for small system sizes and develop methods to address potential crosstalk errors that may arise during the execution of the protocols.

}, url = {https://arxiv.org/abs/2402.07974}, author = {Andrew Y. Guo and Jeremy T. Young and Ron Belyansky and Przemyslaw Bienias and Alexey V. Gorshkov} } @article {3153, title = {Error-correcting codes for fermionic quantum simulation}, year = {2022}, month = {10/16/2022}, abstract = {

We provide ways to simulate fermions by qubits on 2d lattices using Z2 gauge theories (stabilizer codes). By studying the symplectic automorphisms of the Pauli module over the Laurent polynomial ring, we develop a systematic way to increase the code distances of stabilizer codes. We identify a family of stabilizer codes that can be used to simulate fermions with code distances of d=2,3,4,5,6,7 such that any \⌊d\−12\⌋-qubit error can be corrected. In particular, we demonstrate three stabilizer codes with code distances of d=3, d=4, and d=5, respectively, with all stabilizers and logical operators shown explicitly. The syndromes for all Pauli errors are provided. Finally, we introduce a syndrome-matching method to compute code distances numerically.

}, keywords = {FOS: Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Algebra (math.QA), Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2210.08411}, url = {https://arxiv.org/abs/2210.08411}, author = {Chen, Yu-An and Alexey V. Gorshkov and Xu, Yijia} } @article {2457, title = {Entanglement Bounds on the Performance of Quantum Computing Architectures}, journal = {Phys. Rev. Research}, volume = {2}, year = {2020}, month = {9/22/2020}, abstract = {

There are many possible architectures for future quantum computers that designers will need to choose between. However, the process of evaluating a particular connectivity graph\&$\#$39;s performance as a quantum architecture can be difficult. In this paper, we establish a connection between a quantity known as the isoperimetric number and a lower bound on the time required to create highly entangled states. The metric we propose counts resources based on the use of two-qubit unitary operations, while allowing for arbitrarily fast measurements and classical feedback. We describe how these results can be applied to the evaluation of the hierarchical architecture proposed in Phys. Rev. A 98, 062328 (2018). We also show that the time-complexity bound we place on the creation of highly-entangled states can be saturated up to a multiplicative factor logarithmic in the number of qubits.

}, doi = {https://doi.org/10.1103/PhysRevResearch.2.033316}, url = {https://arxiv.org/abs/1908.04802}, author = {Zachary Eldredge and Leo Zhou and Aniruddha Bapat and James R. Garrison and Abhinav Deshpande and Frederic T. Chong and Alexey V. Gorshkov} } @article {2567, title = {Exotic photonic molecules via Lennard-Jones-like potentials}, journal = {Phys. Rev. Lett.}, volume = {125}, year = {2020}, month = {9/19/2020}, abstract = {

Ultracold systems offer an unprecedented level of control of interactions between atoms. An important challenge is to achieve a similar level of control of the interactions between photons. Towards this goal, we propose a realization of a novel Lennard-Jones-like potential between photons coupled to the Rydberg states via electromagnetically induced transparency (EIT). This potential is achieved by tuning Rydberg states to a F{{\"o}}rster resonance with other Rydberg states. We consider few-body problems in 1D and 2D geometries and show the existence of self-bound clusters (\"molecules\") of photons. We demonstrate that for a few-body problem, the multi-body interactions have a significant impact on the geometry of the molecular ground state. This leads to phenomena without counterparts in conventional systems: For example, three photons in 2D preferentially arrange themselves in a line-configuration rather than in an equilateral-triangle configuration. Our result opens a new avenue for studies of many-body phenomena with strongly interacting photons.

}, doi = {https://doi.org/10.1103/PhysRevLett.125.093601}, url = {https://arxiv.org/abs/2003.07864}, author = {Przemyslaw Bienias and Michael Gullans and Marcin Kalinowski and Alexander N. Craddock and Dalia P. Ornelas-Huerta and Steven L. Rolston and J. V. Porto and Alexey V. Gorshkov} } @article {2001, title = {{E}ntanglement area laws for long-range interacting systems}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/07/31}, pages = {050501}, abstract = {

We prove that the entanglement entropy of any state evolved under an arbitrary 1/rα long-range-interacting D-dimensional lattice spin Hamiltonian cannot change faster than a rate proportional to the boundary area for any α \> D + 1. We also prove that for any α \> 2D + 2, the ground state of such a Hamiltonian satisfies the entanglement area law if it can be transformed along a gapped adiabatic path into a ground state known to satisfy the area law. These results significantly generalize their existing counterparts for short-range interacting systems, and are useful for identifying dynamical phase transitions and quantum phase transitions in the presence of long-range interactions.

}, doi = {10.1103/PhysRevLett.119.050501}, url = {https://arxiv.org/abs/1702.05368}, author = {Zhe-Xuan Gong and Michael Foss-Feig and Fernando G. S. L. Brand{\~a}o and Alexey V. Gorshkov} } @article {2059, title = {Efimov States of Strongly Interacting Photons}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/12/04}, pages = {233601}, abstract = {

We demonstrate the emergence of universal Efimov physics for interacting photons in cold gases of Rydberg atoms. We consider the behavior of three photons injected into the gas in their propagating frame, where a paraxial approximation allows us to consider them as massive particles. In contrast to atoms and nuclei, the photons have a large anisotropy between their longitudinal mass, arising from dispersion, and their transverse mass, arising from diffraction. Nevertheless, we show that in suitably rescaled coordinates the effective interactions become dominated by s-wave scattering near threshold and, as a result, give rise to an Efimov effect near unitarity, but with spatially anisotropic wavefunctions in the original coordinates. We show that the three-body loss of these Efimov trimers can be strongly suppressed and determine conditions under which these states are observable in current experiments. These effects can be naturally extended to probe few-body universality beyond three bodies, as well as the role of Efimov physics in the non-equilbrium, many-body regime.

}, doi = {10.1103/PhysRevLett.119.233601}, url = {https://arxiv.org/abs/1709.01955}, author = {Michael Gullans and S. Diehl and S. T. Rittenhouse and B. P. Ruzic and J. P. D{\textquoteright}Incao and P. Julienne and Alexey V. Gorshkov and J. M. Taylor} } @article {1906, title = {Emergent equilibrium in many-body optical bistability}, journal = {Physical Review A}, volume = {95}, year = {2017}, month = {2017/04/17}, pages = {043826}, abstract = {

Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold gases of Rydberg atoms, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, non-equilibrium setting of cavity-QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability---a foundational and patently non-equilibrium model of cavity-QED---the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by identifying a limit in which the quantum dynamics is asymptotically equivalent to non-equilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, producing results consistent with the behavior of a finite-temperature Ising model.

}, doi = {doi.org/10.1103/PhysRevA.95.043826}, url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.043826}, author = {Michael Foss-Feig and Pradeep Niroula and Jeremy T. Young and Mohammad Hafezi and Alexey V. Gorshkov and Ryan M. Wilson and Mohammad F. Maghrebi} } @article {1921, title = {Exact sampling hardness of Ising spin models}, journal = {Physical Review A}, volume = {96}, year = {2017}, month = {2017/09/14}, pages = {032324}, abstract = {

We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of\ exact\ classical sampling, leaving open the important question of whether a much stronger approximate-sampling hardness result holds in this context. The latter is most likely necessary to enable a convincing experimental demonstration of quantum supremacy. As referenced in a recent paper [A. Bouland, L. Mancinska, and X. Zhang, in\ Proceedings of the 31st Conference on Computational Complexity (CCC 2016), Leibniz International Proceedings in Informatics (Schloss Dagstuhl\–Leibniz-Zentrum f{\"u}r Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.

}, doi = {10.1103/PhysRevA.96.032324}, url = {https://arxiv.org/abs/1701.03167}, author = {Bill Fefferman and Michael Foss-Feig and Alexey V. Gorshkov} } @article {1780, title = {Exactly soluble model of boundary degeneracy}, journal = {Physical Review B}, volume = {95}, year = {2017}, month = {2017/01/25}, chapter = {045309}, abstract = {

We investigate the topological degeneracy that can be realized in Abelian fractional quantum spin Hall states with multiply connected gapped boundaries. Such a topological degeneracy (also dubbed as \"boundary degeneracy\") does not require superconducting proximity effect and can be created by simply applying a depletion gate to the quantum spin Hall material and using a generic spin-mixing term (e.g., due to backscattering) to gap out the edge modes. We construct an exactly soluble microscopic model manifesting this topological degeneracy and solve it using the recently developed technique [S. Ganeshan and M. Levin, Phys. Rev. B 93, 075118 (2016)]. The corresponding string operators spanning this degeneracy are explicitly calculated. It is argued that the proposed scheme is experimentally reasonable.

}, doi = {10.1103/PhysRevB.95.045309}, url = {http://journals.aps.org/prb/abstract/10.1103/PhysRevB.95.045309}, author = {Sriram Ganeshan and Alexey V. Gorshkov and Victor Gurarie and Victor M. Galitski} } @article {1784, title = {Effective Field Theory for Rydberg Polaritons}, journal = {Physical Review Letters}, volume = {117}, year = {2016}, month = {2016/09/09}, pages = {113601}, abstract = {

We study non-perturbative effects in N-body scattering of Rydberg polaritons using effective field theory (EFT). We develop an EFT in one dimension and show how a suitably long medium can be used to prepare shallow N-body bound states. We then derive the effective N-body interaction potential for Rydberg polaritons and the associated N-body contact force that arises in the EFT. We use the contact force to find the leading order corrections to the binding energy of the N-body bound states and determine the photon number at which the EFT description breaks down. We find good agreement throughout between the predictions of EFT and numerical simulations of the exact two and three photon wavefunction transmission.

}, doi = {http://dx.doi.org/10.1103/PhysRevLett.117.113601}, url = {http://arxiv.org/abs/1605.05651}, author = {Michael Gullans and J. D. Thompson and Y. Wang and Q. -Y. Liang and V. Vuletic and M. D. Lukin and Alexey V. Gorshkov} } @article {2004, title = {Entanglement and spin-squeezing without infinite-range interactions}, year = {2016}, month = {2016/12/22}, abstract = {

Infinite-range interactions are known to facilitate the production of highly entangled states with applications in quantum information and metrology. However, many experimental systems have interactions that decay with distance, and the achievable benefits in this context are much less clear. Combining recent exact solutions with a controlled expansion in the system size, we analyze quench dynamics in Ising models with power-law (1/r α ) interactions in D dimensions, thereby expanding the understanding of spin squeezing into a broad and experimentally relevant context. In spatially homogeneous systems, we show that for small α the scaling of squeezing with system size is identical to the infinite-range (α = 0) case. This indifference to the interaction range persists up to a critical value α = 2D/3, above which squeezing degrades continuously. Boundaryinduced inhomogeneities present in most experimental systems modify this picture, but it nevertheless remains qualitatively correct for finite-sized systems.

}, url = {https://arxiv.org/abs/1612.07805}, author = {Michael Foss-Feig and Zhe-Xuan Gong and Alexey V. Gorshkov and Charles W. Clark} }