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1. Stability of invertible, frustration-free ground states against large perturbations

   https://doi.org/10.22331/q-2022-09-08-793  

   Bachmann, Sven; De Roeck, Wojciech; Donvil, Brecht; Fraas, Martin (September 2022, Quantum)

   A gapped ground state of a quantum spin system has a natural length scale set by the gap. This length scale governs the decay of correlations. A common intuition is that this length scale also controls the spatial relaxation towards the ground state away from impurities or boundaries. The aim of this article is to take a step towards a proof of this intuition. We assume that the ground state is frustration-free and invertible, i.e. it has no long-range entanglement. Moreover, we assume the property that we are aiming to prove for one specific kind of boundary condition; namely open boundary conditions. This assumption is also known as the "local topological quantum order" (LTQO) condition. With these assumptions we can prove stretched exponential decay away from boundaries or impurities, for any of the ground states of the perturbed system. In contrast to most earlier results, we do not assume that the perturbations at the boundary or the impurity are small. In particular, the perturbed system itself can have long-range entanglement. 

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2. Bound on quantum fluctuations in gravitational waves from LIGO-Virgo

   https://doi.org/10.1088/1475-7516/2023/03/009  

   Hertzberg, Mark P.; Litterer, Jacob A. (March 2023, Journal of Cosmology and Astroparticle Physics)

   Abstract We derive some of the central equations governing quantum fluctuations in gravitational waves, making use of general relativity as a sensible effective quantum theory at large distances. We begin with a review of classical gravitational waves in general relativity, including the energy in each mode. We then form the quantum ground state and coherent state, before then obtaining an explicit class of squeezed states. Since existing gravitational wave detections arise from merging black holes, and since the quantum nature of black holes remains puzzling, one can be open-minded to the possibility that the wave is in an interesting quantum mechanical state, such as a highly squeezed state. We compute the time and space two-point correlation functions for the quantized metric perturbations. We then constrain its amplitude with LIGO-Virgo observations. Using existing LIGO-Virgo data, we place a bound on the (exponential) squeezing parameter of the quantum gravitational wave state of ζ< 41. 

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3. Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States

   https://doi.org/10.1007/s00023-021-01086-5  

   Nachtergaele, Bruno; Sims, Robert; Young, Amanda (February 2022, Annales Henri Poincaré)

   Abstract We study the stability with respect to a broad class of perturbations of gapped ground-state phases of quantum spin systems defined by frustration-free Hamiltonians. The core result of this work is a proof using the Bravyi–Hastings–Michalakis (BHM) strategy that under a condition of local topological quantum order (LTQO), the bulk gap is stable under perturbations that decay at long distances faster than a stretched exponential. Compared to previous work, we expand the class of frustration-free quantum spin models that can be handled to include models with more general boundary conditions, and models with discrete symmetry breaking. Detailed estimates allow us to formulate sufficient conditions for the validity of positive lower bounds for the gap that are uniform in the system size and that are explicit to some degree. We provide a survey of the BHM strategy following the approach of Michalakis and Zwolak, with alterations introduced to accommodate more general than just periodic boundary conditions and more general lattices. We express the fundamental condition known as LTQO by means of an indistinguishability radius, which we introduce. Using the uniform finite-volume results, we then proceed to study the thermodynamic limit. We first study the case of a unique limiting ground state and then also consider models with spontaneous breaking of a discrete symmetry. In the latter case, LTQO cannot hold for all local observables. However, for perturbations that preserve the symmetry, we show stability of the gap and the structure of the broken symmetry phases. We prove that the GNS Hamiltonian associated with each pure state has a non-zero spectral gap above the ground state. 

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4. Ultrastrong magnon–magnon coupling dominated by antiresonant interactions

   https://doi.org/10.1038/s41467-021-23159-z  

   Makihara, Takuma; Hayashida, Kenji; Noe II, G. Timothy; Li, Xinwei; Marquez Peraca, Nicolas; Ma, Xiaoxuan; Jin, Zuanming; Ren, Wei; Ma, Guohong; Katayama, Ikufumi; et al (December 2021, Nature Communications)

   Abstract Exotic quantum vacuum phenomena are predicted in cavity quantum electrodynamics systems with ultrastrong light-matter interactions. Their ground states are predicted to be vacuum squeezed states with suppressed quantum fluctuations owing to antiresonant terms in the Hamiltonian. However, such predictions have not been realized because antiresonant interactions are typically negligible compared to resonant interactions in light-matter systems. Here we report an unusual, ultrastrongly coupled matter-matter system of magnons that is analytically described by a unique Hamiltonian in which the relative importance of resonant and antiresonant interactions can be easily tuned and the latter can be made vastly dominant. We found a regime where vacuum Bloch-Siegert shifts, the hallmark of antiresonant interactions, greatly exceed analogous frequency shifts from resonant interactions. Further, we theoretically explored the system’s ground state and calculated up to 5.9 dB of quantum fluctuation suppression. These observations demonstrate that magnonic systems provide an ideal platform for exploring exotic quantum vacuum phenomena predicted in ultrastrongly coupled light-matter systems. 

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5. Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry

   https://doi.org/10.1038/s41467-023-37587-6  

   Lee, Seunghoon; Lee, Joonho; Zhai, Huanchen; Tong, Yu; Dalzell, Alexander M.; Kumar, Ashutosh; Helms, Phillip; Gray, Johnnie; Cui, Zhi-Hao; Liu, Wenyuan; et al (December 2023, Nature Communications)

   Abstract Due to intense interest in the potential applications of quantum computing, it is critical to understand the basis for potential exponential quantum advantage in quantum chemistry. Here we gather the evidence for this case in the most common task in quantum chemistry, namely, ground-state energy estimation, for generic chemical problems where heuristic quantum state preparation might be assumed to be efficient. The availability of exponential quantum advantage then centers on whether features of the physical problem that enable efficient heuristic quantum state preparation also enable efficient solution by classical heuristics. Through numerical studies of quantum state preparation and empirical complexity analysis (including the error scaling) of classical heuristics, in both ab initio and model Hamiltonian settings, we conclude that evidence for such an exponential advantage across chemical space has yet to be found. While quantum computers may still prove useful for ground-state quantum chemistry through polynomial speedups, it may be prudent to assume exponential speedups are not generically available for this problem. 

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