01794nas a2200157 4500008004100000245010100041210006900142260001400211520126400225100002001489700002201509700001901531700002401550700002501574856003701599 2024 eng d00aExperimental roadmap for optimal state transfer and entanglement generation in power-law systems0 aExperimental roadmap for optimal state transfer and entanglement c2/12/20243 a

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.

1 aGuo, Andrew, Y.1 aYoung, Jeremy, T.1 aBelyansky, Ron1 aBienias, Przemyslaw1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2402.0797401951nas a2200217 4500008004100000245008300041210006900124260001500193490000600208520129200214100002001506700002301526700001701549700002201566700002401588700002301612700001301635700002301648700002501671856003701696 2022 eng d00aImplementing a Fast Unbounded Quantum Fanout Gate Using Power-Law Interactions0 aImplementing a Fast Unbounded Quantum Fanout Gate Using PowerLaw c10/27/20220 v43 a

The standard circuit model for quantum computation presumes the ability to directly perform gates between arbitrary pairs of qubits, which is unlikely to be practical for large-scale experiments. Power-law interactions with strength decaying as 1/rα in the distance r provide an experimentally realizable resource for information processing, whilst still retaining long-range connectivity. We leverage the power of these interactions to implement a fast quantum fanout gate with an arbitrary number of targets. Our implementation allows the quantum Fourier transform (QFT) and Shor's algorithm to be performed on a D-dimensional lattice in time logarithmic in the number of qubits for interactions with α≤D. As a corollary, we show that power-law systems with α≤D are difficult to simulate classically even for short times, under a standard assumption that factoring is classically intractable. Complementarily, we develop a new technique to give a general lower bound, linear in the size of the system, on the time required to implement the QFT and the fanout gate in systems that are constrained by a linear light cone. This allows us to prove an asymptotically tighter lower bound for long-range systems than is possible with previously available techniques. 

1 aGuo, Andrew, Y.1 aDeshpande, Abhinav1 aChu, Su-Kuan1 aEldredge, Zachary1 aBienias, Przemyslaw1 aDevulapalli, Dhruv1 aSu, Yuan1 aChilds, Andrew, M.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2007.0066201670nas a2200145 4500008004100000245008900041210006900130260001500199520119300214100002001407700001601427700001901443700002501462856003701487 2021 eng d00aClustering of steady-state correlations in open systems with long-range interactions0 aClustering of steadystate correlations in open systems with long c10/28/20213 a

Lieb-Robinson bounds are powerful analytical tools for constraining the dynamic and static properties of non-relativistic quantum systems. Recently, a complete picture for closed systems that evolve unitarily in time has been achieved. In experimental systems, however, interactions with the environment cannot generally be ignored, and the extension of Lieb-Robinson bounds to dissipative systems which evolve non-unitarily in time remains an open challenge. In this work, we prove two Lieb-Robinson bounds that constrain the dynamics of open quantum systems with long-range interactions that decay as a power-law in the distance between particles. Using a combination of these Lieb-Robinson bounds and mixing bounds which arise from "reversibility" -- naturally satisfied for thermal environments -- we prove the clustering of correlations in the steady states of open quantum systems with long-range interactions. Our work provides an initial step towards constraining the steady-state entanglement structure for a broad class of experimental platforms, and we highlight several open directions regarding the application of Lieb-Robinson bounds to dissipative systems.

1 aGuo, Andrew, Y.1 aLieu, Simon1 aTran, Minh, C.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2110.1536801198nas a2200169 4500008004100000245006000041210005400101260001400155520069100169100001900860700002000879700002900899700002000928700002500948700001800973856003700991 2021 eng d00aThe Lieb-Robinson light cone for power-law interactions0 aLiebRobinson light cone for powerlaw interactions c3/29/20213 a

The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as 1/rα at distance r? Here, we present a definitive answer to this question for all exponents α>2d and all spatial dimensions d. Schematically, information takes time at least rmin{1,α−2d} to propagate a distance~r. As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.

1 aTran, Minh, C.1 aGuo, Andrew, Y.1 aBaldwin, Christopher, L.1 aEhrenberg, Adam1 aGorshkov, Alexey, V.1 aLucas, Andrew uhttps://arxiv.org/abs/2103.1582802312nas a2200217 4500008004100000245006500041210006400106260001400170490000700184520168700191100001901878700001901897700002001916700002001936700002301956700001601979700001901995700002502014700001802039856003702057 2020 eng d00aHierarchy of linear light cones with long-range interactions0 aHierarchy of linear light cones with longrange interactions c5/29/20200 v103 a

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a "linear light cone," which expands at an emergent velocity analogous to the speed of light. Yet most non-relativistic physical systems realized in nature have long-range interactions: two degrees of freedom separated by a distance r interact with potential energy V(r)∝1/rα. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: at the same α, some quantum information processing tasks are constrained by a linear light cone while others are not. In one spatial dimension, commutators of local operators ⟨ψ|[Ox(t),Oy]|ψ⟩ are negligible in every state |ψ⟩ when |x−y|≳vt, where v is finite when α>3 (Lieb-Robinson light cone); in a typical state |ψ⟩ drawn from the infinite temperature ensemble, v is finite when α>52 (Frobenius light cone); in non-interacting systems, v is finite in every state when α>2 (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones, and their tightness, also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that quantum state transfer and many-body quantum chaos are bounded by the Frobenius light cone, and therefore are poorly constrained by all Lieb-Robinson bounds.

1 aTran, Minh, C.1 aChen, Chi-Fang1 aEhrenberg, Adam1 aGuo, Andrew, Y.1 aDeshpande, Abhinav1 aHong, Yifan1 aGong, Zhe-Xuan1 aGorshkov, Alexey, V.1 aLucas, Andrew uhttps://arxiv.org/abs/2001.1150901333nas a2200157 4500008004100000245008800041210006900129260001400198520082100212100001901033700002301052700002001075700001801095700002501113856003701138 2020 eng d00aOptimal state transfer and entanglement generation in power-law interacting systems0 aOptimal state transfer and entanglement generation in powerlaw i c10/6/20203 a

We present an optimal protocol for encoding an unknown qubit state into a multiqubit Greenberger-Horne-Zeilinger-like state and, consequently, transferring quantum information in large systems exhibiting power-law (1/rα) interactions. For all power-law exponents α between d and 2d+1, where d is the dimension of the system, the protocol yields a polynomial speedup for α>2d and a superpolynomial speedup for α≤2d, compared to the state of the art. For all α>d, the protocol saturates the Lieb-Robinson bounds (up to subpolynomial corrections), thereby establishing the optimality of the protocol and the tightness of the bounds in this regime. The protocol has a wide range of applications, including in quantum sensing, quantum computing, and preparation of topologically ordered states. 

1 aTran, Minh, C.1 aDeshpande, Abhinav1 aGuo, Andrew, Y.1 aLucas, Andrew1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2010.0293001772nas a2200169 4500008004100000245006700041210006600108260001300174490000800187520126400195100002001459700001901479700002301498700002501521700001901546856003701565 2020 eng d00aSignaling and Scrambling with Strongly Long-Range Interactions0 aSignaling and Scrambling with Strongly LongRange Interactions c7/8/20200 v1023 a

Strongly long-range interacting quantum systems---those with interactions decaying as a power-law 1/rα in the distance r on a D-dimensional lattice for α≤D---have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. As a first step towards rectifying this problem, we prove two new Lieb-Robinson-type bounds that constrain the time for signaling and scrambling in strongly long-range interacting systems, for which no tight bounds were previously known. Our first bound applies to systems mappable to free-particle Hamiltonians with long-range hopping, and is saturable for α≤D/2. Our second bound pertains to generic long-range interacting spin Hamiltonians, and leads to a tight lower bound for the signaling time to extensive subsets of the system for all α<D. This result also lower-bounds the scrambling time, and suggests a path towards achieving a tight scrambling bound that can prove the long-standing fast scrambling conjecture. 

1 aGuo, Andrew, Y.1 aTran, Minh, C.1 aChilds, Andrew, M.1 aGorshkov, Alexey, V.1 aGong, Zhe-Xuan uhttps://arxiv.org/abs/1906.0266201741nas a2200205 4500008004100000245007000041210006900111260001500180490000600195520112800201100001901329700002001348700001301368700002401381700002201405700002301427700002301450700002501473856003701498 2019 eng d00aLocality and digital quantum simulation of power-law interactions0 aLocality and digital quantum simulation of powerlaw interactions c07/10/20190 v93 a

The propagation of information in non-relativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance r as a power law, 1/rα. The bound implies an effective light cone tighter than all previous bounds. Our approach is based on a technique for approximating the time evolution of a system, which was first introduced as part of a quantum simulation algorithm by Haah et al. [arXiv:1801.03922]. To bound the error of the approximation, we use a known Lieb-Robinson bound that is weaker than the bound we establish. This result brings the analysis full circle, suggesting a deep connection between Lieb-Robinson bounds and digital quantum simulation. In addition to the new Lieb-Robinson bound, our analysis also gives an error bound for the Haah et al. quantum simulation algorithm when used to simulate power-law decaying interactions. In particular, we show that the gate count of the algorithm scales with the system size better than existing algorithms when α>3D (where D is the number of dimensions).

1 aTran, Minh, C.1 aGuo, Andrew, Y.1 aSu, Yuan1 aGarrison, James, R.1 aEldredge, Zachary1 aFoss-Feig, Michael1 aChilds, Andrew, M.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1808.0522501621nas a2200181 4500008004100000245007900041210006900120260001500189490000800204520106600212100001901278700002001297700002001317700001701337700002301354700002501377856003701402 2019 eng d00aLocality and Heating in Periodically Driven, Power-law Interacting Systems0 aLocality and Heating in Periodically Driven Powerlaw Interacting c2019/11/120 v1003 a

We study the heating time in periodically driven D-dimensional systems with interactions that decay with the distance r as a power-law 1/rα. Using linear response theory, we show that the heating time is exponentially long as a function of the drive frequency for α>D. For systems that may not obey linear response theory, we use a more general Magnus-like expansion to show the existence of quasi-conserved observables, which imply exponentially long heating time, for α>2D. We also generalize a number of recent state-of-the-art Lieb-Robinson bounds for power-law systems from two-body interactions to k-body interactions and thereby obtain a longer heating time than previously established in the literature. Additionally, we conjecture that the gap between the results from the linear response theory and the Magnus-like expansion does not have physical implications, but is, rather, due to the lack of tight Lieb-Robinson bounds for power-law interactions. We show that the gap vanishes in the presence of a hypothetical, tight bound. 

1 aTran, Minh, C.1 aEhrenberg, Adam1 aGuo, Andrew, Y.1 aTitum, Paraj1 aAbanin, Dmitry, A.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1908.02773