01769nas a2200217 4500008004100000024003400041245005000075210005000125260001300175490000600188520108800194653004301282653004301325653002701368653003101395100002101426700002301447700002501470700001901495856003701514 2023 eng d aReport number: LA-UR-22-2023700aAdvantages and limitations of quantum routing0 aAdvantages and limitations of quantum routing c2/1/20230 v43 a

The Swap gate is a ubiquitous tool for moving information on quantum hardware, yet it can be considered a classical operation because it does not entangle product states. Genuinely quantum operations could outperform Swap for the task of permuting qubits within an architecture, which we call routing. We consider quantum routing in two models: (1) allowing arbitrary two-qubit unitaries, or (2) allowing Hamiltonians with norm-bounded interactions. We lower bound the circuit depth or time of quantum routing in terms of spectral properties of graphs representing the architecture interaction constraints, and give a generalized upper bound for all simple connected n-vertex graphs. In particular, we give conditions for a superpolynomial classical-quantum routing separation, which exclude graphs with a small spectral gap and graphs of bounded degree. Finally, we provide examples of a quadratic separation between gate-based and Hamiltonian routing models with a constant number of local ancillas per qubit and of an Ω(n) speedup if we also allow fast local interactions.

10aData Structures and Algorithms (cs.DS)10aFOS: Computer and information sciences10aFOS: Physical sciences10aQuantum Physics (quant-ph)1 aBapat, Aniruddha1 aChilds, Andrew, M.1 aGorshkov, Alexey, V.1 aSchoute, Eddie uhttps://arxiv.org/abs/2206.0176601840nas a2200253 4500008004100000245006100041210006000102260001400162520102500176653002701201653003901228653003101267653004701298653005201345100001401397700001301411700001701424700002301441700002501464700001801489700001801507700002401525856003701549 2022 eng d00aContinuous Symmetry Breaking in a Trapped-Ion Spin Chain0 aContinuous Symmetry Breaking in a TrappedIon Spin Chain c11/2/20223 a

One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Here we use a one-dimensional trapped-ion quantum simulator to prepare states with long-range spin order that extends over the system size of up to 23 spins and is characteristic of the continuous symmetry-breaking phase of matter. Our preparation relies on simultaneous control over an array of tightly focused individual-addressing laser beams, generating long-range spin-spin interactions. We also observe a disordered phase with frustrated correlations. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems.

10aFOS: Physical sciences10aQuantum Gases (cond-mat.quant-gas)10aQuantum Physics (quant-ph)10aStatistical Mechanics (cond-mat.stat-mech)10aStrongly Correlated Electrons (cond-mat.str-el)1 aFeng, Lei1 aKatz, Or1 aHaack, Casey1 aMaghrebi, Mohammad1 aGorshkov, Alexey, V.1 aGong, Zhexuan1 aCetina, Marko1 aMonroe, Christopher uhttps://arxiv.org/abs/2211.0127501894nas a2200193 4500008004100000245005300041210005200094260001400146520125500160653006101415653002701476653003501503653003101538100002901569700002001598700002001618700002501638856003701663 2022 eng d00aDisordered Lieb-Robinson bounds in one dimension0 aDisordered LiebRobinson bounds in one dimension c8/10/20223 a

By tightening the conventional Lieb-Robinson bounds to better handle systems which lack translation invariance, we determine the extent to which "weak links" suppress operator growth in disordered one-dimensional spin chains. In particular, we prove that ballistic growth is impossible when the distribution of coupling strengths μ(J) has a sufficiently heavy tail at small J, and identify the correct dynamical exponent to use instead. Furthermore, through a detailed analysis of the special case in which the couplings are genuinely random and independent, we find that the standard formulation of Lieb-Robinson bounds is insufficient to capture the complexity of the dynamics -- we must distinguish between bounds which hold for all sites of the chain and bounds which hold for a subsequence of sites, and we show by explicit example that these two can have dramatically different behaviors. All the same, our result for the dynamical exponent is tight, in that we prove by counterexample that there cannot exist any Lieb-Robinson bound with a smaller exponent. We close by discussing the implications of our results, both major and minor, for numerous applications ranging from quench dynamics to the structure of ground states.

10aDisordered Systems and Neural Networks (cond-mat.dis-nn)10aFOS: Physical sciences10aMathematical Physics (math-ph)10aQuantum Physics (quant-ph)1 aBaldwin, Christopher, L.1 aEhrenberg, Adam1 aGuo, Andrew, Y.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2208.0550901455nas a2200205 4500008004100000245006000041210005900101260001500160520078600175653002100961653002700982653003501009653003001044653003101074653005201105100001601157700002501173700001401198856003701212 2022 eng d00aError-correcting codes for fermionic quantum simulation0 aErrorcorrecting codes for fermionic quantum simulation c10/16/20223 a

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.

10aFOS: Mathematics10aFOS: Physical sciences10aMathematical Physics (math-ph)10aQuantum Algebra (math.QA)10aQuantum Physics (quant-ph)10aStrongly Correlated Electrons (cond-mat.str-el)1 aChen, Yu-An1 aGorshkov, Alexey, V.1 aXu, Yijia uhttps://arxiv.org/abs/2210.0841101571nas a2200205 4500008004100000245006800041210006700109260001400176520091100190653002701101653003101128100002801159700001801187700003201205700002301237700002201260700002501282700002101307856003701328 2022 eng d00aMonitoring-induced Entanglement Entropy and Sampling Complexity0 aMonitoringinduced Entanglement Entropy and Sampling Complexity c1/29/20223 a

The dynamics of open quantum systems is generally described by a master equation, which describes the loss of information into the environment. By using a simple model of uncoupled emitters, we illustrate how the recovery of this information depends on the monitoring scheme applied to register the decay clicks. The dissipative dynamics, in this case, is described by pure-state stochastic trajectories and we examine different unravelings of the same master equation. More precisely, we demonstrate how registering the sequence of clicks from spontaneously emitted photons through a linear optical interferometer induces entanglement in the trajectory states. Since this model consists of an array of single-photon emitters, we show a direct equivalence with Fock-state boson sampling and link the hardness of sampling the outcomes of the quantum jumps with the scaling of trajectory entanglement.

10aFOS: Physical sciences10aQuantum Physics (quant-ph)1 aVan Regemortel, Mathias1 aShtanko, Oles1 aGarcía-Pintos, Luis, Pedro1 aDeshpande, Abhinav1 aDehghani, Hossein1 aGorshkov, Alexey, V.1 aHafezi, Mohammad uhttps://arxiv.org/abs/2201.1267201358nas a2200181 4500008004100000245003900041210003900080260001300119520083800132653002700970653003100997100002301028700001901051700002101070700002301091700002501114856003701139 2022 eng d00aQuantum Routing with Teleportation0 aQuantum Routing with Teleportation c4/8/20223 a

We study the problem of implementing arbitrary permutations of qubits under interaction constraints in quantum systems that allow for arbitrarily fast local operations and classical communication (LOCC). In particular, we show examples of speedups over swap-based and more general unitary routing methods by distributing entanglement and using LOCC to perform quantum teleportation. We further describe an example of an interaction graph for which teleportation gives a logarithmic speedup in the worst-case routing time over swap-based routing. We also study limits on the speedup afforded by quantum teleportation - showing an O(NlogN−−−−−−−√) upper bound on the separation in routing time for any interaction graph - and give tighter bounds for some common classes of graphs.

10aFOS: Physical sciences10aQuantum Physics (quant-ph)1 aDevulapalli, Dhruv1 aSchoute, Eddie1 aBapat, Aniruddha1 aChilds, Andrew, M.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2204.0418501867nas a2200205 4500008004100000245006500041210006500106260001500171520119000186653003701376653004301413653002701456653003101483100001801514700002301532700002401555700002501579700002001604856003701624 2022 eng d00aSharp complexity phase transitions generated by entanglement0 aSharp complexity phase transitions generated by entanglement c12/20/20223 a

Entanglement is one of the physical properties of quantum systems responsible for the computational hardness of simulating quantum systems. But while the runtime of specific algorithms, notably tensor network algorithms, explicitly depends on the amount of entanglement in the system, it is unknown whether this connection runs deeper and entanglement can also cause inherent, algorithm-independent complexity. In this work, we quantitatively connect the entanglement present in certain quantum systems to the computational complexity of simulating those systems. Moreover, we completely characterize the entanglement and complexity as a function of a system parameter. Specifically, we consider the task of simulating single-qubit measurements of k--regular graph states on n qubits. We show that, as the regularity parameter is increased from 1 to n−1, there is a sharp transition from an easy regime with low entanglement to a hard regime with high entanglement at k=3, and a transition back to easy and low entanglement at k=n−3. As a key technical result, we prove a duality for the simulation complexity of regular graph states between low and high regularity.

10aComputational Complexity (cs.CC)10aFOS: Computer and information sciences10aFOS: Physical sciences10aQuantum Physics (quant-ph)1 aGhosh, Soumik1 aDeshpande, Abhinav1 aHangleiter, Dominik1 aGorshkov, Alexey, V.1 aFefferman, Bill uhttps://arxiv.org/abs/2212.1058201963nas a2200205 4500008004100000245006300041210006200104260001400166520131600180653002701496653003901523653003101562100002401593700001901617700001801636700001901654700002501673700002201698856003701720 2022 eng d00aUltrastrong light-matter interaction in a photonic crystal0 aUltrastrong lightmatter interaction in a photonic crystal c9/29/20223 a

Harnessing the interaction between light and matter at the quantum level has been a central theme in the fields of atomic physics and quantum optics, with applications from quantum computation to quantum metrology. Combining complex interactions with photonic synthetic materials provides an opportunity to investigate novel quantum phases and phenomena, establishing interesting connections to condensed matter physics. Here we explore many-body phenomena with a single artificial atom coupled to the many discrete modes of a photonic crystal. This experiment reaches the ultrastrong light-matter coupling regime using the circuit QED paradigm, by galvanically coupling a highly nonlinear fluxonium qubit to a tight-binding lattice of microwave resonators. In this regime, the transport of a single photon is strongly modified by the presence of multi-photon bound states, owing to interactions that break particle number conservation. Exploiting the effective photon-photon interactions mediated by the qubit, the driven system can be configured as a continuous reservoir of strongly-correlated photons, a resource of interest for quantum networks. This work opens exciting prospects for exploring nonlinear quantum optics at the single-photon level and stabilizing entangled many-body phases of light.

10aFOS: Physical sciences10aQuantum Gases (cond-mat.quant-gas)10aQuantum Physics (quant-ph)1 aVrajitoarea, Andrei1 aBelyansky, Ron1 aLundgren, Rex1 aWhitsitt, Seth1 aGorshkov, Alexey, V.1 aHouck, Andrew, A. uhttps://arxiv.org/abs/2209.1497201811nas a2200205 4500008004100000245005900041210005900100260001300159490000600172520120100178653002701379653003501406653003101441100001601472700002101488700001501509700001901524700002501543856003701568 2022 eng d00aUniversal scattering with general dispersion relations0 aUniversal scattering with general dispersion relations c4/6/20220 v43 a

Many synthetic quantum systems allow particles to have dispersion relations that are neither linear nor quadratic functions. Here, we explore single-particle scattering in general spatial dimension D≥1 when the density of states diverges at a specific energy. To illustrate the underlying principles in an experimentally relevant setting, we focus on waveguide quantum electrodynamics (QED) problems (i.e. D=1) with dispersion relation ϵ(k)=±|d|km, where m≥2 is an integer. For a large class of these problems for any positive integer m, we rigorously prove that when there are no bright zero-energy eigenstates, the S-matrix evaluated at an energy E→0 converges to a universal limit that is only dependent on m. We also give a generalization of a key index theorem in quantum scattering theory known as Levinson's theorem -- which relates the scattering phases to the number of bound states -- to waveguide QED scattering for these more general dispersion relations. We then extend these results to general integer dimensions D≥1, dispersion relations ϵ(k)=|k|a for a D-dimensional momentum vector k with any real positive a, and separable potential scattering.

10aFOS: Physical sciences10aMathematical Physics (math-ph)10aQuantum Physics (quant-ph)1 aWang, Yidan1 aGullans, Michael1 aNa, Xuesen1 aWhitsitt, Seth1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2103.09830