01525nas a2200181 4500008004100000245006100041210006100102260001500163300001100178490000600189520101100195100001601206700001801222700001701240700002401257700002501281856003701306 2020 eng d00aCircuit Complexity across a Topological Phase Transition0 aCircuit Complexity across a Topological Phase Transition c03/16/2020 a0133230 v23 a

We use Nielsen's approach to quantify the circuit complexity in the one-dimensional Kitaev model. In equilibrium, we find that the circuit complexity of ground states exhibits a divergent derivative at the critical point, signaling the presence of a topological phase transition. Out of equilibrium, we study the complexity dynamics after a sudden quench, and find that the steady-state complexity exhibits nonanalytical behavior when quenched across critical points. We generalize our results to the long-range interacting case, and demonstrate that the circuit complexity correctly predicts the critical point between regions with different semi-integer topological numbers. Our results establish a connection between circuit complexity and quantum phase transitions both in and out of equilibrium, and can be easily generalized to topological phase transitions in higher dimensions. Our study opens a new avenue to using circuit complexity as a novel quantity to understand many-body systems.

1 aLiu, Fangli1 aLundgren, Rex1 aTitum, Paraj1 aGarrison, James, R.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1902.1072001493nas a2200193 4500008004100000245007800041210006900119260001400188490000600202520090100208100002201109700001401131700002101145700002401166700002301190700002401213700002501237856003701262 2020 eng d00aEntanglement Bounds on the Performance of Quantum Computing Architectures0 aEntanglement Bounds on the Performance of Quantum Computing Arch c9/22/20200 v23 a

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'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.

1 aEldredge, Zachary1 aZhou, Leo1 aBapat, Aniruddha1 aGarrison, James, R.1 aDeshpande, Abhinav1 aChong, Frederic, T.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1908.0480201741nas 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/1808.0522501814nas a2200169 4500008004100000245006700041210006600108260001400174490000800188520130400196100001701500700002201517700002401539700002501563700001901588856003701607 2019 eng d00aProbing ground-state phase transitions through quench dynamics0 aProbing groundstate phase transitions through quench dynamics c9/11/20190 v1233 a

The study of quantum phase transitions requires the preparation of a many-body system near its ground state, a challenging task for many experimental systems. The measurement of quench dynamics, on the other hand, is now a routine practice in most cold atom platforms. Here we show that quintessential ingredients of quantum phase transitions can be probed directly with quench dynamics in integrable and nearly integrable systems. As a paradigmatic example, we study global quench dynamics in a transverse-field Ising model with either short-range or long-range interactions. When the model is integrable, we discover a new dynamical critical point with a non-analytic signature in the short-range correlators. The location of the dynamical critical point matches that of the quantum critical point and can be identified using a finite-time scaling method. We extend this scaling picture to systems near integrability and demonstrate the continued existence of a dynamical critical point detectable at prethermal time scales. Therefore, our method can be used to approximately locate the quantum critical point. The scaling method is also relevant to experiments with finite time and system size, and our predictions are testable in near-term experiments with trapped ions and Rydberg atoms.

1 aTitum, Paraj1 aIosue, Joseph, T.1 aGarrison, James, R.1 aGorshkov, Alexey, V.1 aGong, Zhe-Xuan uhttps://arxiv.org/abs/1809.0637701611nas a2200205 4500008004100000245008100041210006900122260001500191490000800206520098000214100001701194700001601211700002401227700002201251700002501273700002401298700002101322700002501343856003701368 2019 eng d00aScale-Invariant Continuous Entanglement Renormalization of a Chern Insulator0 aScaleInvariant Continuous Entanglement Renormalization of a Cher c03/27/20190 v1223 a

The multi-scale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chern insulators, however, cannot have scale-invariant discrete MERA circuits with finite bond dimension. In this Letter, we show that the continuous MERA (cMERA), a modified version of MERA adapted for field theories, possesses a fixed point wavefunction with nonzero Chern number. Additionally, it is well known that reversed MERA circuits can be used to prepare quantum states efficiently in time that scales logarithmically with the size of the system. However, state preparation via MERA typically requires the advent of a full-fledged universal quantum computer. In this Letter, we demonstrate that our cMERA circuit can potentially be realized in existing analog quantum computers, i.e., an ultracold atomic Fermi gas in an optical lattice with light-induced spin-orbit coupling. 

1 aChu, Su-Kuan1 aZhu, Guanyu1 aGarrison, James, R.1 aEldredge, Zachary1 aCuriel, Ana, Valdés1 aBienias, Przemyslaw1 aSpielman, I., B.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1807.1148601623nas a2200133 4500008004100000245011100041210006900152260001400221520114300235100002601378700002401404700002401428856003701452 2019 eng d00aSite-by-site quantum state preparation algorithm for preparing vacua of fermionic lattice field theories 0 aSitebysite quantum state preparation algorithm for preparing vac c2019/11/83 a

Answering whether quantum computers can efficiently simulate quantum field theories has both theoretical and practical motivation. From the theoretical point of view, it answers the question of whether a hypothetical computer that utilizes quantum field theory would be more powerful than other quantum computers. From the practical point of view, when reliable quantum computers are eventually built, these algorithms can help us better understand the underlying physics that govern our world. In the best known quantum algorithms for simulating quantum field theories, the time scaling is dominated by initial state preparation. In this paper, we exclusively focus on state preparation and present a heuristic algorithm that can prepare the vacuum of fermionic systems in more general cases and more efficiently than previous methods. With our method, state preparation is no longer the bottleneck, as its runtime has the same asymptotic scaling with the desired precision as the remainder of the simulation algorithm. We numerically demonstrate the effectiveness of our proposed method for the 1+1 dimensional Gross-Neveu model.

1 aMoosavian, Ali, Hamed1 aGarrison, James, R.1 aJordan, Stephen, P. uhttps://arxiv.org/abs/1911.0350501449nas a2200169 4500008004100000245008800041210006900129260001500198490000800213520091700221100001601138700002401154700002001178700001901198700002501217856003701242 2018 eng d00aAsymmetric Particle Transport and Light-Cone Dynamics Induced by Anyonic Statistics0 aAsymmetric Particle Transport and LightCone Dynamics Induced by  c2018/12/200 v1213 a

We study the non-equilibrium dynamics of Abelian anyons in a one-dimensional system. We find that the interplay of anyonic statistics and interactions gives rise to spatially asymmetric particle transport together with a novel dynamical symmetry that depends on the anyonic statistical angle and the sign of interactions. Moreover, we show that anyonic statistics induces asymmetric spreading of quantum information, characterized by asymmetric light cones of out-of-time-ordered correlators. Such asymmetric dynamics is in sharp contrast with the dynamics of conventional fermions or bosons, where both the transport and information dynamics are spatially symmetric. We further discuss experiments with cold atoms where the predicted phenomena can be observed using state-of-the-art technologies. Our results pave the way toward experimentally probing anyonic statistics through non-equilibrium dynamics.

1 aLiu, Fangli1 aGarrison, James, R.1 aDeng, Dong-Ling1 aGong, Zhe-Xuan1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1809.0261401556nas a2200157 4500008004100000245006300041210006300104520105500167100002101222700002201243700002401265700002301289700002401312700002501336856003701361 2018 eng d00aUnitary Entanglement Construction in Hierarchical Networks0 aUnitary Entanglement Construction in Hierarchical Networks3 a

The construction of large-scale quantum computers will require modular architectures that allow physical resources to be localized in easy-to-manage packages. In this work, we examine the impact of different graph structures on the preparation of entangled states. We begin by explaining a formal framework, the hierarchical product, in which modular graphs can be easily constructed. This framework naturally leads us to suggest a class of graphs, which we dub hierarchies. We argue that such graphs have favorable properties for quantum information processing, such as a small diameter and small total edge weight, and use the concept of Pareto efficiency to identify promising quantum graph architectures. We present numerical and analytical results on the speed at which large entangled states can be created on nearest-neighbor grids and hierarchy graphs. We also present a scheme for performing circuit placement--the translation from circuit diagrams to machine qubits--on quantum systems whose connectivity is described by hierarchies.

1 aBapat, Aniruddha1 aEldredge, Zachary1 aGarrison, James, R.1 aDesphande, Abhinav1 aChong, Frederic, T.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1808.0787601600nas a2200145 4500008004100000245005700041210005700098260001500155490000800170520117800178100002101356700002401377700001601401856003701417 2017 eng d00aExtracting entanglement geometry from quantum states0 aExtracting entanglement geometry from quantum states c2017/10/060 v1193 a

Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks as tractable models for holographic dualities. Conventionally, the structure of the network - and hence the geometry - is largely fixed a priori by the choice of tensor network ansatz. Here, we evade this restriction and describe an unbiased approach that allows us to extract the appropriate geometry from a given quantum state. We develop an algorithm that iteratively finds a unitary circuit that transforms a given quantum state into an unentangled product state. We then analyze the structure of the resulting unitary circuits. In the case of non-interacting, critical systems in one dimension, we recover signatures of scale invariance in the unitary network, and we show that appropriately defined geodesic paths between physical degrees of freedom exhibit known properties of a hyperbolic geometry.

1 aHyatt, Katharine1 aGarrison, James, R.1 aBauer, Bela uhttps://arxiv.org/abs/1704.0197401058nas a2200133 4500008004100000245007000041210006800111520062100179100001900800700002400819700001900843700002500862856003700887 2017 eng d00aLieb-Robinson bounds on n-partite connected correlation functions0 aLiebRobinson bounds on npartite connected correlation functions3 a

Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

1 aTran, Minh, C.1 aGarrison, James, R.1 aGong, Zhe-Xuan1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1705.0435504237nas a2200157 4500008004100000245006100041210005900102260001500161490000700176520377200183100001903955700002403974700001903998700002504017856003704042 2017 eng d00aLieb-Robinson bounds on n-partite connected correlations0 aLiebRobinson bounds on npartite connected correlations c2017/11/270 v963 a

Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

1 aTran, Minh, C.1 aGarrison, James, R.1 aGong, Zhe-Xuan1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1705.0435501351nas a2200157 4500008004100000245007200041210006900113260001500182300001100197490000700208520084900215100002401064700002301088700002701111856005501138 2017 eng d00aPartial breakdown of quantum thermalization in a Hubbard-like model0 aPartial breakdown of quantum thermalization in a Hubbardlike mod c2017/02/17 a0542040 v953 a

We study the possible breakdown of quantum thermalization in a model of itinerant electrons on a one-dimensional chain without disorder, with both spin and charge degrees of freedom. The eigenstates of this model exhibit peculiar properties in the entanglement entropy, the apparent scaling of which is modified from a “volume law” to an “area law” after performing a partial, site-wise measurement on the system. These properties and others suggest that this model realizes a new, nonthermal phase of matter, known as a quantum disentangled liquid (QDL). The putative existence of this phase has striking implications for the foundations of quantum statistical mechanics.

1 aGarrison, James, R.1 aMishmash, Ryan, V.1 aFisher, Matthew, P. A. uhttp://link.aps.org/doi/10.1103/PhysRevB.95.054204