Semidefinite programs (SDPs) are a framework for exact or approximate optimization that have widespread application in quantum information theory. We introduce a new method for using reductions to construct integrality gaps for SDPs. These are based on new limitations on the sum-of-squares (SoS) hierarchy in approximating two particularly important sets in quantum information theory, where previously no ω(1)-round integrality gaps were known: the set of separable (i.e. unentangled) states, or equivalently, the 2→4 norm of a matrix, and the set of quantum correlations; i.e. conditional probability distributions achievable with local measurements on a shared entangled state. In both cases no-go theorems were previously known based on computational assumptions such as the Exponential Time Hypothesis (ETH) which asserts that 3-SAT requires exponential time to solve. Our unconditional results achieve the same parameters as all of these previous results (for separable states) or as some of the previous results (for quantum correlations). In some cases we can make use of the framework of Lee-Raghavendra-Steurer (LRS) to establish integrality gaps for any SDP, not only the SoS hierarchy. Our hardness result on separable states also yields a dimension lower bound of approximate disentanglers, answering a question of Watrous and Aaronson et al. These results can be viewed as limitations on the monogamy principle, the PPT test, the ability of Tsirelson-type bounds to restrict quantum correlations, as well as the SDP hierarchies of Doherty-Parrilo-Spedalieri, Navascues-Pironio-Acin and Berta-Fawzi-Scholz.

1 aHarrow, Aram, W.1 aNatarajan, Anand1 aWu, Xiaodi uhttps://arxiv.org/abs/1612.0930601743nas a2200205 4500008004100000245007000041210006900111260001500180490000600195520112800201100002101329700002001350700001301370700002401383700002201407700002301429700002301452700002501475856003701500 2019 eng d00aLocality and digital quantum simulation of power-law interactions0 aLocality and digital quantum simulation of powerlaw interactions c07/10/20190 v93 aThe 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, Cong1 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/1808.0522501139nas a2200133 4500008004100000245004700041210004600088260001200134300001100146520077800157100001600935700001700951856003700968 2018 eng d00aLocal randomness: Examples and application0 aLocal randomness Examples and application c03/2018 a0323243 aWhen two players achieve a superclassical score at a nonlocal game, their outputs must contain intrinsic randomness. This fact has many useful implications for quantum cryptography. Recently it has been observed [C. Miller and Y. Shi, Quantum Inf. Computat. 17, 0595 (2017)] that such scores also imply the existence of local randomness—that is, randomness known to one player but not to the other. This has potential implications for cryptographic tasks between two cooperating but mistrustful players. In the current paper we bring this notion toward practical realization, by offering near-optimal bounds on local randomness for the CHSH game, and also proving the security of a cryptographic application of local randomness (single-bit certified deletion).

1 aFu, Honghao1 aMiller, Carl uhttps://arxiv.org/abs/1708.0433801923nas a2200109 4500008004100000245005100041210004900092520159800141100001801739700001901757856003701776 2018 eng d00aLocality, Quantum Fluctuations, and Scrambling0 aLocality Quantum Fluctuations and Scrambling3 aThermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be diagnosed by out-of-time-order correlators (OTOCs). However, the behavior of OTOCs of local operators in generic chaotic local Hamiltonians remains poorly understood, with some semiclassical and large N models exhibiting exponential growth of OTOCs and a sharp chaos wavefront and other random circuit models showing a diffusively broadened wavefront. In this paper we propose a unified physical picture for scrambling in chaotic local Hamiltonians. We construct a random time-dependent Hamiltonian model featuring a large N limit where the OTOC obeys a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) type equation and exhibits exponential growth and a sharp wavefront. We show that quantum fluctuations manifest as noise (distinct from the randomness of the couplings in the underlying Hamiltonian) in the FKPP equation and that the noise-averaged OTOC exhibits a cross-over to a diffusively broadened wavefront. At small N we demonstrate that operator growth dynamics, averaged over the random couplings, can be efficiently simulated for all time using matrix product state techniques. To show that time-dependent randomness is not essential to our conclusions, we push our previous matrix product operator methods to very large size and show that data for a time-independent Hamiltonian model are also consistent with a diffusively-broadened wavefront.

1 aXu, Shenglong1 aSwingle, Brian uhttps://arxiv.org/abs/1805.0537601060nas a2200133 4500008004100000245007000041210006800111520062100179100002100800700002400821700001900845700002500864856003700889 2017 eng d00aLieb-Robinson bounds on n-partite connected correlation functions0 aLiebRobinson bounds on npartite connected correlation functions3 aLieb 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, Cong1 aGarrison, James, R.1 aGong, Zhe-Xuan1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1705.0435504239nas a2200157 4500008004100000245006100041210005900102260001500161490000700176520377200183100002103955700002403976700001904000700002504019856003704044 2017 eng d00aLieb-Robinson bounds on n-partite connected correlations0 aLiebRobinson bounds on npartite connected correlations c2017/11/270 v963 aLieb 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

We show how to realize two-component fractional quantum Hall phases in monolayer graphene by optically driving the system. A laser is tuned into resonance between two Landau levels, giving rise to an effective tunneling between these two synthetic layers. Remarkably, because of this coupling, the interlayer interaction at non-zero relative angular momentum can become dominant, resembling a hollow-core pseudo-potential. In the weak tunneling regime, this interaction favors the formation of singlet states, as we explicitly show by numerical diagonalization, at fillings ν = 1/2 and ν = 2/3. We discuss possible candidate phases, including the Haldane-Rezayi phase, the interlayer Pfaffian phase, and a Fibonacci phase. This demonstrates that our method may pave the way towards the realization of non-Abelian phases, as well as the control of topological phase transitions, in graphene quantum Hall systems using optical fields and integrated photonic structures.

1 aGhazaryan, Areg1 aGraß, Tobias1 aGullans, Michael, J.1 aGhaemi, Pouyan1 aHafezi, Mohammad uhttps://arxiv.org/abs/1612.0874801669nas a2200145 4500008004100000245006300041210006300104260001500167300001100182490000700193520123200200100002201432700002201454856004701476 2016 eng d00aLandauer formulation of photon transport in driven systems0 aLandauer formulation of photon transport in driven systems c2016/10/20 a1554370 v943 aUnderstanding the behavior of light in non-equilibrium scenarios underpins much of quantum optics and optical physics. While lasers provide a severe example of a non-equilibrium problem, recent interests in the near-equilibrium physics of photon `gases', such as in Bose condensation of light or in attempts to make photonic quantum simulators, suggest one reexamine some near-equilibrium cases. Here we consider how a sinusoidal parametric coupling between two semi-infinite photonic transmission lines leads to the creation and flow of photons between the two lines. Our approach provides a photonic analogue to the Landauer transport formula, and using non-equilbrium Green's functions, we can extend it to the case of an interacting region between two photonic `leads' where the sinusoid frequency plays the role of a voltage bias. Crucially, we identify both the mathematical framework and the physical regime in which photonic transport is directly analogous to electronic transport, and regimes in which other new behavior such as two-mode squeezing can emerge.

1 aWang, Chiao-Hsuan1 aTaylor, Jacob, M. uhttps://doi.org/10.1103/PhysRevB.94.15543701583nas a2200145 4500008004100000245006900041210006900110260001500179300001100194490000900205520112300214100002301337700002301360856005401383 2016 eng d00aLattice Laughlin states on the torus from conformal field theory0 aLattice Laughlin states on the torus from conformal field theory c2016/01/28 a0131020 v20163 aConformal field theory has turned out to be a powerful tool to derive two-dimensional lattice models displaying fractional quantum Hall physics. So far most of the work has been for lattices with open boundary conditions in at least one of the two directions, but it is desirable to also be able to handle the case of periodic boundary conditions. Here, we take steps in this direction by deriving analytical expressions for a family of conformal field theory states on the torus that is closely related to the family of bosonic and fermionic Laughlin states. We compute how the states transform when a particle is moved around the torus and when the states are translated or rotated, and we provide numerical evidence in particular cases that the states become orthonormal up to a common factor for large lattices. We use these results to find the S -matrix of the states, which turns out to be the same as for the continuum Laughlin states. Finally, we show that when the states are defined on a square lattice with suitable lattice spacing they practically coincide with the Laughlin states restricted to a lattice.1 aDeshpande, Abhinav1 aNielsen, Anne, E B uhttp://stacks.iop.org/1742-5468/2016/i=1/a=01310200689nas a2200157 4500008004100000022001400041245006100055210006100116260001500177300001400192490000800206520020400214653002100418100002100439856007100460 2015 eng d a0024-379500aLaplacian matrices and Alexandrov topologies of digraphs0 aLaplacian matrices and Alexandrov topologies of digraphs c2015/09/15 a174 - 1850 v4813 aWe explore the spectral properties of digraph Laplacians and how they relate to topological properties of digraphs (such as openness, closure, and strong connectedness) under the Alexandrov topology.10aLaplacian matrix1 aOstrander, Aaron uhttp://www.sciencedirect.com/science/article/pii/S002437951500284001804nas a2200145 4500008004100000245007600041210006900117260001500186300001100201490000700212520133400219100001801553700001901571856006801590 2015 eng d00aLarge effective three-body interaction in a double-well optical lattice0 aLarge effective threebody interaction in a doublewell optical la c2015/08/03 a0236020 v923 a We study ultracold atoms in an optical lattice with two local minima per unit cell and show that the low energy states of a multi-band Bose-Hubbard (BH) Hamiltonian with only pair-wise interactions is equivalent to an effective single-band Hamiltonian with strong three-body interactions. We focus on a double-well optical lattice with a symmetric double well along the $x$ axis and single well structure along the perpendicular directions. Tunneling and two-body interaction energies are obtained from an exact band-structure calculation and numerically-constructed Wannier functions in order to construct a BH Hamiltonian spanning the lowest two bands. Our effective Hamiltonian is constructed from the ground state of the $N$-atom Hamiltonian for each unit cell obtained within the subspace spanned by the Wannier functions of two lowest bands. The model includes hopping between ground states of neighboring unit cells. We show that such an effective Hamiltonian has strong three-body interactions that can be easily tuned by changing the lattice parameters. Finally, relying on numerical mean-field simulations, we show that the effective Hamiltonian is an excellent approximation of the two-band BH Hamiltonian over a wide range of lattice parameters, both in the superfluid and Mott insulator regions. 1 aPaul, Saurabh1 aTiesinga, Eite uhttp://journals.aps.org/pra/abstract/10.1103/PhysRevA.92.02360200869nas a2200145 4500008004100000245003700041210003600078260001500114300001100129490000700140520049800147100002300645700001800668856003700686 2012 eng d00aLevinson's theorem for graphs II0 aLevinsons theorem for graphs II c2012/11/21 a1022070 v533 a We prove Levinson's theorem for scattering on an (m+n)-vertex graph with n semi-infinite paths each attached to a different vertex, generalizing a previous result for the case n=1. This theorem counts the number of bound states in terms of the winding of the determinant of the S-matrix. We also provide a proof that the bound states and incoming scattering states of the Hamiltonian together form a complete basis for the Hilbert space, generalizing another result for the case n=1. 1 aChilds, Andrew, M.1 aGosset, David uhttp://arxiv.org/abs/1203.6557v201519nas a2200217 4500008004100000245008300041210006900124260001400193490000800207520087700215100002001092700002101112700002201133700001201155700002101167700002301188700002001211700002101231700001201252856003701264 2012 eng d00aLong-lived dipolar molecules and Feshbach molecules in a 3D optical lattice 0 aLonglived dipolar molecules and Feshbach molecules in a 3D optic c2012/2/230 v1083 a We have realized long-lived ground-state polar molecules in a 3D optical lattice, with a lifetime of up to 25 s, which is limited only by off-resonant scattering of the trapping light. Starting from a 2D optical lattice, we observe that the lifetime increases dramatically as a small lattice potential is added along the tube-shaped lattice traps. The 3D optical lattice also dramatically increases the lifetime for weakly bound Feshbach molecules. For a pure gas of Feshbach molecules, we observe a lifetime of >20 s in a 3D optical lattice; this represents a 100-fold improvement over previous results. This lifetime is also limited by off-resonant scattering, the rate of which is related to the size of the Feshbach molecule. Individually trapped Feshbach molecules in the 3D lattice can be converted to pairs of K and Rb atoms and back with nearly 100% efficiency. 1 aChotia, Amodsen1 aNeyenhuis, Brian1 aMoses, Steven, A.1 aYan, Bo1 aCovey, Jacob, P.1 aFoss-Feig, Michael1 aRey, Ana, Maria1 aJin, Deborah, S.1 aYe, Jun uhttp://arxiv.org/abs/1110.4420v101053nas a2200157 4500008004100000245008200041210006900123260001500192490000800207520056400215100001900779700002200798700001900820700001900839856003700858 2011 eng d00aLaser cooling and optical detection of excitations in a LC electrical circuit0 aLaser cooling and optical detection of excitations in a LC elect c2011/12/270 v1073 aWe explore a method for laser cooling and optical detection of excitations in a LC electrical circuit. Our approach uses a nanomechanical oscillator as a transducer between optical and electronic excitations. An experimentally feasible system with the oscillator capacitively coupled to the LC and at the same time interacting with light via an optomechanical force is shown to provide strong electro-mechanical coupling. Conditions for improved sensitivity and quantum limited readout of electrical signals with such an "optical loud speaker" are outlined. 1 aTaylor, J., M.1 aSørensen, A., S.1 aMarcus, C., M.1 aPolzik, E., S. uhttp://arxiv.org/abs/1108.2035v100769nas a2200145 4500008004100000245003400041210003300075260001500108300001100123490000700134520040600141100002300547700001600570856003700586 2011 eng d00aLevinson's theorem for graphs0 aLevinsons theorem for graphs c2011/06/30 a0821020 v523 a We prove an analog of Levinson's theorem for scattering on a weighted (m+1)-vertex graph with a semi-infinite path attached to one of its vertices. In particular, we show that the number of bound states in such a scattering problem is equal to m minus half the winding number of the phase of the reflection coefficient (where each so-called half-bound state is counted as half a bound state). 1 aChilds, Andrew, M.1 aStrouse, DJ uhttp://arxiv.org/abs/1103.5077v201416nas a2200145 4500008004100000245014100041210006900182260001400251490000700265520088800272100002801160700002501188700002001213856003701233 2011 eng d00aLight storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four-wave mixing 0 aLight storage in an optically thick atomic ensemble under condit c2011/6/200 v833 a We study the modification of a traditional electromagnetically induced transparency (EIT) stored light technique that includes both EIT and four-wave mixing (FWM) in an ensemble of hot Rb atoms. The standard treatment of light storage involves the coherent and reversible mapping of one photonic mode onto a collective spin coherence. It has been shown that unwanted, competing processes such as four-wave mixing are enhanced by EIT and can significantly modify the signal optical pulse propagation. We present theoretical and experimental evidence to indicate that while a Stokes field is indeed detected upon retrieval of the signal field, any information originally encoded in a seeded Stokes field is not independently preserved during the storage process. We present a simple model that describes the propagation dynamics of the fields and the impact of FWM on the spin wave. 1 aPhillips, Nathaniel, B.1 aGorshkov, Alexey, V.1 aNovikova, Irina uhttp://arxiv.org/abs/1103.2131v101322nas a2200121 4500008004100000245006100041210006000102260001500162520094400177100002301121700001901144856003701163 2009 eng d00aLimitations on the simulation of non-sparse Hamiltonians0 aLimitations on the simulation of nonsparse Hamiltonians c2009/08/313 a The problem of simulating sparse Hamiltonians on quantum computers is well studied. The evolution of a sparse N x N Hamiltonian H for time t can be simulated using O(||Ht||poly(log N)) operations, which is essentially optimal due to a no--fast-forwarding theorem. Here, we consider non-sparse Hamiltonians and show significant limitations on their simulation. We generalize the no--fast-forwarding theorem to dense Hamiltonians, ruling out generic simulations taking time o(||Ht||), even though ||H|| is not a unique measure of the size of a dense Hamiltonian $H$. We also present a stronger limitation ruling out the possibility of generic simulations taking time poly(||Ht||,log N), showing that known simulations based on discrete-time quantum walk cannot be dramatically improved in general. On the positive side, we show that some non-sparse Hamiltonians can be simulated efficiently, such as those with graphs of small arboricity. 1 aChilds, Andrew, M.1 aKothari, Robin uhttp://arxiv.org/abs/0908.4398v201174nas a2200133 4500008004100000245005700041210005700098260001500155490000600170520076400176100002500940700002400965856005100989 2009 eng d00aLocality Bounds on Hamiltonians for Stabilizer Codes0 aLocality Bounds on Hamiltonians for Stabilizer Codes c2009/09/220 v93 aIn this paper, we study the complexity of Hamiltonians whose groundstate is a stabilizer code. We introduce various notions of k-locality of a stabilizer code, inherited from the associated stabilizer group. A choice of generators leads to a Hamiltonian with the code in its groundspace. We establish bounds on the locality of any other Hamiltonian whose groundspace contains such a code, whether or not its Pauli tensor summands commute. Our results provide insight into the cost of creating an energy gap for passive error correction and for adiabatic quantum computing. The results simplify in the cases of XZ-split codes such as Calderbank-Shor-Steane stabilizer codes and topologically-ordered stabilizer codes arising from surface cellulations. 1 aBullock, Stephen, S.1 aO'Leary, Dianne, P. uhttp://www.cs.umd.edu/~oleary/reprints/j91.pdf01144nas a2200157 4500008004100000245005200041210004800093260001400141300001400155490000700169520070100176100002400877700002300901700001800924856004400942 2007 eng d00aThe limitations of nice mutually unbiased bases0 alimitations of nice mutually unbiased bases c2006/7/11 a111 - 1230 v253 a Mutually unbiased bases of a Hilbert space can be constructed by partitioning a unitary error basis. We consider this construction when the unitary error basis is a nice error basis. We show that the number of resulting mutually unbiased bases can be at most one plus the smallest prime power contained in the dimension, and therefore that this construction cannot improve upon previous approaches. We prove this by establishing a correspondence between nice mutually unbiased bases and abelian subgroups of the index group of a nice error basis and then bounding the number of such subgroups. This bound also has implications for the construction of certain combinatorial objects called nets. 1 aAschbacher, Michael1 aChilds, Andrew, M.1 aWocjan, Pawel uhttp://arxiv.org/abs/quant-ph/0412066v101015nas a2200109 4500008004100000245007300041210006800114260001500182520065500197100001600852856003700868 2007 eng d00aThe Local Consistency Problem for Stoquastic and 1-D Quantum Systems0 aLocal Consistency Problem for Stoquastic and 1D Quantum Systems c2007/12/103 a The Local Hamiltonian problem (finding the ground state energy of a quantum system) is known to be QMA-complete. The Local Consistency problem (deciding whether descriptions of small pieces of a quantum system are consistent) is also known to be QMA-complete. Here we consider special cases of Local Hamiltonian, for ``stoquastic'' and 1-dimensional systems, that seem to be strictly easier than QMA. We show that there exist analogous special cases of Local Consistency, that have equivalent complexity (up to poly-time oracle reductions). Our main technical tool is a new reduction from Local Consistency to Local Hamiltonian, using SDP duality. 1 aLiu, Yi-Kai uhttp://arxiv.org/abs/0712.1388v200857nas a2200145 4500008004100000245003400041210002900075260001500104520048200119100001800601700001800619700001700637700002000654856003700674 2007 eng d00aThe LU-LC conjecture is false0 aLULC conjecture is false c2007/09/093 a The LU-LC conjecture is an important open problem concerning the structure of entanglement of states described in the stabilizer formalism. It states that two local unitary equivalent stabilizer states are also local Clifford equivalent. If this conjecture were true, the local equivalence of stabilizer states would be extremely easy to characterize. Unfortunately, however, based on the recent progress made by Gross and Van den Nest, we find that the conjecture is false. 1 aJi, Zhengfeng1 aChen, Jianxin1 aWei, Zhaohui1 aYing, Mingsheng uhttp://arxiv.org/abs/0709.1266v200452nas a2200121 4500008004100000245005600041210005500097100002300152700002300175700001500198700002600213856009100239 2003 eng d00aLanguage-reconfigurable universal phone recognition0 aLanguagereconfigurable universal phone recognition1 aWalker, Brenton, D1 aLackey, Bradley, C1 aMuller, JS1 aSchone, Patrick, John uhttps://quics.umd.edu/publications/language-reconfigurable-universal-phone-recognition01085nas a2200145 4500008004100000245005000041210004900091260001400140490000700154520067800161100001900839700001900858700001800877856004400895 2003 eng d00aLong-lived memory for mesoscopic quantum bits0 aLonglived memory for mesoscopic quantum bits c2003/5/200 v903 aWe describe a technique to create long-lived quantum memory for quantum bits in mesoscopic systems. Specifically we show that electronic spin coherence can be reversibly mapped onto the collective state of the surrounding nuclei. The coherent transfer can be efficient and fast and it can be used, when combined with standard resonance techniques, to reversibly store coherent superpositions on the time scale of seconds. This method can also allow for ``engineering'' entangled states of nuclear ensembles and efficiently manipulating the stored states. We investigate the feasibility of this method through a detailed analysis of the coherence properties of the system. 1 aTaylor, J., M.1 aMarcus, C., M.1 aLukin, M., D. uhttp://arxiv.org/abs/cond-mat/0301323v100715nas a2200145 4500008004100000245006300041210006300104260001500167490000700182520026200189100002300451700002600474700002500500856004400525 2003 eng d00aLower bounds on the complexity of simulating quantum gates0 aLower bounds on the complexity of simulating quantum gates c2003/11/180 v683 a We give a simple proof of a formula for the minimal time required to simulate a two-qubit unitary operation using a fixed two-qubit Hamiltonian together with fast local unitaries. We also note that a related lower bound holds for arbitrary n-qubit gates. 1 aChilds, Andrew, M.1 aHaselgrove, Henry, L.1 aNielsen, Michael, A. uhttp://arxiv.org/abs/quant-ph/0307190v100390nas a2200109 4500008004100000245005600041210005400097260001300151300001400164100001700178856008500195 1998 eng d00aA Lichnerowicz Vanishing Theorem for Finsler Spaces0 aLichnerowicz Vanishing Theorem for Finsler Spaces bSpringer a227–2431 aLackey, Brad uhttps://quics.umd.edu/publications/lichnerowicz-vanishing-theorem-finsler-spaces