01697nas a2200169 4500008004100000245008100041210006900122260001500191520115700206100002001363700002301383700001901406700002001425700002001445700002501465856003701490 2019 eng d00aComplexity phase diagram for interacting and long-range bosonic Hamiltonians0 aComplexity phase diagram for interacting and longrange bosonic H c06/10/20193 aRecent years have witnessed a growing interest in topics at the intersection of many-body physics and complexity theory. Many-body physics aims to understand and classify emergent behavior of systems with a large number of particles, while complexity theory aims to classify computational problems based on how the time required to solve the problem scales as the problem size becomes large. In this work, we use insights from complexity theory to classify phases in interacting many-body systems. Specifically, we demonstrate a "complexity phase diagram" for the Bose-Hubbard model with long-range hopping. This shows how the complexity of simulating time evolution varies according to various parameters appearing in the problem, such as the evolution time, the particle density, and the degree of locality. We find that classification of complexity phases is closely related to upper bounds on the spread of quantum correlations, and protocols to transfer quantum information in a controlled manner. Our work motivates future studies of complexity in many-body systems and its interplay with the associated physical phenomena.

1 aMaskara, Nishad1 aDeshpande, Abhinav1 aTran, Minh, C.1 aEhrenberg, Adam1 aFefferman, Bill1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1906.0417812409nas a2200169 45000080041000002450055000412100055000963000047001514900008001985201188600206100002312092700002012115700001912135700002312154700002512177856003712202 2018 eng d00aDynamical phase transitions in sampling complexity0 aDynamical phase transitions in sampling complexity a12 pages, 4 figures. v3: published version0 v1213 aWe make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a function of time t due to evolution generated by spatially local quadratic bosonic Hamiltonians. We obtain an upper bound on the scaling of t with the number of bosons n for which approximate sampling is classically efficient. We also obtain a lower bound on the scaling of t with n for which any instance of the boson sampling problem reduces to this problem and hence implies that the problem is hard, assuming the conjectures of Aaronson and Arkhipov [Proc. 43rd Annu. ACM Symp. Theory Comput. STOC '11]. This establishes a dynamical phase transition in sampling complexity. Further, we show that systems in the Anderson-localized phase are always easy to sample from at arbitrarily long times. We view these results in the light of classifying phases of physical systems based on parameters in the Hamiltonian. In doing so, we combine ideas from mathematical physics and computational complexity to gain insight into the behavior of condensed matter, atomic, molecular and optical systems.

1 aDeshpande, Abhinav1 aFefferman, Bill1 aTran, Minh, C.1 aFoss-Feig, Michael1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1703.0533212362nas a2200169 45000080041000002450055000412100055000962600015001514900008001665201187100174100002312045700002012068700001912088700002312107700002512130856003712155 2018 eng d00aDynamical phase transitions in sampling complexity0 aDynamical phase transitions in sampling complexity c2018/08/050 v1213 aWe make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a function of time t due to evolution generated by spatially local quadratic bosonic Hamiltonians. We obtain an upper bound on the scaling of t with the number of bosons n for which approximate sampling is classically efficient. We also obtain a lower bound on the scaling of t with n for which any instance of the boson sampling problem reduces to this problem and hence implies that the problem is hard, assuming the conjectures of Aaronson and Arkhipov [Proc. 43rd Annu. ACM Symp. Theory Comput. STOC '11]. This establishes a dynamical phase transition in sampling complexity. Further, we show that systems in the Anderson-localized phase are always easy to sample from at arbitrarily long times. We view these results in the light of classifying phases of physical systems based on parameters in the Hamiltonian. In doing so, we combine ideas from mathematical physics and computational complexity to gain insight into the behavior of condensed matter, atomic, molecular and optical systems.

1 aDeshpande, Abhinav1 aFefferman, Bill1 aTran, Minh, C.1 aFoss-Feig, Michael1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1703.0533205805nas a2200145 4500008004100000245004900041210004900090260001500139520537700154100002305531700002005554700002305574700002505597856003705622 2017 eng d00aComplexity of sampling as an order parameter0 aComplexity of sampling as an order parameter c2017/03/153 aWe consider the classical complexity of approximately simulating time evolution under spatially local quadratic bosonic Hamiltonians for time t. We obtain upper and lower bounds on the scaling of twith the number of bosons, n, for which simulation, cast as a sampling problem, is classically efficient and provably hard, respectively. We view these results in the light of classifying phases of physical systems based on parameters in the Hamiltonian and conjecture a link to dynamical phase transitions. In doing so, we combine ideas from mathematical physics and computational complexity to gain insight into the behavior of condensed matter systems.

1 aDeshpande, Abhinav1 aFefferman, Bill1 aFoss-Feig, Michael1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1703.0533201583nas 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=01310201095nas a2200157 4500008004100000245009500041210007100136260001500207300001100222490000700233520056700240100001600807700002300823700002300846856006800869 2014 eng d00aRemote tomography and entanglement swapping via von Neumann–Arthurs–Kelly interaction 0 aRemote tomography and entanglement swapping via von Neumann–Arth c2014/05/09 a0521070 v893 aWe propose an interaction-based method for remote tomography and entanglement swapping. Alice arranges a von Neumann-Arthurs-Kelly interaction between a system particle P and two apparatus particles A1,A2, and then transports the latter to Bob. Bob can reconstruct the unknown initial state of particle P not received by him by quadrature measurements on A1,A2. Further, if another particle P′ in Alice's hands is EPR entangled with P, it will be EPR entangled with the distant pair A1,A2. This method will be contrasted with the usual teleportation protocols.1 aRoy, S., M.1 aDeshpande, Abhinav1 aSakharwade, Nitica uhttp://journals.aps.org/pra/abstract/10.1103/PhysRevA.89.052107