Boulder School 2018: Student Poster Abstracts

Please note that while there is not one required or mandatory size, all posters should fit in a space no longer than 36” (91 cm) wide and preferably be no more than about 48” (122 cm) in height. Arrangements can be made for other sizes as necessary.

Session #1 Session #2 Session #3

Session #1

Deanna Abrams (Rigetti University)

Title: Crosstalk challenges in scaling up superconducting qubit lattices

Abstract: A central challenge in building a scalable quantum computer is the execution of high-fidelity operations within an architecture containing many resonant elements. As elements are added, or as the multiplicity of couplings between elements is increased, the frequency space of the design becomes crowded and device performance suffers. Characterizing and controlling crosstalk between qubit subsystems will become necessary in order to maintain high-fidelity operations as the density and connectivity of devices grows.

Mirko Amico (The City University of New York)

Title: Tuning the quantum entanglement of three qubits in a nonstationary cavity

Abstract: We have studied the quantum entanglement and the probabilities of excitations in a system of three qubits in a nonstationary cavity. This system can be physically realized with three superconducting qubits coupled to a coplanar waveguide. The entanglement between the qubits arises because of the dynamical Lamb effect, which is a novel quantum phenomenon caused by nonadiabatic fast change of the boundary conditions of the cavity. We evaluated the transition amplitudes and the probabilities of excitation of qubits due to the dynamical Lamb effect. Furthermore, we introduced the conditional concurrence and the conditional residual tangle for each fixed number of created photons in the cavity as measures of the pairwise or three-way dynamical quantum entanglement of the qubits. A prescription on how to increase the values of those quantities by controlling the frequency of the cavity photons was found.

Mark Arildsen (University of California, Santa Barbara)

Title: Finding the Generalized Gibbs Ensemble in the Real Space Entanglement Spectra of (2+1)-dimensional Chiral Topological Systems

Abstract: The numerical calculation of entanglement spectra has become a useful way to diagnose the entanglement properties of various interesting many-body ground states. For (2+1)-dimensional quantum Hall states a correspondence between the levels of the low-lying entanglement spectrum and of the physical spectrum of the edge states was observed in Ref. [1]. When the entanglement spectrum is computed with a (finite) real space entanglement cut by bipartitioning an infinite cylinder, additional physics should be visible in the splitting of the degeneracies of the lower energy levels arising from the presence of higher-order conserved quantities (irrelevant in the renormalization group sense) in the generalized Gibbs ensemble (GGE) associated to the theory on the edge. We have analyzed the real space entanglement spectra obtained in several previous numerical studies of (2+1)-dimensional models with edges hosting (1+1)-dimensional conformal field theories (CFTs) with SU(2)-level-1 symmetry, such as the chiral spin liquid. We fitted those spectra with sets of (irrelevant) conserved quantities in order to see how well they correspond to the GGE picture. These methods may also be useful in probing thermalization properties of the quantum quench that gives rise [2] to the correspondence noted by Ref. [1] (see also Refs. [3,4,5]). Future directions include examination of SU(2)-level-k CFTs for k > 1, which may have applications in the investigation of candidate non-abelian fractional quantum Hall states.

  1. H. Li and F. D. M. Haldane, Phys. Rev. Lett. 101, 010504 (2008).
  2. X.-L. Qi, H. Katsura, and A. W. W. Ludwig, Phys. Rev. Lett. 108, 196402 (2012).
  3. A. Sterdyniak et al., Phys. Rev. B 85, 125308 (2012).
  4. Brian Swingle and T. Senthil, Phys. Rev. B 86, 045117 (2012).
  5. J. Dubail, N. Read, and E. H. Rezayi, Phys. Rev. B 86, 245310 (2012).

Tanja Behrle (ETH Zurich)

Title: Repeated multi-qubit parity measurement, feedback and stabilization using a mixed-species ion crystal

Abstract: Quantum error correction involves repeated rounds of syndrome extraction and recovery, involving multi-qubit non-demolition measurements along with conditional feedback. This requires the use of systems in which, measurement and decision times are short compared to relevant decoherence timescales, and in which the act of measurement does not destroy subspace coherence or disrupt future operations. Using a mixed-species ion chain, we demonstrate repeated parity measurement on two beryllium ion “clock” qubits by coupling these to a co-trapped calcium ion. Fluorescence readout of the calcium ancilla has no direct effect on the internal states of beryllium ions but heats up the ions’ motion, from which we re-cover by sympathetically cooling the ion chain using calcium. Using the ability to rapidly make sequence branches in our classical computer control, we perform feedback on the beryllium qubits conditioned on the ancilla readout, which we use to prepare and stabilize entangled states and parity subspaces. Our work takes place in a multi-zone segmented trap setup in which we have demonstrated full quantum control of both species and multi-well ion shuttling. The methods demonstrated here could be applied to quantum error correcting codes as well as quantum metrology and are key ingredients for realizing a hybrid universal quantum computer based on trapped ions.

Alexander Bogatskiy (University of Chicago)

Title: Emergent phenomena in 2D vortex dynamics.

Abstract: We study the coarse-grained dynamics of N vortices in an ideal incompressible fluid on an arbitrary curved surface in the limit of large N and the effects of curvature on stationary solutions. Furthermore, we examine the emergent edge phenomena in discrete vorticity patches.

Megan Briggeman (University of Pittsburgh)

Title: Experimental solid state quantum simulation using 1D superlattice structures

Abstract: Quantum systems exhibit behavior that is difficult to model. One approach is to use configurable quantum systems in which the Hamiltonian can be mapped onto the system of interest. This approach, known as quantum simulation, requires a rich system whose quanta and interactions can be controlled precisely, at the level of single electrons and other degrees of freedom. Here we describe steps toward developing a quantum simulation platform using the complex oxide heterostructure LaAlO3/SrTiO3 by creating systems with features comparable to the mean spacing between electrons. The interface has strong, sign changing, gate-tunable e-e interactions that can influence the quantum ground state. We explore magnetotransport of 1D superlattices, where periodic modulation produces dispersive features not seen in control devices. These results can be compared with effective 1D model Hamiltonians to bridge experiment and theory and enable quantum simulation of more complex systems.

Amos Chan (University of Oxford)

Title: Spectral statistics in many-body quantum chaotic systems

Abstract: We study spectral statistics in spatially extended chaotic quantum many-body systems, using simple 1D lattice Floquet models without time-reversal symmetry. Computing the spectral form factor K(t) analytically and numerically, we show that it follows random matrix theory (RMT) at times longer than a many-body Thouless time, t_Th. The t_Th diverges logarithmically with system size and for a large system, two regimes clearly emerge: for t>>t_Th, the spectral form factor agrees with the RMT form.

Yevheniia Cheipesh (University Of Gottingen)

Title: Entanglement entropy with the flow equation holography method

Abstract: In this work we consider the method of the analytical calculation of min entanglement entropy introduced in [S. Kehrein, arXiv 1703.03925] for the case of the system with local interactions. A simple expression is derived that relates a unitary disentangling flow in an emergent RG-like direction to the min-entropy of the region under consideration. Explicit calculations for critical free fermions in one and two dimensions illustrate this relation. Also the corrections to the entanglement entropy induced by interactions are found. It appears that the presence of the interaction does not change the scaling of the entropy in the leading order, but adds a pre-factor that is the quasi-particle residue.

Yanzhu Chen (Stony Brook)

Title: Universal quantum computing using (Zd)3 symmetry-protected topologically ordered states

Authors: Yanzhu Chen, Abhishodh Prakash, and Tzu-Chieh Wei

Abstract: Measurement-based quantum computation describes a scheme where entanglement of resource states is utilized to simulate arbitrary quantum gates via local measurements. Recent works sug-gest that symmetry-protected topologically non-trivial, short-ranged entangled states are promising candidates for such a resource. Miller and Miyake [npj Quantum Inf. 2, 16036 (2016)] recently con-structed a particular Z2 × Z2 × Z2 symmetry-protected topological state on the Union Jack lattice and established its quantum computational universality. However, they suggested that the same construction on the triangular lattice might not lead to a universal resource. Instead of qubits, we generalize the construction to qudits and show that the resulting (d−1) qudit nontrivial Zd ×Zd ×Zd symmetry-protected topological states are universal on the triangular lattice, for d being a prime number greater than 2. The same construction also holds for other 3-colorable lattices, including the Union Jack lattice.

Su-Kuan Chu (University of Maryland: College Park

Title: Continuous Entanglement Renormalization of a Chern Insulator

Abstract: Multi-scale entanglement renormalization ansatz (MERA) is a tensor network ansatz for many-body physics which can be interpreted as a quantum circuit that renormalizes entanglement in real space at different length scales. In this paper, 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, which has been shown to be impossible within the framework of the conventional lattice MERA. We propose that this continuous circuit generated by a quench Hamiltonian may be realized experimentally by loading fermions on an optical lattice and introducing the Rashba interaction. We present detailed techniques for achieving these interactions. Our scheme can be employed to prepare the chiral topological state efficiently in time that scales logarithmically with the size of the system.

Jonathan Curtis (University of Maryland, College Park)

Title: Analogue Hawking Radiation From Interacting Bosons

Abstract: Interacting bosonic systems often admit a partitioning into two fluids: a hydrodynamic condensate and a dilute quasiparticle gas. It has been known for some time that for suitably smooth condensate textures quasiparticles may be described as propagating ballistically through an emergent spacetime fixed by the condensate. Within this description the onset of viscosity in a supersonic superfluid is equivalent to the formation of an event horizon and the production of Hawking radiation.

We study the emergence of this gravitational description in a model system consisting of interacting bosons for which the quasiparticles are described by the Bogoliubov-de Gennes equation. This enables us to microscopically analyze the mechanism underlying the production of Hawking radiation. In doing so we place a specific emphasis on near-horizon effects and consequences of the violation of Lorentz invariance.

Ceren Dag (University of Michigan)

Title: Detection of out-of-time-order correlators and information scrambling in cold atoms

Abstract: We propose a scalable locally interacting cold-atom model to detect the information scrambling and quantum chaos with out-of-time-order correlators (OTOCs). We show that our model is quantum-chaotic and demonstrates exponential decay in its early-time dynamics with power-law scaling tails for a certain parameter range. Our model also shows various lightcones from sub-ballistic to super-ballistic information propagation during the time-evolution. We describe the scrambling detection protocol where we explain how to reverse the overall sign of the Hamiltonian for the evolution backward in time. In conclusion, our model can be tuned to show different scrambling behaviors that can be probed in cold-atom experiments.

Christoph Dittel (University of Innsbruck)

Title: Totally Destructive Many-Particle Interference

Authors: Christoph Dittel, Gabriel Dufour, Mattia Walschaers, Gregor Weihs, Andreas Buchleitner, and Robert Keil

Abstract: Ever since Hong, Ou and Mandel (HOM) [C. K. Hong, Z. Y. Ou and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987)] observed the totally destructive interference of two indistinguishable photons on a two-mode beam splitter, there has been an intense effort searching for possible generalisations of this phenomenon towards growing particle and mode numbers. A range of particular cases has been found and experimentally investigated. However, whether all these distinct interference scenarios can be attributed to a single generalisation of the HOM interference has remained an outstanding question to date.

Here, we formulate a criterion that identifies unitary transformation matrices that exhibit totally destructive interference, given only the initial many-particle configuration. We show how to construct these unitaries and relate the prediction of suppressed many-particle transmission events to the simple evaluation of an associated set of eigenvalues. This formalism unifies all known cases of many-particle suppression laws under one general perspective and allows targeted design of multi-mode multi-particle setups.

Furthermore, beyond many-particle Fock states on input, we consider arbitrary pure initial states and derive suppression laws which stem from the wave function's permutation symmetry alone. Finally, we identify conditions for totally destructive interference to persist when the involved particles become partially distinguishable.

Andrew Guo (University of Maryland, College Park)

Title: Lieb-Robinson-type bounds on systems with long-ranged interactions

Abstract: In 1972, Elliot Lieb and Derek Robinson proved that non-relativistic quantum systems evolving under Hamiltonians with finite-range or exponentially decaying interactions possess finite group velocities. These “Lieb-Robinson” velocities dictate the maximal rate at which correlations may spread through the system. We extend their bound to spin systems with long-ranged, non-extensive, power-law decaying interactions. In particular, we focus on finite-sized lattices with highly non-local interactions. We apply our result to problems of entanglement generation in many-body AMO systems, and derive lower bounds on the time required to perform optimal quantum state transfer.

Connor Hann (Yale University)

Title: Robust readout of bosonic qubits in the dispersive coupling regime

Abstract: High-fidelity qubit measurements play a crucial role in quantum computation, communication, and metrology. In recent experiments, it has been shown that readout fidelity may be improved by performing repeated quantum non-demolition (QND) readouts of a qubit’s state through an ancilla. For a qubit encoded in a two-level system, the fidelity of such schemes is limited by the fact that a single error can destroy the information in the qubit. On the other hand, if a bosonic system is used, this fundamental limit could be overcome by utilizing higher levels such that a single error still leaves states distinguishable. In this work, we present a robust readout scheme, applicable to bosonic systems dispersively coupled to an ancilla, which leverages both repeated QND readouts and higher-level encodings to asymptotically suppress the effects of qubit/cavity relaxation and individual measurement infidelity. We calculate the measurement fidelity in terms of general experimental parameters, provide an information-theoretic description of the scheme, and describe its application to several encodings, including cat and binomial codes.


Session #2

Sabrina Hong (University of California: Los Angeles (UCLA))

Title: Demonstration of Universal Parametric Entangling Gates on a 19 Qubit Lattice

Abstract: A central challenge in building a scalable quantum computer is the execution of high-fidelity entangling gates within an architecture containing many resonant elements. As elements are added or multiplicity of couples is increased, the frequency space of the design becomes crowded and device performance suffers. We show that parametric coupling techniques can be used to generate selective entangling interactions for multi-qubit processors in a scalable way. By inducing coherent population exchange between adjacent qubits under frequency modulation, we implement a universal gate set for a lattice of 19 superconducting transmon qubits. 

Olivia Lanes (University of Pittsburgh)

Title: Broadband, bi-directional amplification via simultaneous parametric drives

Abstract: Quantum-limited parametric amplifiers have become a ubiquitous and necessary component of superconducting qubit research. This is due to the fact they enable near quantum limited measurements. However, they have important limitations, such as a lack of directionality and a fixed gain/bandwidth product. I will present on how one can eliminate these limitations by turning on multiple, simultaneous parametric drives. This will require a more complete understanding of the Hamiltonian and the ability to control the often forgotten higher order terms.

Nicholas LaRacuente (University of Illinois, Urbana-Champaign)

Title: Relating Coherence, Entanglement and Uncertainty via Asymmetry

Abstract: Coherence, entanglement and uncertainty are 3 of the most fundamental quantum notions. In 1991, Petz [Math Z 206, 351-361] proved an inequality for C* algebra entropies that generalizes the strong subadditivity inequality in quantum information theory and some entropic uncertainty relations. Physical interpretations of Petz's result suggest a possible unification of subsystem correlations with single-system uncertainties. A modern, information-theoretic way to view entanglement is as a resource for non-classical tasks that does not increase under local operations and classical communication. Similar approaches have emerged to quantify coherence and related notions of asymmetry. Previous work has noted links between these resource theories and sought deeper connections.

We show how coherence, entanglement and uncertainty relate to and through a generalized theory of asymmetry. We prove positivity and monotonicity of generalized asymmetry and information measures. We are developing a resource theory from these monotones that allows conversion between mutual coherence and entanglement. The primary tools of this work are commuting squares of von Neumann algebras and complex interpolation. Via similar techniques, we estimate approximate positivity and monotonicity in settings near those in which these properties hold exactly. Finally, we show how existing resource theories fit within our structure.

Joint work with Marius Junge and Li Gao.

Jong Yeon Lee (Harvard University)

Title: Emergent Multi-flavor QED3 at the Plateau Transition between Fractional Chern Insulators: Applications to graphene heterostructures

Abstract: Recent experiments in graphene heterostructures have observed Chern insulators - integer and fractional Quantum Hall states made possible by a periodic substrate potential. Here we study theoretically that the competition between different Chern insulators, which can be tuned by the amplitude of the periodic potential, leads to a new family of quantum critical points described by QED$_3$-Chern-Simons theory. At these critical points, $N_f$ flavors of Dirac fermions interact through an emergent U$(1)$ gauge theory at Chern-Simons level $K$, and remarkably, the \emph{entire} family (with any $N_f$ or $K$) can be realized at special values of the external magnetic field. Transitions between particle-hole conjugate Jain states realize ``pure'' QED$_3$ in which multiple flavors of Dirac fermion interact with a Maxwell U$(1)$ gauge field. The multi-flavor nature of the critical point leads to an emergent $\SU(N_f)$ symmetry. Specifically, at the transition from a $\nu=$1/3 to 2/3 quantum Hall state, the emergent SU(3) symmetry predicts an octet of charge density waves with enhanced susceptibilities, which is verified by DMRG numerical simulations on microscopic models applicable to graphene heterostructures. We propose experiments on Chern insulators that could resolve open questions in the study of 2+1 dimensional conformal field theories and test recent duality inspired conjectures.

Joonho Lee (University of California:Berkeley)

Title: Qualitatively Correct Description for Strong Spin Correlations via Coupled-Cluster Valence Bond Theory

Spin-coupled valence bond (SCVB) states (also known as resonating valence bond (RVB) states) provide a qualitatively correct description for strong spin correlations. Because its complexity scales exponentially with the system size, the practical limit of SCVB in quantum chemistry is 10-15 atoms. We have developed a coupled cluster (CC) approximation to SCVB which has only a quadratic number of wavefunction parameters. We name this quantum chemical model CCVB. If all the Hamiltonian elements are provided, CCVB scales only cubically with the system size and by construction it yields spin eigenfunctions. We numerically show that CCVB can successfully describe strong spin correlations of systems that are beyond the scope of SCVB or exact diagonalization. Those systems include a molecular magnet with 9 chromium atoms which can be potentially used as a building block of quantum computers.

Stephanie Matern (University of St. Andrews)

Title: Non-Markovian Decay of Nuclear Spins Coupled to Itinerant Electrons

Abstract: We study the full time evolution of a nuclear spin coupled to itinerant electrons through the hyperfine inter- action, with a particular focus on memory effects leading to a non-Markovian behavior. We show that even a noninteracting electron system causes a notable memory effect due to the restriction of fluctuations by the Fermi surface. The resulting short time dynamics of the nuclear spin is dominated by a logarithmic, temperature independent decay before crossing over to the standard, thermally induced exponential decay. But even at the longer time scales the initial non-Markovian decay causes a systematic reduction of the decay amplitude that should be detectable. Our approach is based on an expansion of the exact Nakashima-Zwanzig equation in the hyperfine coupling constant, set up to preserve the analytical structure of the memory kernel that causes the non- Markovian behavior. Our results are analytical and describe the full time range from the novel non-Markovian contributions to the well-known exponential decay expressions.

Brad Mitchell (University of California, Berkeley

Title: Running a hybrid algorithm for simulating bond-torsion in Ethylene

Abstract: Electronic structure simulations on near-term quantum hardware has potential for being one of the earliest useful applications of quantum information processing. In particular, hybrid algorithms leveraging classical resources have demonstrated promising initial results, such as the calculation of energy spectra of molecular hydrogen, as well as the ground states of lithium hydride and beryllium hydride. In this work, I discuss an experimental implementation simulating the bond-torsion energies of Ethylene in a (2,2)-active space using four superconducting qubits.

Amir MohammadAghaei (University of California, Riverside)

Title: Representing Gutzwiller-Projected Variational Wavefunctions as Matrix Product States

Abstract: Gapless free fermion states are notoriously challenging to represent with tensor network state methods. In a recent breakthrough, Fishman and White [PRB 92, 075132 (2015)] described an algorithm for efficiently representing the ground states of fermionic quadratic Hamiltonians in one spatial dimension as matrix product states (MPSs). We investigate generalizations of this method to construct efficient MPS representations of Gutzwiller-projected model variational wavefunctions for various quantum spin liquid states in 1D and quasi-1D. We compare numerical effort of these calculations to that required for traditional variational Monte Carlo techniques and analyze the feasibility of our approach for constructing good initial states for ground-state DMRG simulations of model Hamiltonians.

Chaitanya Murthy (University of California: Santa Barbara)

Title: Relaxation to Gaussian and generalized Gibbs states in systems of particles with quadratic Hamiltonians

Abstract: The generalized Gibbs ensemble (GGE) conjecture concerns the long-time behavior of local observables in thermodynamically large integrable closed quantum systems. It states that, for generic non-equilibrium initial states, local observables relax at late times to stationary values that can be computed using the GGE density matrix, which maximizes the entropy subject to constraints imposed by all local conserved charges of the integrable system.

We present an elementary, general, and semi-quantitative description of relaxation to GGEs in models of fermions or bosons with quadratic Hamiltonians. Our arguments apply to arbitrary initial states that satisfy a weak condition on clustering of correlations. We also show that similar arguments can be used to understand relaxation (or its absence) in systems with time-dependent quadratic Hamiltonians, and provide a semi-quantitative description of relaxation in quadratic periodically driven ("Floquet") systems.

Khadijeh Najafi (Georgetown University)

Title: Influence of the initial state on the evolution of quantum spin chains

Collaborators: Mohammad Ali Rajabpour, Instituto de F´ısica, Universidade Federal Fluminense and Jacopo Viti, 3ECT & Instituto Internacional de F´ısica, UFRN, Campos Universit´ario

Abstract: The Lieb-Robinson theorem proves the existence of a maximal velocity for correlations to develop for short-range hamiltonians. However, the observed propagation velocity is actually state-dependent and non-trivially predictable. We study the light-cone velocity for global quenches in the XY chain starting from a class of initial states. We point out how translation invariance of the initial state can affect the maximal speed at which correlations spread in the system and provide analytic predictions. Analogous considerations are drawn for the evolution of the entanglement entropy and the Loschmidt echo.

John Napp (Massachusetts Institute of Technology (MIT)

Title: Toward an area law for stoquastic Hamiltonians

Abstract: A Hamiltonian is defined to be stoquastic with respect to some basis if all of its off-diagonal matrix elements are real and nonpositive. Many naturally occurring Hamiltonians fall into this class, and such Hamiltonians are also relevant to the study of certain quantum algorithms. These Hamiltonians possess the property that they can be interpreted as generating a classical Markov process whose equilibrium distribution corresponds to the quantum ground state, for which all amplitudes are real and nonnegative. One might hope that proving an area law for the entanglement entropy could be possible for stoquastic Hamiltonians by exploiting this quantum-classical correspondence. Toward this goal, I will give conditions on the classical side of this correspondence which are sufficient for the corresponding quantum ground state to obey an area law for the entanglement entropy, and will give classes of stoquastic quantum Hamiltonians which obey these conditions.

Anirban Narayan Chowdhury (University of New Mexico)

Title: Improved implementation of reflection operators

Contributing Authors: Yigit Subasi, Rolando Somma

Abstract: Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation. Here we use a linear combination of unitaries and a version of amplitude amplification to approximate reflection operators over eigenvectors of unitary operators using exponentially less ancillary qubits in terms of a precision parameter. The gate complexity of our method is also comparable to that of the phase estimation approach in a certain limit of interest. Like phase estimation, our method requires the implementation of controlled unitary operations. We then extend our results to the Hamiltonian case where the target state is an eigenvector of a Hamiltonian whose matrix elements can be queried. Our results are useful in that they reduce the resources required by various quantum algorithms in the literature. Our improvements also rely on an efficient quantum algorithm to prepare a quantum state with Gaussian-like amplitudes that may be of independent interest. We also provide a lower bound on the query complexity of implementing approximate reflection operators on a quantum computer. Paper available at arXiv:1803.02466.

Silvia Pappalardi (SISSA, Scuola Internazionale Superiore di Studi Avanzati)

Title: Scrambling and entanglement dynamics in long range spin chains

Abstract:  Out of Time Ordered Correlators (OTOCs) have been suggested as a probe of scrambling (generically referred as the delocalization of quantum information) and as a measure of chaos in quantum many-body systems. We explore scrambling in connection to entanglements dynamics in generic long-range systems: in integrable, non-integrable and chaotic models. In the infinite-range Ising model, we study both bipartite and multipartite entanglement dynamics and we compare the results with the OTOCs of collective spin operators. We argue that scrambling and entanglement growth are two distinct phenomena, characterized by two different time scales.

While entanglements saturate at a time $t_{\text{Eher}}\sim \sqrt N$  at which the semi-classical approximation breaks, the OTOCs keep growing in time up to $N$. In this model, by expanding in spin waves on top of the classical solution,

we are able to device an approximated semi-analytic method that predicts the behavior of the OTOC up to  $t_{\text{Eher}}$ and  coincides with the classical limit, computed within the Truncated Wigner Approximation (TWA). This method seems to be generic for long-range interacting hamiltonians.

Furthermore, we study the kicked version of this model: the kicked top, a textbook example of quantum chaos. A expected, in the chaotic regime, the OTOC grows exponentially in time, with the same Lyapunov exponent of his semi-classical limit.

Pablo Sala (Technical University of Munich)

Title: A time-dependent variational study of (1+1)D lattice gauge theories with fermionic Gaussian states

Abstract: We introduce three unitary transformations and combined them with fermionic Gaussian states, to construct a family of variational ansatzs in order to study the in- and out- equilibrium properties of (1+1)-dimensional lattice gauge theories ((1+1)D LGT). The accuracy of this approach to describe U(1) and SU(2) (1+1)D LGT, relies on the use of these transformations which (1) eliminate the gauge field for Abelian and non-Abelian groups and (2) decouple the external charges from the dynamical fermions, catching the entanglement between the gauge and fermionic degrees of freedom. This allows us to accurately describe the equilibrium and out of equilibrium physics related to the phenomenon of string-breaking and compare our results with those obtained via Matrix Product States.

Frank Schindler (University of Zurich)

Title: Higher-Order Topological Phases

Abstract: The mathematical field of topology has become a framework to describe the low-energy electronic structure of crystalline solids. A typical feature of a bulk insulating three-dimensional topological crystal are conducting two-dimensional surface states. This constitutes the topological bulk-boundary correspondence. Here, we extend the notion of three-dimensional topological insulators to systems that host no gapless surface states, but exhibit topologically protected gapless hinge states. Their topological character is protected by spatio-temporal symmetries. We furthermore establish that the electronic structure of bismuth, an element consistently described as topologically trivial, is in fact topological and follows this generalized bulk-boundary correspondence of higher-order. The type of hinge states discussed here may be used for lossless electronic transport, spintronics, or — when proximitized with superconductivity — for topological quantum computation.

James Seddon (University College London)

Title: Resource-theoretic characterization of non-stabilizer operations

Authors: James Seddon, Earl Campbell and Mark Howard

Abstract: As experimentalists start to build prototype quantum computers, it would be useful to be able to classically simulate the operation of these devices, for the purposes of benchmarking and verification. The well-known Gottesman-Knill theorem shows that if a quantum circuit involves only stabilizer state preparations, Clifford gates, Pauli measurements, and classical randomness and feed-forward, then it can be efficiently simulated with classical computational resources. For more general quantum circuits, it is expected that the classical simulation cost will scale exponentially with the amount of non-stabilizer resources required. Nevertheless, it is hoped that for some subclass of circuit involving modest amounts of non-stabilizer resource, the exponential scaling may be tamed somewhat so that classical simulation is at least practically possible within some reasonable timeframe. It is therefore desirable to be able to quantify resource costs for non-stabilizer states and operations. This is also of interest in the context of the magic state model of fault-tolerant computation, where non-stabilizer states represent a costly experimental resource consumed in order to implement non-Clifford gates. In 2017, Howard and Campbell introduced robustness of magic, a well-behaved quantifier of non-stabilizer resource for states, which is non-increasing under operation of stabilizer circuits. Howard and Campbell also presented a classical simulation algorithm for stabilizer circuits taking non-stabilizer states as input, where the simulation cost is quantified by the robustness of magic. This immediately yields a means to quantify the resource cost associated with diagonal gates in the third level of the Clifford hierarchy, since such gates can be implemented by deterministic injection of non-stabilizer resource states. The question of how best to quantify the cost of more general non-stabilizer operations on qubits remains open. In this poster we present steps toward the extension of this framework toward general quantum operations on qubits.


Session #3

Khadijeh Najafi (Georgetown University)

Title: High accuracy many-body algorithms on quantum computers

Abstract: There is growing interest in implementing new quantum algorithms that can help us to study strongly correlated systems on a quantum computer. Although understanding the properties of the ground state of a physical system is one of the most fundamental problems, here, we focus on the realization of quantum systems at a finite temperature that is described in terms of their Green’s functions. We develop an algorithm that enables us to directly measure an equilibrium fermionic Green’s function at finite temperature without requiring adiabatic state preparation or Gibbs state preparation. We propose an efficient and fast algorithm that can be applied to systems satisfy the eigenstate thermalization (ETH) hypothesis. The Green's functions can be shown to be exact at short times, and they deviate from the exact solution at increasingly longer times for larger systems. We also discuss some cooling ideas, which allow the system to reach even lower temperatures.

Collaborators: Jim Freericks (Georgetown University), Jeff Cohn(Georgetown University, IBM), Forest yang (UC Berkeley)

Hassan Shapourian (University Of Chicago)

Title: Entanglement negativity of fermions

Abstract: The partial transpose of density matrices in many-body systems has been known as an important tool to diagnose quantum entanglement of mixed states. In particular, it can be used to define the (logarithmic) entanglement negativity for bosonic systems. Here, we introduce partial time-reversal transformation as an analog of partial transpose for fermions. Our definition naturally arises from the spacetime picture of partially transposed density matrices in which partial transpose is equivalent to reversing the arrow of time for one subsystem relative to the other subsystem. We show the success of this definition in capturing the entanglement of fermionic symmetry-protected topological phases as well as conformal field theories in (1+1) dimensions.

Kunal Sharma (Louisiana State University, Baton Rouge)

Title: Bounding the energy-constrained quantum and private capacities of phase-insensitive Gaussian channels.

Abstract: One of the main aims of quantum information theory is to characterize the capacities of quantum communication channels. Bosonic Gaussian channels are some of the most important channels to consider, as they model practical communication links in which the mediators of information are photons. Of particular interest is the bosonic thermal channel, which is a more realistic model than the pure-loss channel because it incorporates environmental imperfections. In our work, we establish different upper bounds on the energy-constrained quantum and private capacities of bosonic thermal channels. We also discuss closeness of these upper bounds to a known lower bound for different parameter regimes of background thermal radiation and transmission loss. In particular, our results establish strong limitations on any potential superadditivity of coherent information of the thermal channel. We also find improved achievable rates of private communication through bosonic thermal channels, by employing coding schemes that use of displaced thermal states. Although we mainly focus on thermal channels, using the techniques developed in our work we also establish bounds on the energy-constrained quantum and private capacities of other important Gaussian channels such as quantum amplifier channels and additive-noise Gaussian channels. We end by proving that an optimal Gaussian input state for the energy-constrained, generalized channel divergence of two particular Gaussian channels is the two-mode squeezed vacuum state that saturates the energy constraint. 

Joint work with Mark M. Wilde, Sushovit Adhikari, and Masahiro Takeoka, and available at

Ashmeet Singh (Caltech)

Title: Quantum Mereology: Factorizing Hilbert Space into Subsystems with Quasi-Classical Dynamics

Abstract: How we talk about quantum systems depends crucially on how Hilbert space is factorized, or equivalently on a set of preferred observables. We tackle the question, given a finite-dimensional Hilbert space and a Hamiltonian, without any additional structure, how does one decompose the Hilbert space into a tensor factorization of sub-systems with quasi-classical behavior? A quasi-classical decomposition has features such as low entropy states resilient to entanglement production, existence of preferred pointer observables robust under evolution, and preserving predictive power while decohering sub-systems relatively quickly. We connect these features with properties of the Hamiltonian, in particular locality, and show that arbitrary factorizations will not exhibit quasi-classicality. We make contact with conjugate operators and point out conditions under which they correspond to classical conjugate variables, characterized by classical dynamics. An algorithm which minimizes an entropy-based quantity sifting through factorizations of Hilbert space to select the quasi-classical one is outlined. We remark on the application of this formalism to the emergence of spacetime from quantum dynamics.

Kevin Slagle (Caltech)

Title: Beyond Topological Order: Fractons, Field Theory, and Universal Properties

Abstract: Recently, exactly solvable 3D lattice models (e.g. Haah's code and Chamon's model) have been discovered for a new kind of phase of matter, dubbed fracton topological order, in which the topological excitations are immobile or are bound to lines or surfaces. Unlike liquid topologically ordered phases (e.g. Z_2 gauge theory), which are only sensitive to topology (e.g. the ground state degeneracy only depends on the topology of spatial manifold), fracton orders are also highly sensitive to the geometry of the lattice, which results in remarkably new physics.

We show how the X-cube model of fracton order can be described by a quantum field theory that is analogous to BF theory, which describes toric code. Remarkably, the gauge invariance of the field theory results in the mobility restrictions of the topological excitations by imposing a new kind of geometric charge conservation, which allows well-defined braiding of point-like particles in 3D. [1708.04619]

We also show how the X-cube lattice model can be defined on more general lattices and manifold topologies via a layered construction. Lattices with curvature defects can result in a robust ground state degeneracy on a manifold with trivial topology. In a sense, rotated and rescaled lattices result in different phases of matter; however, the classification of phases can be coarsened by equating states that can be related by quasi-isometric spatial transformations and/or free 2d resource states. [1712.04511, 1712.05892]

Xueyang Song (Harvard University)

Title: Monopoles in $(2+1)$D $U(1)$ Dirac liquids and spin orders

Abstract: The spin-$1/2$ system on triangular/kagome lattice with Heisenberg antiferromagnetic interactions bears a rich phase diagram with intriguing physics due to geometrical frustration and quantum fluctuations. A low-energy effective theory with flavor $N_f=4$ two-component massless Dirac fermions coupled to $U(1)$ gauge field describes putative ground state of such systems. The critical nature of the gapless phase unifies the most studied proximate symmetry-breaking orders - valence bond solid (VBS) and noncollinear $120^.$magnetic order - by virtue of the emergent $SU(4)$ flavor symmetry. In this work, through projective symmetry group (PSG) analysis of low energy fermions and monopoles, we demonstrate the proliferation of magnetic monopoles - a topological defect operator in $U(1)$ gauge field - as essential to the proximate ordered phases. Monopoles in frustrated lattice systems have a smaller symmetry group than their corresponding fermion masses and hence determine the actual lattice patterns of spin orders after proliferating them. This contrasts with the square/honeycomb(bi-partite) lattice system, where gauge neutral fermion masses suffice to account for Neel/ VBS orders. We conjecture that this crucial difference originates from the gauge group structures of the continuum Dirac fermions on different lattices.

Nat Tantivasadakarn (Harvard University)

Title: Commuting Projector Models for Interacting Fermionic Symmetry-Protected Topological Phases

Abstract: We construct Finite Depth Local Unitaries (FDLUs) that realizes the decorated domain wall procedure for fermionic Symmetry-Protected Topological (SPT) phases. This results in commuting projector Hamiltonians, which can be thought of the "square root" phases of the bosonic SPTs. We construct explicit examples for 1D phases protected by ℤ2T×ℤ2F (class BDI) and ℤ4×ℤ4F, and 2D phases protected by ℤ2×ℤ2F. These models also provide proof that such phases can be realized by tensor networks and admit many-body localization.

Cong Minh Tran (University of Maryland, College Park)

Title: Lieb-Robinson bound and digital quantum simulation for long-range interactions 

Abstract: The propagation of information in a non-relativistic quantum system obeys a speed limit known as a Lieb-Robinson bound.  Here, we prove a new, tighter Lieb-Robinson bound for systems with interactions that decay as a power law, 1/r^alpha.  Our approach is based on a generalization of the work of Haah et al. [arXiv:1801.03922], which presented a best-in-class digital quantum simulation algorithm that takes advantage of the inherent Lieb-Robinson locality for systems with short-range interactions.  First, we generalize Haah et al.'s framework to interactions that decay as a power law. We find that their simulation algorithm scales better with system size than any existing algorithm when alpha > 3D (where D is the number of dimensions).  We also show that a modification of their framework can itself be used to prove a tighter Lieb-Robinson bound than is used in its analysis.  This result brings the analysis full circle, hinting at a deep connection between Lieb-Robinson bounds and quantum simulation.

Carrie Weidner (University of Colorado Boulder)

Title: Shaken Lattice Interferometry

Abstract: In this work, we report on results of interferometry using atoms trapped in an optical lattice. That is, we start with atoms in the ground state of a optical lattice potential V(x) = -\frac{V_0}{2} cos(2k_Lx) and by a prescribed phase modulation (“shaking”) function, transform from one momentum state to another. In this way, we implement the standard interferometric sequence of beam splitting, propagation, reflection, reverse propagation, and recombination. Through the use of a genetic algorithm [1], we computationally demonstrate a scalable accelerometer that provides information on the sign of the applied acceleration. The interferometer sensitivity is determined through the use of the classical Fisher information. Furthermore, we show that we can optimize the interferometer response to a signal of interest. In addition, we report on the experimental realization of the shaken lattice system. In particular, we demonstrate experimentally a shaken lattice interferometer where the optimization of the shaking function is done via a closed-loop optimal control algorithm [3]. We show the response of the system to an acceleration signal and first steps towards the optimization to a signal of interest [4]. Finally, we discuss progress towards scalability and improved sensitivity.

  1. S. Pötting, et al. PRA 64, 063613, (2001).
  2. C.A. Weidner, et al. PRA 95, 043624, (2017).
  3. T. Caneva et al. PRA 84, 022326, (2011).
  4. C.A. Weidner and D.Z. Anderson, accepted for publication in PRL.

Jiaxin Wu (The Ohio State University)

Title: Spin pumping and entanglement spectrum of quantum spin hall states in a pi-flux model

Abstract: We propose a new way of realizing quantum spin Hall effect in cold atoms by shaking an optical lattice, which produces an effective pi flux per plaquette on the square lattice. We demonstrate a spin pumping process during flux insertion in this quantum spin hall state. We also study the evolution of entanglement spectrum under the flux insertion, which provides a sharp signature for the quantum spin Hall effects.

Zhicheng Yang (Boston University)

Title: Entanglement Spectrum in Quantum Many-Body Dynamics and Braiding of Non-Abelian Anyons

Abstract: We study the entanglement spectrum of highly entangled states in two different contexts: (1) time evolved states after a quantum quench with Hamiltonians exhibiting different dynamical phases; (2) braiding of non-abelian anyons capable or not of universal quantum computation. In the first case, we show that the three distinct dynamical phases known as thermalization, Anderson localization, and many-body localization are marked by different patterns in the entanglement spectrum after a quantum quench. While the entanglement spectrum displays Poisson statistics for the case of Anderson localization, it displays universal Wigner-Dyson statistics for both the cases of many-body localization and thermalization, albeit within very different time scales. We further show that the complexity of entanglement, revealed by the possibility of disentangling the state through a Metropolis-like algorithm, is signaled by whether the entanglement spectrum is Poisson or Wigner-Dyson. In the second part, we study the entanglement spectrum of states generated out of braiding two types of non-abelian anyons: the Majorana fermions and the Fibonacci anyons. We show that the information on whether certain representations of the braid group associated with non-abelian anyons are capable of universal quantum computation can also be extracted from the entanglement spectrum.

Sina Zeytinoglu (ETH Zurich)

Title: Engineering Interactions Through Squeezing

Abstract: Flexibility of control of interactions in artificial quantum systems is crucial for various information processing applications including quantum simulation and communication. We study a quantum control architecture, based on squeezed vacuum, which has drastically increased flexibility as compared to the established cavity quantum electrodynamics setups. In particular, we show that the interaction strength and its spatial dependence can be controlled as a function of time. We discuss the cooperativity factor for experimentally realised squeezing parameters, and the intrinsic chirality of the framework.

Mengzhen Zhang (Yale University)

Title: From quantum teleportation to quantum transduction with adaptive control

Abstract: Continuous variable (CV) quantum teleportation is a powerful tool for perfect quantum state transfer. CV quantum teleportation can be viewed as a adaptive control scheme using infinitely squeezed ancilla states, homodyne measurement and controlled displacement for a special kind of Gaussian unitary, i.e. beam-splitter network. Based on this observation, we develop a general perfect adaptive quantum state transfer scheme for arbitrary Gaussian unitaries. A faithful quantum transducer, which can convert quantum signals between different bosonic modes, plays a crucial role in hybrid quantum networks. Current quantum transducers designs are usually based on Gaussian unitaries, where perfect quantum state transfer can only be realized by assuming stringent conditions such as impedance matching. Our adaptive scheme can help relax these stringent conditions, and make faithful quantum state transfer achievable for current transduction designs. Because of the mathematical correspondence between Gaussian operations and Clifford operations, our scheme can also be extended to discrete variable systems

Collaborations: Chang-Ling Zou (Yale, USTC), Liang Jiang (Yale)

Paper available at

Ruixing Zhang (The Pennsylvania State University)

Title: Crystalline symmetry protects Majorana.

Abstract: One of the cornerstones for topological quantum computations is Majorana zero mode, which has been intensively searched in fractional quantum Hall systems and topological superconductors. Several recent works suggest that such exotic mode can also exist in one dimensional (1D) interacting double-wire setup even without long-range superconductivity. A notable instability in these proposals comes from inter-channel single-particle tunneling that spoils the topological ground state degeneracy. Here we show that 1D Dirac semimetal (DSM) nanowire is an ideal number-conserving platform to realize such Majorana physics. By inserting magnetic flux, a DSM nanowire is driven into 1D crystalline-symmetry-protected semimetallic phase. Interaction enables the emergence of boundary Majorana zero modes, which is robust as a result of crystalline symmetry protection. We also explore several experimental consequences of Majorana signals.

Tian Zhang (Oxford University)

Title: Quantum Error Correction as a Time Crystal

Abstract: We propose a new definition of time crystals, based on extending the notion of long-range order to the temporal domain. To that end, we resort to the novel tool of a pseudo-density matrix, proposed in (Fitzsimons et al., arXiv:1302.2731), which is a quantum state that stretches across multiple times. Via this approach, we establish two results. One is that there is no time crystal, unless the evolution is purely unitary. This is analogous to the absence of discrete or continuous 1-d spatial order. The other is that temporal long-range order can be restored by quantum error correction. This time crystal with noise and error correction is similar to Floquet time crystal. Thus quantum error correction is the only viable realisation of a time crystal. NMR Experiments have been conducted to verify the theory and show that quantum error correction does make a remarkable difference in the presence of time crystals.

Hengyun (Harry) Zhou (Harvard University)

Title: Discrete Time Crystals in Black Diamond

Abstract: The interplay of periodic driving, disorder, and strong interactions has recently been predicted to result in exotic "time-crystalline" phases, which spontaneously break the discrete time-translation symmetry of the underlying drive. Here, we report the experimental observation of such discrete time-crystalline order in a driven, disordered ensemble of ~10^6 dipolar spin impurities in diamond at room-temperature. We observe long-lived temporal correlations at integer multiples of the fundamental driving period, experimentally identify the phase boundary and find that the temporal order is protected by strong interactions. We also discuss how such order can be utilized as a probe of thermalization, as well as how new pulse sequences can engineer interactions and potentially enable sensitive magnetometry with these spin ensembles.

Jingfang Zhou (University Of Tokyo)

Title: Rank of contextuality

Abstract: Quantum contextuality is one of the oldest genuinely quantum phenomena which have been intensively investigated in recent years. Considering nonlocality, the special case of contextuality, is a resource in communication task, a natural question is whether contextuality is a resource to some task. Recently contextuality was identified as a resource of some communication task, and also anticipated a role in the quantum speedup of quantum computation. Then the next question is how can we quantify or simulate contextuality as a resource? Here we provide a new measure of contextuality, rank of contextuality (RC). We defined RC as the minimum number of noncontextual box you need to switch between, when you want to simulate a contextual box. We showed the faithfulness, monotonicity under some noncontextual preserving operation, and additivity of RC. We also provide a construction of contextual box with arbitrary RC, which means a contextual box with extremely high logical contradiction. Joint work with Karol Horodecki, Pawel Horodecki,Robert Raussendorf, Ryszard Horodecki, Ravishankar Ramanathan, Emily Tyhurst.

Sisi Zhou (Yale University)

Title: A modern description of Rayleigh’s criterion

Abstract: Rayleigh's criterion states that it becomes essentially difficult to resolve two incoherent optical point sources separated by a distance below the width of point spread functions (PSF), namely in the subdiffraction limit. Recently, researchers have achieved superresolution for two incoherent point sources with equal strengths using a new type of measurement technique, surpassing Rayleigh's criterion. However, situations where more than two point sources needed to be resolved have not been fully investigated. Here we prove that for any incoherent sources with arbitrary strengths, a one- or two-dimensional image can be precisely resolved up to its second moment in the subdiffraction limit, i.e. the Fisher information (FI) is non-zero. But the FI with respect to higher order moments always tends to zero polynomially as the size of the image decreases, for any type of measurement. We call this phenomenon a modern description of Rayleigh's criterion. For PSFs under certain constraints, the optimal measurement basis estimating all moments in the subdiffraction limit for 1D weak-source imaging is constructed. Such basis also generates the optimal-scaling FI with respect to the size of the image for 2D or strong-source imaging, which achieves an overall quadratic improvement compared to direct imaging.


Guanyu Zhu (Joint Quantum Institute and Condensed Matter Theory Center, University of Maryland)

Title: Universal logical gates with constant depth circuits

Abstract: A fundamental question in the theory of quantum computation is to understand the ultimate space-time resource costs for performing a universal set of logical quantum gates to arbitrary precision. To date, all proposed schemes for implementing a universal logical gate set, such as magic state distillation or code switching, require a substantial space-time overhead, including a time overhead that necessarily diverges in the limit of vanishing logical error rate. Here we demonstrate that non-Abelian anyons in Turaev-Viro quantum error correcting codes can be moved over a distance of order the code distance by a constant depth local quantum circuit followed by a permutation of qubits. In addition, we also show how Dehn twists, which generate the whole mapping class group of a high-genus surface, can be implemented in constant time with a similar approach. When applied to the Fibonacci surface code, our results imply the possibility of a universal logical gate set implemented on encoded qubits through a constant depth unitary quantum circuit, and without increasing the asymptotic scaling of the space overhead. The resulting space-time overhead is optimal for topological codes with local syndromes. Our result reformulates the notion of anyon braiding as an effectively instantaneous process, rather than as an adiabatic, slow process.