Itay Hen

The dynamics of spatial behavior: how can robust smoothing techniques help?

A variety of setups and paradigms are used in the neurosciences for automatically tracking the location of an animal in an experiment and for extracting features of interest out of it. Many of these features, however, are critically sensitive to the unavoidable noise and artifacts of tracking. Here, we examine the relevant properties of several smoothing methods and suggest a combination of methods for retrieving locations and velocities and recognizing arrests from time series of coordinates of an animals center of gravity. We accomplish these by using robust nonparametric methods, such as Running Median (RM) and locally weighted regression methods. The smoothed data may, subsequently, be segmented to obtain discrete behavioral units with proven ethological relevance. New parameters such as the length, duration, maximal speed, and acceleration of these units provide a wealth of measures for, e.g., mouse behavioral phenotyping, studies on spatial orientation in vertebrates and invertebrates, and studies on rodent hippocampal function. This methodology may have implications for many tests of spatial behavior.

Probing for quantum speedup in spin-glass problems with planted solutions

The availability of quantum annealing devices with hundreds of qubits has made the experimental demonstration of a quantum speedup for optimization problems a coveted, albeit elusive goal. Going beyond earlier studies of random Ising problems, here we introduce a method to construct a set of frustrated Ising-model optimization problems with tunable hardness. We study the performance of a D-Wave Two device (DW2) with up to 503 qubits on these problems and compare it to a suite of classical algorithms, including a highly optimized algorithm designed to compete directly with the DW2. The problems are generated around predetermined ground-state configurations, called planted solutions, which makes them particularly suitable for benchmarking purposes. The problem set exhibits properties familiar from constraint satisfaction (SAT) problems, such as a peak in the typical hardness of the problems, determined by a tunable clause density parameter. We bound the hardness regime where the DW2 device either does not or might exhibit a quantum speedup for our problem set. While we do not find evidence for a speedup for the hardest and most frustrated problems in our problem set, we cannot rule out that a speedup might exist for some of the easier, less frustrated problems. Our empirical findings pertain to the specific D-Wave processor and problem set we studied and leave open the possibility that future processors might exhibit a quantum speedup on the same problem set.

Performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs

In this paper we study the performance of the quantum adiabatic algorithm on random instances of two combinatorial optimization problems, 3-regular 3-XORSAT and 3-regular Max-Cut. The cost functions associated with these two clause-based optimization problems are similar as they are both defined on 3-regular hypergraphs. For 3-regular 3-XORSAT the clauses contain three variables and for 3-regular Max-Cut the clauses contain two variables. The quantum adiabatic algorithms we study for these two problems use interpolating Hamiltonians which are stoquastic and therefore amenable to sign-problem free quantum Monte Carlo and quantum cavity methods. Using these techniques we find that the quantum adiabatic algorithm fails to solve either of these problems efficiently, although for different reasons.

Unraveling Quantum Annealers using Classical Hardness

Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealing optimizers that contain hundreds of quantum bits. These optimizers, commonly referred to as ‘D-Wave’ chips, promise to solve practical optimization problems potentially faster than conventional ‘classical’ computers. Attempts to quantify the quantum nature of these chips have been met with both excitement and skepticism but have also brought up numerous fundamental questions pertaining to the distinguishability of experimental quantum annealers from their classical thermal counterparts. Inspired by recent results in spin-glass theory that recognize ‘temperature chaos’ as the underlying mechanism responsible for the computational intractability of hard optimization problems, we devise a general method to quantify the performance of quantum annealers on optimization problems suffering from varying degrees of temperature chaos: A superior performance of quantum annealers over classical algorithms on these may allude to the role that quantum effects play in providing speedup. We utilize our method to experimentally study the D-Wave Two chip on different temperature-chaotic problems and find, surprisingly, that its performance scales unfavorably as compared to several analogous classical algorithms. We detect, quantify and discuss several purely classical effects that possibly mask the quantum behavior of the chip.

Hexagonal Structure of Baby Skyrmion Lattices

We study the zero-temperature crystalline structure of baby Skyrmions by applying a full-field numerical minimization algorithm to baby Skyrmions placed inside different parallelogramic unit cells and imposing periodic boundary conditions. We find that within this setup, the minimal energy is obtained for the hexagonal lattice, and that in the resulting configuration the Skyrmion splits into quarter Skyrmions. In particular, we find that the energy in the hexagonal case is lower than the one obtained on the well-studied rectangular lattice, in which splitting into half Skyrmions is observed.

Period finding with adiabatic quantum computation

We outline an efficient quantum-adiabatic algorithm that solves Simons problem, in which one has to determine the “period”, or xor mask, of a given black-box function. We show that the proposed algorithm is exponentially faster than its classical counterpart and has the same complexity as the corresponding circuit-based algorithm. Together with other related studies, this result supports a conjecture that the complexity of adiabatic quantum computation is equivalent to the circuit-based computational model in a stronger sense than the well-known, proven polynomial equivalence between the two paradigms. We also discuss the importance of the algorithm and its theoretical and experimental implications for the existence of an adiabatic version of Shors integer factorization algorithm that would have the same complexity as the original algorithm.

Continuous-time quantum algorithms for unstructured problems

We consider a family of unstructured optimization problems, for which we propose a method for constructing analogue, continuous-time (not necessarily adiabatic) quantum algorithms that are faster than their classical counterparts. In this family of problems, which we refer to as ?scrambled input? problems, one has to find a minimum-cost configuration of a given integer-valued n-bit black-box function whose input values have been scrambled in some unknown way. Special cases within this set of problems are Grover?s search problem of finding a marked item in an unstructured database, certain random energy models, and the functions of the Deutsch?Josza problem. We consider a couple of examples in detail. In the first, we provide an O(1) deterministic analogue quantum algorithm to solve the seminal problem of Deutsch and Josza, in which one has to determine whether an n-bit boolean function is constant (gives 0 on all inputs or 1 on all inputs) or balanced (returns 0 on half the input states and 1 on the other half). We also study one variant of the random energy model, and show that, as one might expect, its minimum energy configuration can be found quadratically faster with a quantum adiabatic algorithm than with classical algorithms.

Temperature scaling law for quantum annealing optimizers

Physical implementations of quantum annealing unavoidably operate at finite temperatures. We point to a fundamental limitation of fixed finite temperature quantum annealers that prevents them from functioning as competitive scalable optimizers and show that to serve as optimizers annealer temperatures must be appropriately scaled down with problem size. We derive a temperature scaling law dictating that temperature must drop at the very least in a logarithmic manner but also possibly as a power law with problem size. We corroborate our results by experiment and simulations and discuss the implications of these to practical annealers.

Energetic Cost of Superadiabatic Quantum Computation

We discuss the energetic cost of superadiabatic models of quantum computation. Specifically, we investigate the energy-time complementarity in general transitionless controlled evolutions and in shortcuts to the adiabatic quantum search over an unstructured list. We show that the additional energy resources required by superadiabaticity for arbitrary controlled evolutions can be minimized by using probabilistic dynamics, so that the optimal success probability is fixed by the choice of the evolution time. In the case of analog quantum search, we show that the superadiabatic approach induces a non-oracular counter-diabatic Hamiltonian, with the same energy-time complexity as equivalent adiabatic implementations.

Review of Rotational Symmetry Breaking in Baby Skyrme Models

We discuss one of the most interesting phenomena exhibited by baby skyrmions – breaking of rotational symmetry. The topics we will deal with here include the appearance of rotational symmetry breaking in the static solutions of baby Skyrme models, both in flat as well as in curved spaces, the zero-temperature crystalline structure of baby skyrmions, and finally, the appearance of spontaneous breaking of rotational symmetry in rotating baby skyrmions. 1.1. Breaking of Rotational Symmetry in Baby Skyrme Models The Skyrme model 1,2 is an SU(2)-valued nonlinear theory for pions in (3+1) dimensions with topological soliton solutions called skyrmions. Apart from a kinetic term, the Lagrangian of the model contains a ‘Skyrme’ term which is of the fourth order in derivatives, and is used to introduce scale to the model. 3 The existence of stable solutions in the Skyrme model is a consequence of the nontrivial topology of the mapping M of the physical space into the field space at a given time, M : S 3 → SU(2) ∼ S 3 , where the physical space R 3 is compactified to S 3 by requiring the spatial infinity to be equivalent in each direction. The topology which stems from this one-point compactification allows the classification of maps into equivalence classes, each of which has a unique conserved quantity called the topological charge. The Skyrme model has an analogue in (2+1) dimensions known as the baby Skyrme model, also admitting stable field configurations of a solitonic nature. 4 Due to its lower dimension, the baby Skyrme model serves as a simplification of the original model, but nonetheless it has a physical significance in its own right, having several applications in condensed-matter physics, 5 specifically in ferromagnetic quantum Hall systems. 6–9 There, baby skyrmions describe the excitations relative to ferromagnetic quantum Hall states, in terms of a gradient expansion in the spin density, a field with properties analogous to the pion field in the 3D case. 10 The target manifold in the baby model is described by a three-dimensional vector � = (�1,�2,�3) with the constraint �� � = 1. In analogy with the (3+1)D case, the domain of this model R 2 is compactified to S 2 , yielding the topology required for 1 to appear in: G. Brown and M. Rho, Eds., Multifaceted Skyrmions, (World Scientific, Singapore,