N/A

We study (d−1)-dimensional excitations in the d-dimensional color code that are created by transversal application of the R_d phase operators on connected subregions of qubits. We find that such excitations are superpositions of electric charges and can be characterized by fixed-point wavefunctions of (d−1) dimensional bosonic SPT phases with (Z_2)^(\otimes d) symmetry.

Quantum field theory provides the framework for the Standard Model of particle physics and plays a key role in physics. However, calculations are generally computationally complex and limited to weak interaction strengths. I'll describe polynomial-time quantum algorithms for computing relativistic scattering amplitudes in both scalar and fermionic quantum field theories. The algorithms achieve exponential speedup over known classical methods. One of the motivations for this work comes from computational complexity theory.

In this talk I’ll present recent results relating the time of preparation of thermal states by quantum Gibbs samplers, the analogue of classical metropolis sampling. In particular I will connect the efficiency of quantum Gibbs samplers to the static properties of the thermal state, in particular whether it has a finite correlation length.

In recent years, deep learning has achieved great success in many areas of artificial intelligence, such as computer vision, speech recognition, natural language processing, etc. Its central idea is to build a hierarchy of successively more abstract representations of data (e.g. image, audio, text) by using a neural network with many layers. Training such a deep neural network, however, can be very time-consuming. In this talk, we will investigate whether quantum computing can make this process more efficient.

One of the best known problem that a quantum computer is expected to solve more efficiently than a classical one is the simulation of quantum systems. While significant work has considered the case of discrete, finite dimensional quantum systems, the study of fast quantum simulation methods for continuous-variable systems has only received little attention. In this talk, I will present quantum methods to simulate the time evolution of two quantum systems, namely the quantum harmonic oscillator and the quantum particle in a quartic potential.

We propose a quantum voting system in the spirit of quantum games such as the quantum Prisoner’s Dilemma. Our scheme violates a quantum analogue of Arrow’s Impossibility Theorem, which states that every (classical) constitution endowed with three innocuous-seeming properties is a dictatorship. Superpositions, interference, and entanglement of votes feature in voting tactics available to quantum voters but not to classical. (This work was conducted with Ning Bao. Reference: arXiv:1501.00458v1.)

The celebrated theorem of A. Fine implies that the CHSH inequality is violated if and only if the joint probability distribution for the quadruples of observables involved in the EPR-Bohm-Bell experiment does not exist, i.e., it is impossible to use the classical probabilistic model (Kolmogorov, 1933). In this talk we demonstrate that, in spite of Fine's theorem, the results of observations in the EPR-Bohm-Bell experiment can be described in the classical probabilistic framework.

In this talk I will give a broad overview of the topics I am interested in and was working on, and then concentrate on one recent result. Specifically, I will discuss an approach to the optimization of quantum Clifford+T circuits. The algorithm works in two stages: first, it efficiently (in polynomial time) optimizes {CNOT ,T} circuits with performance guarantee (optimally), and secondly, it is modified to handle Hadamard gates.

I'll give a broad overview of my research over the last decade aimed at understanding the relationship between computational complexity and physics—and in particular, the capabilities and limitations of quantum computers.

The study of ground state energies of local Hamiltonians is a natural generalization of the study of classical constraint satisfaction problems, and has thus played a fundamental role in quantum complexity theory. In this talk, we take a new direction by introducing the physically well-motivated notion of "ground state connectivity" of local Hamiltonians, which can be thought of as a quantum generalization of classical reconfiguration problems. In particular, ground state connectivity captures problems in areas ranging from quantum stabilizer codes to quantum memories.