QuICS seminar

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.

Over the past decade, it has become increasingly clear that there are deep connections between high energy physics and quantum information, with entanglement serving as a bridge. The Ryu-Takayanagi conjecture is one of the seminal results which translates questions about the entanglement entropy of a CFT state to the task of calculating the lengths of minimal geodesics. These computations are especially tractable for 1+1d CFTs, where there are a variety of additional symmetries.

I divide the applications of quantum communications into three

categories: quantum cryptographic functions, quantum sensor networks, and distributed quantum computation. Some of these functions are drop-in replacements for existing, classical functionality, with additional, desirable characteristics. At least one of the most exciting is an entirely new capability brought by quantum computation.