QuICS seminar

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.

We have developed an efficient quantum control scheme that allows for arbitrary operations on a cavity mode using strongly dispersive qubit-cavity interaction and time-dependent drives [1,2]. In addition, we have discovered a new class of bosonic quantum error correcting codes, which can correct both cavity loss and dephasing errors. Our control scheme can readily be implemented using circuit QED systems, and extended for quantum error correction to protect information encoded in bosonic codes.

Just like all other quantum information processing methods, quantum annealing requires error correction in order to become scalable. I will report on our progress in developing and analyzing quantum annealing correction methods, and their implementation using the D-Wave Two processor at USC.