QuICS seminar

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.

Quantum mechanics is a statistical theory. It cannot with certainty predict the outcome of all single events, but instead it predicts probabilities of outcomes. This probabilistic nature of quantum theory is at odds with the determinism inherent in Newtonian physics and relativity, where outcomes can be exactly predicted given sufficient knowledge of a system.

The classical capacity of a classical channel is found by maximizing the mutual information between the input and output of a single use of the channel. In contrast, the different capacities of quantum channels are obtained by the infinite regularization of particular entropic quantities. In this talk I will review our current understanding of the need for regularization.

In this talk I will discuss a general method to obtain quantum speedups of classical algorithms which are based on the technique of backtracking, a standard approach for solving constraint satisfaction problems (CSPs). Backtracking algorithms explore a tree whose vertices are partial solutions to a CSP in an attempt to find a complete solution.

Motivated by the phenomenal experimental progress in the coherent control of superconducting resonators, I will describe theoretical progress in how to perform full quantum computation using these devices operating with d (>2) dimensional quantum states (qudits). This progress includes multiple routes to single-qudit logic, entangled state synthesis, and two-qudit logic gates.

In this talk, I will discuss correlations that can be generated by performing local measurements on bipartite quantum systems. I'll present an algebraic characterization of the set of quantum correlations which allows us to identify an easy-to-compute lower bound on the smallest Hilbert space dimension needed to generate a quantum correlation. I will then discuss some examples showing the tightness of our lower bound.

We describe a quantum algorithm that generalizes the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] to arbitrary problem specifications. We develop a state preparation routine that can initialize generic states, show how simple ancilla measurements can be used to calculate many quantities of interest, and integrate a quantum-compatible preconditioner that greatly expands the number of problems that can achieve exponential speedup over classical linear systems solvers.

Span programs are a model of computation that completely characterize quantum query complexity, and have also been used in some cases to get upper bounds on quantum time complexity. Any span program can be converted to a quantum algorithm that, given an input x, decides whether x is "accepted" by the span program, or "rejected" by the span program.