QuICS Special Seminar

We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this construction, the movement of one particle is controlled by the presence or absence of other particles, an effective quantum field effect transistor that allows the construction of controlled-NOT and controlled-rotation gates.

Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods.

The most powerful existing threshold theorems for fault tolerant quantum computing require one- and two-qubit gates that are within 1e-3 to 1e-4 (in diamond norm distance) of ideal. Certifying that an experimental qubit system achieves this threshold thus requires (1) characterizing the full process matrices of its gates, and (2), assigning reliable uncertainty regions. These requirements must be met for both one- and two-qubit gates, with errors that are small in the diamond norm distance.

Quantum algorithms for scientific computing require modules implementing fundamental functions, such as inverses, logarithms, trigonometric functions, and others. We require modules that have a well-controlled numerical error, that are uniformly scalable and reversible (unitary), and that can be implemented efficiently. Such modules are an important first step in the development of quantum libraries and standards for numerical computation.

We introduce a new method for proving limitations on the ability of semidefinite programs (SDPs) to approximately solve optimization problems. We use this to show specifically that SDPs have limited ability to approximate two particularly important sets in quantum information theory:

1. The set of separable (i.e. unentangled) states.

2. The set of quantum correlations; i.e. conditional probability distributions achievable with local measurements on a shared entangled state.

Fault-tolerant quantum computation (FTQC) can be done in principle: the threshold theorems show that, for sufficiently low error rates, it is possible to do quantum computations of arbitrary size. However, current schemes that allow such scaling--using concatenated or surface codes--require very large overhead to achieve quantum computation at realistic error rates. One approach to reduce this overhead is to encode multiple logical qubits in a single code block.

Quantum information processing aims to leverage the properties of quantum mechanics to manipulate information in ways that are not otherwise possible. This would enable, for example, quantum computers that could solve certain problems exponentially faster than a conventional supercomputer. One promising approach for building such a machine is to use gated silicon quantum dots. In the approach taken at HRL Laboratories, individual electrons are trapped in a gated potential well at the barrier of a Si/SiGe heterostructure.

Quantum theory is a theory of information, imposing new -- and often counter-intuitive -- rules on how it can be acquired, processed and shared. To understand these rules, one can draw on the framework of causal Bayesian networks, which successfully addresses questions concerning knowledge, causation and inference in the context of classical statistics. The process of adapting classical causal models to accommodate quantum theory provides a new perspective on the fundamental differences between the two.

We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators --- for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically-local bounded-strength Hamiltonian.

Suppose you have access to iid samples from an unknown probability distribution $p = (p_1, …, p_d)$ on $[d]$, and you want to learn or test something about it. For example, if one wants to estimate $p$ itself, then the empirical distribution will suffice when the number of samples, $n$, is $O(d/epsilon^2)$. In general, you can ask many more specific questions about $p$---Is it close to some known distribution $q$? Does it have high entropy? etc.