Adiabatic and time-independent universal computing on a 2D lattice with simple 2-qubit interactions

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.

Enabling fault tolerance with GST

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 and Circuits for Scientific Computing

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.

Visualising two-qubit correlations using quantum steering ellipsoids

The quantum steering ellipsoid formalism naturally extends the Bloch vector picture to provide a visualisation of two-qubit systems. If Alice and Bob share an entangled state then a local measurement by Bob steers Alice’s Bloch vector; given all possible measurements by Bob, the set of states to which Alice can be steered forms her steering ellipsoid inside the Bloch sphere. This gives us a novel geometric perspective on a number of quantum correlation measures such as entanglement, CHSH nonlocality and singlet fraction.