High-fidelity measurement and quantum feedback control in circuit QED

Circuit QED is a promising solid-state quantum computing architecture. It also has excellent potential as a platform for quantum control-especially quantum feedback control-experiments. However, the current scheme for measurement in circuit QED is low efficiency and has low signal-to-noise ratio for single-shot measurements. The low quality of this measurement makes the implementation of feedback difficult, and here we propose two schemes for measurement in circuit QED architectures that can significantly improve signal-to-noise ratio and potentially achieve quantum-limited measurement. Such measurements would enable the implementation of quantum feedback protocols and we illustrate this with a simple entanglement-stabilization scheme.

A geometric approach to quantum circuit lower bounds

What is the minimal size quantum circuit required to exactly implement a specified n-qubit unitary operation, U, without the use of ancilla qubits? We show that a lower bound on the minimal size is provided by the length of the minimal geodesic between U and the identity, I, where length is defined by a suitable Finsler metric on the manifold SU(2(n)). The geodesic curves on these manifolds have the striking property that once an initial position and velocity are set, the remainder of the geodesic is completely determined by a second order differential equation known as the geodesic equation. This is in contrast with the usual case in circuit design, either classical or quantum, where being given part of an optimal circuit does not obviously assist in the design of the rest of the circuit. Geodesic analysis thus offers a potentially powerful approach to the problem of proving quantum circuit lower bounds. In this paper we construct several Finsler metrics whose minimal length geodesics provide lower bounds on quantum circuit size. For each Finsler metric we give a procedure to compute the corresponding geodesic equation. We also construct a large class of solutions to the geodesic equation, which we call Pauli geodesics, since they arise from isometries generated by the Pauli group. For any unitary U diagonal in the computational basis, we show that: (a) provided the minimal length geodesic is unique, it must be a Pauli geodesic; (b) finding the length of the minimal Pauli geodesic passing from I to U is equivalent to solving an exponential size instance of the closest vector in a lattice problem (CVP); and (c) all but a doubly exponentially small fraction of such unitaries have minimal Pauli geodesics of exponential length.

JKSimFloat V6.1 Plus: Improving flotation circuit performance by simulation

Analyzing, optimizing and designing flotation circuits using models and simulators have improved significantly over the last 15 years. Mineral flotation is now generally better understood through major advances in measuring and modeling the sub-processes within the flotation system. In addition, new and better methods have been derived to represent the floatability of particles as they move around a flotation circuit. A simulator has been developed that combines the effects of all of these sub-processes to predict the metallurgical performance of a flotation circuit. This paper presents an overview of the simulator, JKSimFloat V6.1PLUS, and its use in improving the industrial flotation plant performance. The application of the simulator at various operations is discussed with particular emphasis on the use of JKSimFloat V6.1PLUS in improving the flotation circuit performance.

JKSimFloat V6: Improving flotation circuit performance and understanding

Methods of analysing and optimising flotation circuits have improved significantly over the last 15 years. Mineral flotation is now generally better understood through major advances in measuring and modelling the sub-processes within the flotation system. JKSimFloat V6 is a user-friendly Windows-based software package incorporating simulation, mass balancing, and, currently under development, liberation data viewing and model fitting. This paper presents an overview of the development of the program up to its current status, and the plans established for the future. The application of the simulator, in particular, at various operations is also discussed with emphasis on the use of the program in improving flotation circuit performance.