Keeping the experimentalist honest: Why Bayesian state estimation is the Right Thing to Do

Robin Blume-Kohout (Caltech)

Before a quantum information processor can be useful, we need very high-precision knowledge of its state. This requirement presents new challenges for the old task of quantum state estimation. I'll present an ansatz which attempts to frame the state estimation problem rigorously. It leads us to the [somewhat surprising] conclusion that Bayesian inference is the only safe and honest way to estimate a quantum system's state. Along the way, I'll point out some [major] problems with maximum likelihood estimation (MLE), the prevailing technique.

Estimating a bilinear form given by a quantum oracle

David Bulger (Macquarie University)

Suppose $A$ is an unknown $d\times d$ matrix and we have a quantum oracle mapping $\ket{x,y,z}$ to $\ket{x,y,z+x^{\sf T}Ay}$, where $x$, $y$ and $z$ are fixed-point binary values and the addition is performed modulo the third register's range. Work in progress suggests that a single oracle call may suffice to estimate $A$. Details, and applications to optimisation, will be discussed.

Optical Cluster State Quantum Computing

Chris Dawson (University of Sydney)

Quantum complexity as geometry

Mile Gu (University of Queensland)

Quantum computers offer the possibility to solve certain computational problems exponentially faster than classical counterparts, but it remains unclear what properties of a computational problem allow for this exponential improvement. Indeed, computing the complexity of a given problem remains a challenging problem. We show that the quantum complexity of a given problem is essentially equivalent the scaling of the distance between two points in a certain curved geometry. By recasting the problem of computing quantum complexity as a geometric problem, we open up the possibility to prove limitations on the power of quantum computers, and suggest new quantum algorithms.

One-Way Quantum Computation via Continuous-Variable Cluster States

Nicolas Menicucci (University of Queensland)

I will describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, the extra requirement of a nonlinear element can be fulfilled by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself may be constructed entirely by Gaussian operations. Homodyne detection alone suffices to perform an arbitrary multi-mode Gaussian transformation via the cluster state.

Efficient quantum algorithms for simulating sparse Hamiltonians

Barry Sanders (University of Calgary)

We present an efficient quantum algorithm for simulating the evolution of an arbitrary sparse Hamiltonian for a given time in terms of a procedure for computing the matrix entries of the Hamiltonian. In particular, for a fixed number of qubits and at most a constant number of nonzero entries in each row or column, with the norm of the Hamiltonian bounded by a constant, we show that the Hamiltonian system can be simulated on a quantum computer in slightly superlinear time with log-star accesses to matrix elements of the Hamiltonian matrix. These results suggest that physical systems can be simulated on a quantum computer with a time-cost nearly linear in the physical time of evolution, and the cost of the simulation is effectively independent of the number of qubits used.

Quantum voting

John Vaccaro (Griffith University)

Simulation of quantum many-body systems using a tensor network

Guifre Vidal (University of Queensland)

I will discuss recent progress in simulating quantum many-body systems with a classical computer. A tensor network (a network made of matrices and tensors) offers a very compact description for the 2^n coefficients that characterize the state of n qubits. However, only for very specific network shapes (for instance, a chain or a tree) the relevant information of the system can be efficiently extracted.