**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 (

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 **

Chris Dawson (

**Quantum complexity as geometry**

Mile Gu (

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 (

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 (

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 (

**Simulation of quantum many-body systems using a tensor
network**

Guifre Vidal (

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.