Ian Fuss

Open parallel cooperative and competitive decision processes: a potential provenance for quantum probability decision models.

In recent years quantum probability models have been used to explain many aspects of human decision making, and as such quantum models have been considered a viable alternative to Bayesian models based on classical probability. One criticism that is often leveled at both kinds of models is that they lack a clear interpretation in terms of psychological mechanisms. In this paper we discuss the mechanistic underpinnings of a quantum walk model of human decision making and response time. The quantum walk model is compared to standard sequential sampling models, and the architectural assumptions of both are considered. In particular, we show that the quantum model has a natural interpretation in terms of a cognitive architecture that is both massively parallel and involves both co-operative (excitatory) and competitive (inhibitory) interactions between units. Additionally, we introduce a family of models that includes aspects of the classical and quantum walk models.

Cryogenic gallium phosphide acousto-optic deflectors

We present measurements of the acoustic intensity in a gallium phosphide acousto-optic deflector for the 0.6-1.3-GHz frequency range and the 8-295-K temperature range. The data show a significant increase in the available time aperture of this deflector as a result of cryogenic cooling.

Quantum walks, automata, and structured search

We explore the application of a quantum algorithm to optimisation problems over a structured space. For example, problems in automated planning can be represented as automata. These automata are shown to posses algebraic structure that can be exploited by a quantum period finding algorithm. The fact that the quantum walk also provides exponential speed-up over these same structures is of particular interest and results of our investigation will be presented.

Cryogenic large bandwidth acoustooptic deflectors

At high frequencies (~1 GHz) acoustic attenuation severely limits the time aperture of acoustooptic deflectors (AOD). It is shown in this paper that decreasing the operating temperature of an AOD to ~4 K significantly reduces the acoustic attenuation. Due to this decrease in attenuation, at a fixed bandwidth the time-bandwidth product of an AOD is increased. Measurements are presented for a longitudinal mode tellurium dioxide AOD which demonstrate up to a factor of 10 increase in the time-bandwidth product.

What are the mechanics of quantum cognition

Pothos & Busemeyer (P&B) argue that quantum probability (QP) provides a descriptive model of behavior and can also provide a rational analysis of a task. We discuss QP models using Marrs levels of analysis, arguing that they make most sense as algorithmic level theories. We also highlight the importance of having clear interpretations for basic mechanisms such as interference.

A rigorous description of optical phase

We represent the phase of an optical field by an operator valued distribution thus enabling a rigorous analysis of its statistics and new approaches to its approximation and measurement.

Analytic views of quantum walks

The first general analytic solutions for the one-dimensional quantum walk in position and momentum space are derived. These solutions reveal new symmetry features of quantum walk probability densities and insight into the behaviour of their moments. The analytic expressions for the quantum walk probability distributions provide a means of modelling quantum phenomena that is analogous to that provided by random walks in the classical domain.

A systems approach to the quantum random walk

In this paper we address the quantum random walk on the real line. Specifically, we utilize a dynamical system formulation of the walk, which leads to a momentum space expression of the probability amplitude that is a function of only the initial condition. Our focus is, for the most part, limited to the Hadamard walk. As such, this closed form expression is not as general as that given by [1]. This lack of generality is offset by the ease with which we obtain the expression, and the insight offered by it. Our closed form expression allows us to easily compute the walk pdf, hence the cdf (cumulative distribution function). It is shown that the cdf converges to its limiting form relatively quickly. We push the simple mathematics in an to attempt to obtain a closed form expression for this form. But it becomes too involved to take it to completion in this paper, without running the risk of losing appreciation for the simplicity of our approach.

Digital communication and quantum phase detection

A theory of symmetric phase shift keying is developed using quantum mechanics. The minimum average probability of error is then determined for phase-shift-keyed optical communication systems which use physical states. It is shown that this minimum error is achieved by using states which are represented in the number state basis by discrete prolate spheroidal sequences.<<ETX>>