Interference Effects in Quantum Belief Networks

Probabilistic graphical models such as Bayesian Networks are one of the most powerful structures known by the Computer Science community for deriving probabilistic inferences. However, modern cognitive psychology has revealed that human decisions could not follow the rules of classical probability theory, because humans cannot process large amounts of data in order to make judgements. Consequently, the inferences performed are based on limited data coupled with several heuristics, leading to violations of the law of total probability. This means that probabilistic graphical models based on classical probability theory are too limited to fully simulate and explain various aspects of human decision making. Quantum probability theory was developed in order to accommodate the paradoxical findings that the classical theory could not explain. Recent findings in cognitive psychology revealed that quantum probability can fully describe human decisions in an elegant framework. Their findings suggest that, before taking a decision, human thoughts are seen as superposed waves that can interfere with each other, influencing the final decision. In this work, we propose a new Bayesian Network based on the psychological findings of cognitive scientists. We made experiments with two very well known Bayesian Networks from the literature. The results obtained revealed that the quantum like Bayesian Network can affect drastically the probabilistic inferences, specially when the levels of uncertainty of the network are very high (no pieces of evidence observed). When the levels of uncertainty are very low, then the proposed quantum like network collapses to its classical counterpart

Error-power tradeoffs in QCA design

In this work we present an error-power tradeoff study in a Quantum-dot Cellular Automata (QCA) circuit design. Device parameter variation to optimize performance is a very crucial step in the development of a technology. In this work we vary the maximum kink energy of a QCA circuit to perform an error-power tradeoff study in QCA design. We make use of graphical probabilistic models to estimate polarization errors and non-adiabatic energy dissipated in a clocked QCA circuit and demonstrate the tradeoff studies on the basic QCA circuits such as majority gate and inverter. We also show how this study can be used by comparing two single bit adder designs. The study will be of great use to designers and fabrication scientists to choose the most optimum size and spacing of QCA cells to fabricate QCA logic designs

Conservation of information and the foundations of quantum mechanics

We review a recent approach to the foundations of quantum mechanics inspired by quantum information theory. The approach is based on a general framework, which allows one to address a large class of physical theories which share basic information-theoretic features. We first illustrate two very primitive features, expressed by the axioms of causality and purity-preservation, which are satisfied by both classical and quantum theory. We then discuss the axiom of purification, which expresses a strong version of the Conservation of Information and captures the core of a vast number of protocols in quantum information. Purification is a highly non-classical feature and leads directly to the emergence of entanglement at the purely conceptual level, without any reference to the superposition principle. Supplemented by a few additional requirements, satisfied by classical and quantum theory, it provides a complete axiomatic characterization of quantum theory for finite dimensional systems.Comment: 11 pages, contribution to the Proceedings of the 3rd International Conference on New Frontiers in Physics, July 28-August 6 2014, Orthodox Academy of Crete, Kolymbari, Cret

Quantum Markov Chain Monte Carlo with Digital Dissipative Dynamics on Quantum Computers

Modeling the dynamics of a quantum system connected to the environment is critical for advancing our understanding of complex quantum processes, as most quantum processes in nature are affected by an environment. Modeling a macroscopic environment on a quantum simulator may be achieved by coupling independent ancilla qubits that facilitate energy exchange in an appropriate manner with the system and mimic an environment. This approach requires a large, and possibly exponential number of ancillary degrees of freedom which is impractical. In contrast, we develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. By combining periodic modulation of the ancilla energies, or spectral combing, with periodic reset operations, we are able to mimic interaction with a large environment and generate thermal states of interacting many-body systems. We evaluate the algorithm by simulating preparation of thermal states of the transverse Ising model. Our algorithm can also be viewed as a quantum Markov chain Monte Carlo (QMCMC) process that allows sampling of the Gibbs distribution of a multivariate model. To demonstrate this we evaluate the accuracy of sampling Gibbs distributions of simple probabilistic graphical models using the algorithm