Tight Limits on Nonlocality from Nontrivial Communication Complexity; a.k.a. Reliable Computation with Asymmetric Gate Noise

It has long been known that the existence of certain superquantum nonlocal correlations would cause communication complexity to collapse. The absurdity of a world in which any nonlocal binary function could be evaluated with a constant amount of communication in turn provides a tantalizing way to distinguish quantum mechanics from incorrect theories of physics; the statement "communication complexity is nontrivial" has even been conjectured to be a concise information-theoretic axiom for characterizing quantum mechanics. We directly address the viability of that perspective with two results. First, we exhibit a nonlocal game such that communication complexity collapses in any physical theory whose maximal winning probability exceeds the quantum value. Second, we consider the venerable CHSH game that initiated this line of inquiry. In that case, the quantum value is about 0.85 but it is known that a winning probability of approximately 0.91 would collapse communication complexity. We show that the 0.91 result is the best possible using a large class of proof strategies, suggesting that the communication complexity axiom is insufficient for characterizing CHSH correlations. Both results build on new insights about reliable classical computation. The first exploits our formalization of an equivalence between amplification and reliable computation, while the second follows from a rigorous determination of the threshold for reliable computation with formulas of noise-free XOR gates and $\varepsilon$-noisy AND gates.Comment: 64 pages, 6 figure

The Role of Correlated Noise in Quantum Computing

This paper aims to give an overview of the current state of fault-tolerant quantum computing, by surveying a number of results in the field. We show that thresholds can be obtained for a simple noise model as first proved in [AB97, Kit97, KLZ98], by presenting a proof for statistically independent noise, following the presentation of Aliferis, Gottesman and Preskill [AGP06]. We also present a result by Terhal and Burkard [TB05] and later improved upon by Aliferis, Gottesman and Preskill [AGP06] that shows a threshold can still be obtained for local non-Markovian noise, where we allow the noise to be weakly correlated in space and time. We then turn to negative results, presenting work by Ben-Aroya and Ta-Shma [BT11] who showed conditional errors cannot be perfectly corrected. We end our survey by briefly mentioning some more speculative objections, as put forth by Kalai [Kal08, Kal09, Kal11]

Parameter Identification And Fault Detection For Reliable Control Of Permanent Magnet Motors

The objective of this dissertation is to develop new fault detection, identification, estimation and control algorithms that will be used to detect winding stator fault, identify the motor parameters and optimally control machine during faulty condition. Quality or proposed algorithms for Fault detection, parameter identification and control under faulty condition will validated through analytical study (Cramer-Rao bound) and simulation. Simulation will be performed for three most applied control schemes: Proportional-Integral-Derivative (PID), Direct Torque Control (DTC) and Field Oriented Control (FOC) for Permanent Magnet Machines. New detection schemes forfault detection, isolation and machine parameter identification are presented and analyzed. Different control schemes as PID, DTC, FOC for Control of PM machines have different control loops and therefore it is probable that fault detection and isolation will have different sensitivity. It is very probable that one of these control schemes (PID, DTC or FOC) are more convenient for fault detection and isolation which this dissertation will analyze through computer simulation and, if laboratory condition exist, also running a physical models

A survey of induction algorithms for machine learning

Central to all systems for machine learning from examples is an induction algorithm. The purpose of the algorithm is to generalize from a finite set of training examples a description consistent with the examples seen, and, hopefully, with the potentially infinite set of examples not seen. This paper surveys four machine learning induction algorithms. The knowledge representation schemes and a PDL description of algorithm control are emphasized. System characteristics that are peculiar to a domain of application are de-emphasized. Finally, a comparative summary of the learning algorithms is presented

Physical Limits of Heat-Bath Algorithmic Cooling

Simultaneous near-certain preparation of qubits (quantum bits) in their ground states is a key hurdle in quantum computing proposals as varied as liquid-state NMR and ion traps. “Closed-system” cooling mechanisms are of limited applicability due to the need for a continual supply of ancillas for fault tolerance and to the high initial temperatures of some systems. “Open-system” mechanisms are therefore required. We describe a new, efficient initialization procedure for such open systems. With this procedure, an $n$-qubit device that is originally maximally mixed, but is in contact with a heat bath of bias $\varepsilon \gg 2^{-n}$, can be almost perfectly initialized. This performance is optimal due to a newly discovered threshold effect: For bias $\varepsilon \ll 2^{-n}$ no cooling procedure can, even in principle (running indefinitely without any decoherence), significantly initialize even a single qubit