There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The organization of behavior: A neuropsychological theory

The Personal Interview

What is modal logic

IEEE transactions on computer-aided design of integrated circuits and systems : a publication of the IEEE Circuits and Systems Society

Test pattern generation is an electronic design automation tool that attempts to find an input (or test) sequence that, when applied to a digital circuit, enables one to distinguish between the correct circuit behavior and the faulty behavior caused by particular faults. The effectiveness of this classical method is measured by the fault coverage achieved for the fault model and the number of generated vectors, which should be directly proportional to test application time. This work address the quantum process validation problem by considering the quantum mechanical adaptation of test pattern generation methods used to test classical circuits. We found that quantum mechanics allows one to execute multiple test vectors concurrently, making each gate realized in the process act on a complete set of characteristic states in space/time complexity that breaks classical testability lower bounds.

/pdf/fault-testing-quantum-switching-circuits-3tvseibo2b.pdf

Fault Testing Quantum Switching Circuits

This paper investigates the synthesis of quantum networks built to realize hybrid switching circuits in the absence of ancilla qudits. We prove that all mixed qudit, binary/ternary, circuits can be constructed by hybrid Not and Multiple-Controlled-Not gates without any ancilla qudits.

Universality of hybrid quantum gates and synthesis without ancilla qudits

This paper presents a new approach to reversible cascade evolution based on a 3D cellular automaton. As a research platform we used the ATR's CAMBrain Machine (CBM). Reversible circuits are investigated because they are expected to dissipate much less energy than their irreversible counterparts. One day they will be implemented as nano-scale 3-dimensional chips. A circuit is reversible if the number of its inputs equals the number of its outputs and there is a one-to-one mapping between spaces of input vectors and output vectors. This paper provides: (1) a brief introduction to reversible logic concentrating on definitions and properties of the Feynman, Toffoli, Fredkin gates; (2) an introduction to the 3D cellular logic machine (CLM) that is a cellular automaton with frozen and pulsing state variables; and (3) a collection of reversible structures evolved using a dedicated GA and located in the CBM using the NeuroMaze 3.0 Pro, a software tool for computer-aided design of CBM-style structures.

/pdf/evolved-reversible-cascades-realized-on-the-cam-brain-51n3wuk22b.pdf

Evolved reversible cascades realized on the CAM-brain machine

Quantum Finite State Machines (QFSM) are a well known model of computation that was originally formalized by Watrous [Wat95a, Wat95b, Wat97], Kondacs [KW97] and more generally Quantum Turing Machines (QTM) have been described by Bernstein [BV97]. In particular the 2-way QFSM have been shown to be more powerful than classical FSM [KW97]. Thus the interest in quantum computational models of automata and machines is not only theoretical but has also possible applications realization of future quantum computer and robotics controllers. In this chapter we present the evolutionary approach to the synthesis of QFSM’s specified by a quantum circuits. This approach was originally proposed by [LP09] and is possible on yet only theoretical basis. In particular this approach requires a selective qubit-initialization in a quantum register. In contrast the current methodology and approaches to practical Quantum Computation, the current practical realization of quantum computation always starts with the initialization of the whole quantum register and terminates by the measurement of either all of the qubits or by the measurement of a given subset of qubits. Moreover in general there is no reuse of any element of the quantum register. In this text we analyze in details what type of QFSM can be successfully synthesized. The evolutionary approach will evaluate the results based on both the correctness and the cost of the evolved machines. Multiple parameters such as type of error evaluation, synthesis constraints and evolutionary operators will be discussed when evaluating to the obtained results. In particular we show how to synthesize QFSMs as sequence detectors and illustrate their functionality both in the quantum world and in the classical (observable) world. The application of the synthesized quantum devices is illustrated by the analysis of recognized sequences. Finally, we provide analytic method for the used evolutionary approach and we describe the experimental protocol, and its heuristic improvements. We also discuss the results. In addition, we investigate the following aspects of the Evolutionary Quantum Logic Synthesis: • Quantum probabilistic FSM and Reversible FSM. • Hardware acceleration for the Fitness evaluation using CBLAS [cbl] and using CUBLAS [cud] (CUDA[cud] implemented Basic Linear Algebra Subprograms (BLAS)[cbl] subroutines).

/pdf/evolutionary-logic-synthesis-of-quantum-finite-state-rowi192c22.pdf

Evolutionary Logic Synthesis of Quantum Finite State Machines for Sequence Detection

A novel approach utilising the emerging memristor technology is introduced for realising a 2-input primitive XNOR gate. This gate enables in-memory computing and is used as a building block of mult...

Marek Perkowski

Papers

Fault Testing Quantum Switching Circuits

Universality of hybrid quantum gates and synthesis without ancilla qudits

Evolved reversible cascades realized on the CAM-brain machine

Evolutionary Logic Synthesis of Quantum Finite State Machines for Sequence Detection

Multi-input Volistor Logic XNOR Gates