Related papers: Boolean Functions, Quantum Gates, Hamilton Operato…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and circuits are naturally interpretable in such structures. We consider…
We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modelled classically. This question is useful for providing upper bounds on fault tolerant thresholds, and for understanding…
We derive a spectral interpretation of the pivot operation on a graph and generalise this operation to hypergraphs. We establish lower bounds on the number of flat spectra of a Boolean function, depending on internal structures, with…
A historical review is given of the emergence of the idea of the quantum logic gate from the theory of reversible Boolean gates. I highlight the quantum XOR or controlled NOT as the fundamental two-bit gate for quantum computation. This…
A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level…
We introduce a new scheme for quantum circuit design called controlled gate networks. Rather than trying to reduce the complexity of individual unitary operations, the new strategy is to toggle between all of the unitary operations needed…
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the…
Using a quantumlike description for light propagation in nonhomogeneous optical fibers, quantum information processing can be implemented by optical means. Quantum-like bits (qulbits) are associated to light modes in the optical fiber and…
We show how to construct quantum gate arrays that can be programmed to perform different unitary operations on a data register, depending on the input to some program register. It is shown that a universal quantum gate array - a gate array…
A review is given of recent work aimed at constructing a quantum theory of cosmology in which all observables refer to information measurable by observers inside the universe. At the classical level the algebra of observables should be…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
The quantum harmonic oscillator is one of the most fundamental objects in physics. We consider the case where it is extended to an arbitrary number modes and includes all possible terms that are bilinear in the annihilation and creation…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
Quantum computing employs controllable interactions to perform sequences of logical gates and entire algorithms on quantum registers. This paradigm has been widely explored, e.g., for simulating dynamics of manybody systems by decomposing…
We study truncated Bose operators in finite dimensional Hilbert spaces. Spin coherent states for the truncated Bose operators and canonical coherent states for Bose operators are compared. The Lie algebra structure and the spectrum of the…
The role of operational quantum mechanics, quantum axiomatics and quantum structures in general is presented as a contribution to a compendium on quantum physics, its history and philosophy.
We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the…
We propose a scheme for the construction of charge and spin linear-response functions of an interacting electronic system via quantum phase estimation and statistical sampling on a quantum computer. By using the unitary decomposition of…
Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact,…
We introduce new families of pure quantum states that are constructed on top of the well-known Gilmore-Perelomov group-theoretic coherent states. We do this by constructing unitaries as the exponential of operators quadratic in Cartan…