Related papers: Mathematical Foundations of Holonomic Quantum Comp…
We explore in the framework of Quantum Computation the notion of {\em Computability}, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm for Hilbert's tenth problem, which is equivalent to…
This article is an attempt to generalize the classical theory of reversible computing, principally developed by Bennet [IBM J. Res. Develop., 17(1973)] and by Fredkin and Toffoli [Internat. J. Theoret. Phys., 21(1982)], to the quantum case.…
Quantum computing is presently undergoing rapid development to achieve a significant speedup promised in certain applications. Nonetheless, scaling quantum computers remains a formidable engineering challenge, prompting exploration of…
Quantum computing for machine learning attracts increasing attention and recent technological developments suggest that especially adiabatic quantum computing may soon be of practical interest. In this paper, we therefore consider this…
The quantum Fourier transform (QFT) is a powerful tool in quantum computing. The main ingredients of QFT are formed by the Walsh-Hadamard transform H and phase shifts P(.), both of which are 2x2 unitary matrices as operators on the…
Quantum computation of the energy of molecules and materials is one of the most promising applications of fault-tolerant quantum computers. Practical applications require development of quantum algorithms with reduced resource requirements.…
We propose an implementation scheme for holonomic, i.e., geometrical, quantum information processing based on semiconductor nanostructures. Our quantum hardware consists of coupled semiconductor macroatoms addressed/controlled by ultrafast…
Quantum computing promises to tackle technological and industrial problems insurmountable for classical computers. However, today's quantum computers still have limited demonstrable functionality, and it is expected that scaling up to…
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…
Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational…
The correct Hamiltonian for an extended Hubbard model with quantum group symmetry as introduced by A. Montorsi and M. Rasetti is derived for a D-dimensional lattice. It is shown that the superconducting SUq(2) holds as a true quantum…
We consider how the Hamiltonian Quantum Computing scheme introduced in [arXiv:1509.01278] can be implemented using a 2D array of superconducting transmon qubits. We show how the scheme requires the engineering of strong attractive…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
As quantum computers mature, the applicability in practice becomes more important. Many uses of quantum computers will be hybrid, with classical computers still playing an important role in operating and using the quantum computer. The term…
Major breakthrough in quantum computation has recently been achieved using quantum annealing to develop analog quantum computers instead of gate based computers. After a short introduction to quantum computation, we retrace very briefly the…
We revisit the question of universality in quantum computing and propose a new paradigm. Instead of forcing a physical system to enact a predetermined set of universal gates (e.g., single-qubit operations and CNOT), we focus on the…
By holonomic guessing, we denote the process of finding a linear differential equation with polynomial coefficients satisfied by the generating function of a sequence, for which only a few first terms are known. Holonomic guessing has been…
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 use the benefits and components of classical computers every day. However, there are many types of problems which, as they grow in size, their computational complexity grows larger than classical computers will ever be able to solve.…
Following the B. Hiley belief that unresolved problems of conventional quantum mechanics could be the result of a wrong mathematical structure, an alternative basic structure is suggested. Critical part of the structure is modification of…