Related papers: Quantum computation and real multiplication
We introduce the Mixed-Integer Quadratically Constrained Quadratic Programming framework for the quantum compilation problem and apply it in the context of topological quantum computing. In this setting, quantum gates are realized by…
The circuit model of quantum computation can be interpreted as a scattering process. In particular, factorised scattering operators result in integrable quantum circuits that provide universal quantum computation and are potentially less…
We present a constructive proof that anyonic magnetic charges with fluxes in a non-solvable finite group can perform universal quantum computations. The gates are built out of the elementary operations of braiding, fusion, and vacuum pair…
A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from \fun\ to \uqg\ , given by elements of the pure braid group. These operators --- the `reflection matrix' $Y \equiv…
For quantum computer circuits, it is proposed that they have, besides the presently used compact graphs, an expanded system of subgraphs, in line with the quantum mechanics superposition axiom. The representation of each process by these…
Is it possible to define, for certain values n the product of vectors of the real vector space of n dimensions, such that this is, with respect to multiplication and the ordinary addition of vectors, a numerical system which contains the…
The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the…
A binary mapping from Fock space of bosonic state to qubits is given. Based on the binary mapping, we construte an algorithm of qubitization of bosons with complexity O(log(N)). As an example, the algorithm of qubitization of bosons in…
There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…
Read-Rezayi fractional quantum Hall states are among the prime candidates for realizing non-Abelian anyons which in principle can be used for topological quantum computation. We present a prescription for efficiently finding braids which…
A variety of universal similarity factorization equalities over real Clifford algebras ${\cal R}_{p,q}$ are established. On the basis of these equalities, real, complex and quaternion matrix representations of elements in ${\cal R}_{p,q}$…
We show that quantum theory allows for transformations of black boxes that cannot be realized by inserting the input black boxes within a circuit in a pre-defined causal order. The simplest example of such a transformation is the classical…
Recently de La Torre et al. [1] reconstructed Quantum Theory from its local structure on the basis of local discriminability and the existence of a one-parameter group of bipartite transformations containing an entangling gate. This result…
We construct the Fock space representations of classical quantum affine algebras using combinatorics of Young walls. We also show that the crystal graphs of the Fock space representations can be realized as the abstract crystal consisting…
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other…
The following article summarizes research where theorems and their respective demonstrations are postulated based on quadratic equations with special properties given by the Pythagorean triplets and the Fibonacci sequence given the second…
We provide a comprehensive systematic method for the numerical computation of elementary braid operations in topological quantum computation (TQC). This {procedure} is systematically applicable to all anyon models, including $SU(2)_k$.…
We present a constructive method to translate small quantum circuits into their optical analogues, using linear components of present-day quantum optics technology only. These optical circuits perform precisely the computation that the…
We study fault-tolerant error correction in a quantum memory constructed as a two-dimensional model of Fibonacci anyons on a torus, in the presence of thermal noise represented by pair-creation processes and measurement errors. The…
Quantum computing has been increasingly applied in nuclear physics. In this work, we combine quantum computing with the complex scaling method to address the resonance problem. Due to the non-Hermiticity introduced by complex scaling,…