Related papers: Quantum implementation of non-unitary operations w…
Unitary operations are a fundamental component of quantum algorithms, but they seem to be far more useful if given with a "quantum control" as a controlled unitary operation. However, quantum operations are not limited to unitary…
We present a quantum algorithm for the dynamical simulation of time-dependent Hamiltonians. Our method involves expanding the interaction-picture Hamiltonian as a sum of generalized permutations, which leads to an integral-free Dyson series…
Non-Abelian geometry phase has attracted significant attention for the robust holonomic unitary behavior exhibited, which arises from the degenerate subspace evolving along a trajectory in Hilbert space. It has been regarded as a promising…
A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a…
Let $D$ and $U$ be linear operators in a vector space (or more generally, elements of an associative algebra with a unit). We establish binomial-type identities for $D$ and $U$ assuming that either their commutator $[D,U]$ or the second…
Quantum-inspired algorithms can deliver substantial speedups over classical state-of-the-art methods by executing quantum algorithms with tensor networks on conventional hardware. Unlike circuit models restricted to unitary gates, tensor…
Quantum machine learning techniques have been proposed as a way to potentially enhance performance in machine learning applications. In this paper, we introduce two new quantum methods for neural networks. The first one is a quantum…
This paper is dedicated to the problem of verification of matrices for unitary similarity. For the case of nonderogatory matrices, we have been able to present the new solution for this problem based on geometric approach. The main…
We propose a quantum algorithm that emulates the action of an unknown unitary transformation on a given input state, using multiple copies of some unknown sample input states of the unitary and their corresponding output states. The…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
The solution of pseudo initial value differential equations, either ordinary or partial (including those of fractional nature), requires the development of adequate analytical methods, complementing those well established in the ordinary…
We propose an algebraic formulation for two distinct quantum algorithms: a quantum classification algorithm and a quantum search algorithm with a non-uniform initial distribution, both based on Clifford algebras and spinorial…
Hypercomplex image processing extends conventional techniques in a unified paradigm encompassing algebraic and geometric principles. This work leverages quaternions and the two-dimensional orthogonal planes split framework (splitting of a…
A quantum world-line Monte Carlo method for high-symmetrical quantum models is proposed. Firstly, based on a representation of a partition function using the Matsubara formula, the principle of quantum world-line Monte Carlo methods is…
New non-unitary representations of the SU(2) algebra are introduced for the case of the Dirac equation with a Coulomb potential; an extra phase, needed to close the algebra, is also introduced. The new representations does not require…
There is a decomposition of a Lie algebra for open matrix chains akin to the triangular decomposition. We use this decomposition to construct unitary irreducible representations. All multiple meson states can be retrieved this way.…
Modelling non-linear activation functions on quantum computers is vital for quantum neurons employed in fully quantum neural networks, however, remains a challenging task. We introduce an amplitude-based implementation for approximating…
We give an algorithm for computing matrix corepresentations for special linear and special unitary quantum groups using a combinatorial re-indexing of basis elements.
The Linear Combination of Unitaries (LCU) method is a powerful scheme for the block encoding of operators but suffers from high overheads. In this work, we discuss the parallelisation of LCU and in particular the SELECT subroutine of LCU…
We construct a weak dilation of a not necessarily unital CP-semigroup to an E-semigroup acting on the adjointable operators of a Hilbert module with a unit vector. We construct the dilation in such a way that the dilating E-semigroup has a…