Related papers: Quantum singular value transformation for an arbit…
The vector transform operators are investigated; these operators are used at the solution of boundary value problems in piecewise homogeneous spherically symmetric areas. In particular, examples of transformation operators for vector…
We investigate modifications of quantum mechanics (QM) that replace the unitary group in a finite dimensional Hilbert space with a finite group and determine the minimal sequence of subgroups necessary to approximate QM arbitrarily closely…
Quantum computing with qudits, quantum systems with $d > 2$ levels, offers a powerful extension beyond qubits, expanding the computational possibilities of quantum systems, allowing the simplification of the implementation of several…
We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier…
Today's quantum computers operate with a binary encoding that is the quantum analog of classical bits. Yet, the underlying quantum hardware consists of information carriers that are not necessarily binary, but typically exhibit a rich…
In recent years, quantum algorithms have been proposed which use quantum phase estimation (QPE) coherently as a subroutine without measurement. In order to do this effectively, the routine must be able to distinguish eigenstates with…
The optimal control of unitary transformations is a fundamental problem in quantum control theory and quantum information processing. The feasibility of performing such optimizations is determined by the computational and control resources…
For one qubit systems, we present a short, elementary argument characterizing unital quantum operators in terms of their action on Bloch vectors. We then show how our approach generalizes to multi-qubit systems, obtaining inequalities that…
We study the most general continuous transformation on the generators of bilinear master equations of a quantum oscillator. We find that transformation operators that preserve the hermiticity of density operators and conserve the…
In spite of their evident logical character, particle statistics symmetries are not among the inherently quantum features exploited in quantum computation. A difficulty may be that, being a constant of motion of a unitary evolution, a…
We present a probabilistic quantum processor for qudits. The processor itself is represented by a fixed array of gates. The input of the processor consists of two registers. In the program register the set of instructions (program) is…
The problem of Phase Estimation (or Amplitude Estimation) admits a quadratic quantum speedup. Wang, Higgott and Brierley [2019, Phys. Rev. Lett. 122 140504] have shown that there is a continuous trade-off between quantum speedup and circuit…
While many classical algorithms rely on Laplace transforms, it has remained an open question whether these operations could be implemented efficiently on quantum computers. In this work, we introduce the Quantum Laplace Transform (QLT),…
Signal processing stands as a pillar of classical computation and modern information technology, applicable to both analog and digital signals. Recently, advancements in quantum information science have suggested that quantum signal…
Quantum neural network architectures that have little-to-no inductive biases are known to face trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in machine learning address this challenge by…
Quadratic Unconstrained Binary Optimization (QUBO) is a general-purpose modeling framework for combinatorial optimization problems and is a requirement for quantum annealers. This paper utilizes the eigenvalue decomposition of the…
The quantum Schur transform is a fundamental building block that maps the computational basis to a coupled basis consisting of irreducible representations of the unitary and symmetric groups. Equivalently, it may be regarded as a change of…
Recent developments in the field of quantum machine learning have promoted the idea of incorporating physical symmetries in the structure of quantum circuits. A crucial milestone in this area is the realization of $S_{n}$-permutation…
This paper continues the previous work (Quantum Inf. Process (2019)) by two authors of the present paper about a spectral mapping property of chiral symmetric unitary operators. In physics, they treat non-unitary time-evolution operators to…
Quantum algorithms can enhance machine learning in different aspects. In 2014, Rebentrost $et~al.$ constructed a least squares quantum support vector machine (LS-QSVM), in which the Swap Test plays a crucial role in realizing the…