Related papers: A Quantum Algorithm for Functions of Multiple Comm…
The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their…
Quantum signal processing (QSP) is a highly successful algorithmic primitive in quantum computing which leads to conceptually simple and efficient quantum algorithms using the block-encoding framework of quantum linear algebra. Multivariate…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identified when quantum…
We study quantum equivalents of non-commutative operators in quantum mechanics. Any matrix "$B$" satisfying the non-commuting relation $[A,B]\neq 0$ with "$A$", can be used via $B^{-1} AB$ to reproduce eigenvalues of "$A$". This…
We propose a quantum algorithm for solving the following problem: given the Hamiltonian of a physical system and one of its eigenvalues, how to obtain the corresponding eigenstate? The algorithm is based on the resonance phenomena. For a…
The quantum singular value transformation is a powerful quantum algorithm that allows one to apply a polynomial transformation to the singular values of a matrix that is embedded as a block of a unitary transformation. This paper shows how…
The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse…
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary…
We present a quantum algorithm that analyzes time series data simulated by a quantum differential equation solver. The proposed algorithm is a quantum version of the dynamic mode decomposition algorithm used in diverse fields such as fluid…
MQuantum algorithms of matrix operations are of great significance in many fields in science and technology. In this paper, by leveraging multi-qubit Toffoli gates and basic single-qubit operations, the quantum algorithms of matrix…
This article is a brief introduction to quantum algorithms for the eigenvalue problem in quantum many-body systems. Rather than a broad survey of topics, we focus on providing a conceptual understanding of several quantum algorithms that…
As in classical reversible computing, Quantum Arithmetic is typically seen as a set of tools that process binary data encoded into a quantum register to set the value of another quantum register. This article presents another approach to…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the dimension of the problem space grows exponentially, finding the eigenvalues of certain…
The problem of the quantum harmonic oscillator is investigated in the framework of bicomplex numbers, which are pairs of complex numbers making up a commutative ring with zero divisors. Starting with the commutator of the bicomplex position…
Quantum machine learning deals with leveraging quantum theory with classic machine learning algorithms. Current research efforts study the advantages of using quantum mechanics or quantum information theory to accelerate learning time or…
Recent developments in mathematics have provided powerful tools for comparing the eigenvalues of matrices related to each other via a moment map. In this paper we survey some of the more concrete aspects of the approach with a particular…
It is difficult to calculate the energy levels and eigenstates of a large physical system on a classical computer because of the exponentially growing size of the Hilbert space. In this work, we experimentally demonstrate a quantum…
Quantum signal processing provides an optimal procedure for simulating Hamiltonian evolution on a quantum computer using calls to a block encoding of the Hamiltonian. In many situations it is possible to control between forward and reverse…
We describe a new polynomial time quantum algorithm that uses the quantum fast fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases (commonly found in ab initio physics and…