Related papers: Efficient Quantum Circuits for the Hilbert Transfo…
Suppose that a quantum circuit with K elementary gates is known for a unitary matrix U, and assume that U^m is a scalar matrix for some positive integer m. We show that a function of U can be realized on a quantum computer with at most…
The design and optimization of quantum circuits is central to quantum computation. This paper presents new algorithms for compiling arbitrary 2^n x 2^n unitary matrices into efficient circuits of (n-1)-controlled single-qubit and…
A crucial subroutine in quantum computing is to load the classical data of $N$ complex numbers into the amplitude of a superposed $n=\lceil \log_2N\rceil$-qubit state. It has been proven that any algorithm universally implementing this…
Recently, constant-depth quantum circuits are proved more powerful than their classical counterparts at solving certain problems, e.g., the two-dimensional (2D) hidden linear function (HLF) problem regarding a symmetric binary matrix. To…
Quantum machine learning is emerging as a promising application of quantum computing due to its distinct way of encoding and processing data. It is believed that large-scale quantum machine learning demonstrates substantial advantages over…
The classification of big data usually requires a mapping onto new data clusters which can then be processed by machine learning algorithms by means of more efficient and feasible linear separators. Recently, Lloyd et al. have advanced the…
The quantum Fourier transform (QFT) has emerged as the primary tool in quantum algorithms which achieve exponential advantage over classical computation and lies at the heart of the solution to the abelian hidden subgroup problem, of which…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
Recent breakthroughs have opened the possibility to intermediate-scale quantum computing with tens to hundreds of qubits, and shown the potential for solving classical challenging problems, such as in chemistry and condensed matter physics.…
Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although…
We study the use of the quantum wavelet transform to extract efficiently information about the multifractal exponents for multifractal quantum states. We show that, combined with quantum simulation algorithms, it enables to build quantum…
We briefly review what a quantum computer is, what it promises to do for us, and why it is so hard to build one. Among the first applications anticipated to bear fruit is quantum simulation of quantum systems. While most quantum computation…
Quantum classifiers are trainable quantum circuits used as machine learning models. The first part of the circuit implements a quantum feature map that encodes classical inputs into quantum states, embedding the data in a high-dimensional…
Quantum signal processing (QSP) and the quantum singular value transformation (QSVT) are pivotal tools for simplifying the development of quantum algorithms. These techniques leverage polynomial transformations on the eigenvalues or…
Unlike most classical algorithms that take an input and give the solution directly as an output, quantum algorithms produce a quantum circuit that works as an indirect solution to computationally hard problems. In the full quantum computing…
A hybrid classical-quantum approach for evaluation of multi-dimensional Walsh-Hadamard transforms and its applications to quantum image processing are proposed. In this approach, multidimensional Walsh-Hadamard transforms are obtained using…
In contexts where relevant problems can easily attain configuration spaces of enormous sizes, solving Linear Differential Equations (LDEs) can become a hard achievement for classical computers; on the other hand, the rise of quantum…
The whole Hilbert state space of an n-qubit spin system can be divided into (n+1) state subspaces according to the angular momentum theory of quantum mechanics. Here it is shown that any unknown state in such a state subspace, whose…
Designing quantum processors is a complex task that demands advanced verification methods to ensure their correct functionality. However, traditional methods of comprehensively verifying quantum devices, such as quantum process tomography,…
Quantum Fourier Transform (QFT) plays a principal role in the development of efficient quantum algorithms. Since the number of quantum bits that can currently built is limited, while many quantum technologies are inherently three- (or more)…