Related papers: Approximate Quantum Fourier Transform with $O(n \l…
Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…
This paper discusses the compilation, optimization, and error mitigation of quantum algorithms, essential steps to execute real-world quantum algorithms. Quantum algorithms running on a hybrid platform with QPU and CPU/GPU take advantage of…
Using the circulant symmetry of a Hamiltonian describing three qubits, we realize the quantum Fourier transform. This symmetry allows us to construct a set of eigenvectors independently on the magnitude of physical parameters involved in…
We present a quantum algorithm for multiplying two $n$-bit integers with overall circuit depth and $T$-depth both bounded by $O(\log^{2} n)$, while using $O(n^{2})$ gates and ancillary qubits. Our construction generates partial products via…
The quantum Fourier transform (QFT) brings efficiency in many respects, especially usage of resource, for most operations on quantum computers. In this study, the existing QFT-based and non-QFT-based quantum arithmetic operations are…
In fault-tolerant quantum circuit synthesis, T gates supplied via magic states dominate space-time cost, while Clifford gates incur negligible overhead. Conventional flows minimize AND count in an {XOR, AND, NOT} basis as a proxy for T,…
Performing large-scale, accurate quantum simulations of many-fermion systems is a central challenge in quantum science, with applications in chemistry, materials, and high-energy physics. Despite significant progress, realizing generic…
Quantum computing has the potential to solve many complex algorithms in the domains of optimization, arithmetics, structural search, financial risk analysis, machine learning, image processing, and others. Quantum circuits built to…
We introduce a novel framework for Generalized Tensor Transforms (GTTs), constructed through an $n$-fold tensor product of an arbitrary $b \times b$ unitary matrix $W$. This construction generalizes many established transforms, by providing…
Simulating the dynamics of electrons and other fermionic particles in quantum chemistry, materials science, and high-energy physics is one of the most promising applications of fault-tolerant quantum computers. However, the overhead in…
We show that many well-known signal transforms allow highly efficient realizations on a quantum computer. We explain some elementary quantum circuits and review the construction of the Quantum Fourier Transform. We derive quantum circuits…
We describe an efficient quantum algorithm for the quantum Schur transform. The Schur transform is an operation on a quantum computer that maps the standard computational basis to a basis composed of irreducible representations of the…
In the paper it is shown that there exist infinite classes of fast DFT algorithms having multiplicative complexity lower than O(NlogN), i.e. smaller than their arithmetical complexity. The derivation starts with nesting of Discrete Fourier…
We give a novel procedure for approximating general single-qubit unitaries from a finite universal gate set by reducing the problem to a novel magnitude approximation problem, achieving an immediate improvement in sequence length by a…
The quantum Fourier transform (QFT) plays an important role in many known quantum algorithms such as Shor's algorithm for prime factorisation. In this paper we show that the QFT algorithm can, on a restricted set of input states, be…
Fourier states are multi-qubit registers that facilitate phase rotations in fault-tolerant quantum computing. We propose distillation protocols for constructing the fundamental, $n$-qubit Fourier state with error $O(2^{-n})$ at a cost of…
Quantum noise in real-world devices poses a significant challenge in achieving practical quantum advantage, since accurately compiled and executed circuits are typically deep and highly susceptible to decoherence. To facilitate the…
For a number of useful quantum circuits, qudit constructions have been found which reduce resource requirements compared to the best known or best possible qubit construction. However, many of the necessary qutrit gates in these…
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…
We propose a method for the realization of the two-qubit quantum Fourier transform (QFT) using a Hamiltonian which possesses the circulant symmetry. Importantly, the eigenvectors of the circulant matrices are the Fourier modes and do not…