Related papers: Space-efficient quantum multiplication of polynomi…
We study the algorithmic problem of multiplying large matrices that are rectangular. We prove that the method that has been used to construct the fastest algorithms for rectangular matrix multiplication cannot give algorithms with…
Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-not (CNOT), are universal when assisted by arbitrary one-qubit gates, it has only…
Efficient arithmetic operations are a prerequisite for practical quantum computing. Optimization efforts focus on two primary metrics: Quantum Cost (QC), determined by the number of non-linear gates, and Logical Depth, which defines the…
The field of linear optical quantum computation (LOQC) will soon need a repertoire of experimental milestones. We make progress in this direction by describing several experiments based on Grover's algorithm. These experiments range from a…
The exponential and Gaussian functions are among the most fundamental and important operations, appearing ubiquitously throughout all areas of science, engineering, and mathematics. Whereas formally, it is well-known that any function may…
Multi-controlled unitary gates have been a subject of interest in quantum computing since its inception, and are widely used in quantum algorithms. The current state-of-the-art approach to implementing n-qubit multi-controlled gates…
Two different algorithms are presented for generating a quantum circuit realization of a matrix representing a permutation on $2^n$ letters. All circuits involve $n$ qubits and only use multi--controlled Toffoli gates. The first algorithm…
Elementary symmetric polynomials $S_n^k$ are used as a benchmark for the bounded-depth arithmetic circuit model of computation. In this work we prove that $S_n^k$ modulo composite numbers $m=p_1p_2$ can be computed with much fewer…
Quantum computers promise great improvements in solving problems such as factoring large integers, simulating quantum systems, and database searching. Using a photon as a quantum bit (qubit) is one of the most promising ways to realize a…
Polynomial multiplication is fundamental in lattice-based cryptography. While the Number Theoretic Transform (NTT) enables fast multiplication, it imposes constraints on the modulus of the coefficient field. Hafiz et al. (2025) addressed…
The $N$th power of a polynomial matrix of fixed size and degree can be computed by binary powering as fast as multiplying two polynomials of linear degree in~$N$. When Fast Fourier Transform (FFT) is available, the resulting complexity is…
Controlled quantum gates play a crucial role in enabling quantum universal operations by facilitating interactions between qubits. Direct implementation of three-qubit gates simplifies the design of quantum circuits, thereby being conducive…
We first show how to construct an O(n)-depth O(n)-size quantum circuit for addition of two n-bit binary numbers with no ancillary qubits. The exact size is 7n-6, which is smaller than that of any other quantum circuit ever constructed for…
Solving non-linear Diophantine systems lies at the mathematical core of integer optimization and cryptography. While the general unbounded problem is undecidable, even over bounded integer domains it remains classically intractable in the…
In this paper, we study the optimal simulation of three-qubit unitary by using two-qubit gates. First, we give a lower bound on the two-qubit gates cost of simulating a multi-qubit gate. Secondly, we completely characterize the two-qubit…
We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the…
We show that it is possible to reduce the number of two-qubit gates needed for the construction of an arbitrary controlled-unitary transformation by up to two times using a tunable controlled-phase gate. On the platform of linear optics,…
We present a novel Clifford+T decomposition of a Toffoli gate. Our decomposition requires no SWAP gates in order to be implemented on 2D square lattices of qubits. This decomposition enables shallower, more fault-tolerant quantum…
Boolean circuits of McCulloch-Pitts threshold gates are a classic model of neural computation studied heavily in the late 20th century as a model of general computation. Recent advances in large-scale neural computing hardware has made…
We construct simplified quantum circuits for Shor's order-finding algorithm for composites N given by products of the Fermat primes 3, 5, 17, 257, and 65537. Such composites, including the previously studied case of 15, as well as 51, 85,…