Related papers: Efficient quantum circuits for binary elliptic cur…
Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit…
We present some basic integer arithmetic quantum circuits, such as adders and multipliers-accumulators of various forms, as well as diagonal operators, which operate on multilevel qudits. The integers to be processed are represented in an…
The quantum Fourier transform (QFT) is a ubiquitous quantum operation that is used in numerous quantum computing applications. The major obstacle to constructing a QFT circuit is that numerous elementary gates are required. Among the…
We review the staircase algorithm to decompose the exponential of a generalized Pauli matrix and we propose two alternative recursive methods which offer more efficient quantum circuits. The first algorithm we propose, defined as the…
In this paper, we propose an elliptic curve key generation processor over GF(2m) and GF(P) with Network-on-Chip (NoC) design scheme based on binary scalar multiplication algorithm. Over the Two last decades, Elliptic Curve Cryptography…
We give quantum circuits that simulate an arbitrary two-qubit unitary operator up to global phase. For several quantum gate libraries we prove that gate counts are optimal in worst and average cases. Our lower and upper bounds compare…
Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers,…
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…
In the paper, we consider quantum circuits for the Quantum Fourier Transform (QFT) algorithm. The QFT algorithm is a very popular technique used in many quantum algorithms. We present a generic method for constructing quantum circuits for…
We show, within the circuit model, how any quantum computation can be efficiently performed using states with only real amplitudes (a result known within the Quantum Turing Machine model). This allows us to identify a 2-qubit (in fact…
In recent decades, the field of quantum computing has experienced remarkable progress. This progress is marked by the superior performance of many quantum algorithms compared to their classical counterparts, with Shor's algorithm serving as…
We present e cient algorithms for computing isogenies between hyperelliptic curves, leveraging higher genus curves to enhance cryptographic protocols in the post-quantum context. Our algorithms reduce the computational complexity of isogeny…
We show that $n$-bit integers can be factorized by independently running a quantum circuit with $\tilde{O}(n^{3/2})$ gates for $\sqrt{n}+4$ times, and then using polynomial-time classical post-processing. The correctness of the algorithm…
This work shows that minimizing the depth of a quantum circuit composed of commuting operations reduces to a vertex coloring problem on an appropriately constructed graph, where gates correspond to vertices and edges encode…
Elliptic curves are planar curves which can be used to define an abelian group. The efficient computation of discrete logarithms over this group is a longstanding problem relevant to cryptography. It may be possible to efficiently compute…
Linear-Optical Passive (LOP) devices and photon counters are sufficient to implement universal quantum computation with single photons, and particular schemes have already been proposed. In this paper we discuss the link between the…
The multiplicative depth of a logic network over the gate basis $\{\land, \oplus, \neg\}$ is the largest number of $\land$ gates on any path from a primary input to a primary output in the network. We describe a dynamic programming based…
Parametrized quantum optical circuits are a class of quantum circuits in which the carriers of quantum information are photons and the gates are optical transformations. Classically optimizing these circuits is challenging due to the…
Quantum circuits for mathematical functions such as division are necessary to use quantum computers for scientific computing. Quantum circuits based on Clifford+T gates can easily be made fault-tolerant but the T gate is very costly to…
In quantum computation every unitary operation can be decomposed into quantum circuits-a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-NOT (CNOT) gates. Two measures are important when…