Related papers: Efficient quantum circuits for binary elliptic cur…
Probabilistic graphical models such as Bayesian networks are widely used to model stochastic systems to perform various types of analysis such as probabilistic prediction, risk analysis, and system health monitoring, which can become…
This paper introduces a novel cryptographic approach based on the continuous logarithm in the complex circle, designed to address the challenges posed by quantum computing. By leveraging its multi-valued and spectral properties, this…
Elliptic curves over finite fields with predefined conditions in the order are practically constructed using the theory of complex multiplication. The stage with longest calculations in this method reconstructs some polynomial with integer…
We present generalized and improved constructions for simulating quantum computers with a polynomial slowdown on lattices composed of qubits on which certain global versions of one- and two-qubit operations can be performed.
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of near-term quantum devices. We introduce…
We design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size of the base field, assuming solely the generalized Riemann…
It has previously been established that the logarithmic-depth approximate quantum Fourier transform (AQFT) provides a suitable replacement for the regular QFT in many quantum algorithms. Since the AQFT is less accurate by definition,…
The Quantum Fourier Transform (QFT) is a fundamental component of many quantum computing algorithms. In this paper, we present an alternative method for factoring this transformation. Inspired by this approach, we introduce a new quantum…
We associate a half-integer number, called {\em the quantum index}, to algebraic curves in the real plane satisfying to certain conditions. The area encompassed by the logarithmic image of such curves is equal to $\pi^2$ times the quantum…
We present an algorithm which speeds scalar multiplication on a general elliptic curve by an estimated 3.8 % to 8.5 % over the best known general methods when using affine coordinates. This is achieved by eliminating a field multiplication…
When designing quantum circuits for a given unitary, it can be much cheaper to achieve a good approximation on most inputs than on all inputs. In this work we formalize this idea, and propose that such "optimistic quantum circuits" are…
Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient…
In the past years, research on Shor's algorithm for solving elliptic curves for discrete logarithm problems (Shor's ECDLP), the basis for cracking elliptic curve-based cryptosystems (ECC), has started to garner more significant interest. To…
We present an enhanced algorithm for exploring mirror symmetry for elliptic curves through the correspondence of algebraic and tropical geometry, focusing on Gromov-Witten invariants of elliptic curves and, in particular, Hurwitz numbers.…
In quantum circuits, qubits and the quantum gates acting on them have traditionally been analysed using matrix algebra and Dirac notation. While powerful, these can be unintuitive for conceptual understanding and rapid problem solving. In…
In this paper, we describe non invertible matrix in GF(2)which can be used as multiplication matrix in Hill Cipher technique for one way hash algorithm. The matrices proposed are permutation matrices with exactly one entry 1 in each row and…
Quantum circuits are considered more powerful than classical circuits and require exponential resources to simulate classically. Clifford circuits are a special class of quantum circuits that can be simulated in polynomial time but still…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
Over a decade ago, it was demonstrated that quantum computing has the potential to revolutionize numerical linear algebra by enabling algorithms with complexity superior to what is classically achievable, e.g., the seminal HHL algorithm for…
In this paper, we study the problem of learning an unknown quantum circuit of a certain structure. If the unknown target is an $n$-qubit Clifford circuit, we devise an efficient algorithm to reconstruct its circuit representation by using…