Related papers: t-multiple discrete logarithm problem and solving …
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
We present a quantum-inspired tensor network algorithm for solving tridiagonal Quadratic Unconstrained Binary Optimization (QUBO) problems and quadratic unconstrained discrete optimization (QUDO) problems. We also solve the more general…
We investigate the computational complexity of the discrete logarithm, the computational Diffie-Hellman and the decisional Diffie-Hellman problems in some identity black-box groups G_{p,t}, where p is a prime number and t is a positive…
In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process…
The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their…
The continuous-time query model is a variant of the discrete query model in which queries can be interleaved with known operations (called "driving operations") continuously in time. Interesting algorithms have been discovered in this…
Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground…
This papers introduces an algorithm for the solution of multiple kernel learning (MKL) problems with elastic-net constraints on the kernel weights. The algorithm compares very favourably in terms of time and space complexity to existing…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
We show in some detail how to implement Shor's efficient quantum algorithm for discrete logarithms for the particular case of elliptic curve groups. It turns out that for this problem a smaller quantum computer can solve problems further…
Finding the solution to linear systems is at the heart of many applications in science and technology. Over the years a number of algorithms have been proposed to solve this problem on a digital quantum device, yet most of these are too…
We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the…
In this paper we consider the problem of testing whether two finite groups are isomorphic. Whereas the case where both groups are abelian is well understood and can be solved efficiently, very little is known about the complexity of…
As quantum hardware rapidly advances toward the early fault-tolerant era, a key challenge is to develop quantum algorithms that are not only theoretically sound but also hardware-friendly on near-term devices. In this work, we propose a…
Even after decades of quantum computing development, examples of generally useful quantum algorithms with exponential speedups over classical counterparts are scarce. Recent progress in quantum algorithms for linear-algebra positioned…
The hidden subgroup problem (HSP) plays an important role in quantum computation, because many quantum algorithms that are exponentially faster than classical algorithms can be casted in the HSP structure. In this paper, we present a new…
Since Harrow, Hassidim, and Lloyd (2009) showed that a system of linear equations with $N$ variables and condition number $\kappa$ can be solved on a quantum computer in $\operatorname{poly}(\log(N), \kappa)$ time, exponentially faster than…
Ordinary approach to quantum algorithm is based on quantum Turing machine or quantum circuits. It is known that this approach is not powerful enough to solve NP-complete problems. In this paper we study a new approach to quantum algorithm…
The elliptic curve discrete logarithm problem is of fundamental importance in public-key cryptography. It is in use for a long time. Moreover, it is an interesting challenge in computational mathematics. Its solution is supposed to provide…
We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an $N\times N$ matrix $\mathcal{M}$, an $N$-dimensional vector $\textbf{\emph{b}}$, and an initial vector $\textbf{\emph{x}}(0)$,…