相关论文: Geometric-Algebra Quantum-Like Algorithms: Simon's…
A new type of algorithms is presented that combine the advantages of quantum and classical ones. Those combined advantages along with aspects of Geometric Algebra that open possibilities unavailable to both of these computations are…
The first quantum algorithm to offer an exponential speedup (in the query complexity setting) over classical algorithms was Simon's algorithm for identifying a hidden exclusive-or mask. Here we observe how part of Simon's algorithm can be…
In this Letter, we construct the quantum algorithms for the Simon problem and the period-finding problem, which do not require initializing the auxiliary qubits involved in the process of functional evaluation but are as efficient as the…
Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…
The abelian Hidden Subgroup Problem (HSP) is extremely general, and many problems with known quantum exponential speed-up (such as integers factorisation, the discrete logarithm and Simon's problem) can be seen as specific instances of it.…
Many quantum algorithms for attacking symmetric cryptography involve the rank problem of quantum linear equations. In this paper, we first propose two quantum algorithms for solving quantum linear systems of equations with coherent…
Simon's algorithm was one of the first problems to demonstrate a genuine quantum advantage. The algorithm, however, assumes access to noise-free qubits. In our work we use Simon's algorithm to benchmark the error rates of devices currently…
The quantum hidden subgroup approach is an actively studied approach to solve combinatorial problems in quantum complexity theory. With the success of the Shor's algorithm, it was hoped that similar approach may be useful to solve the other…
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 consider a recently proposed generalisation of the abelian hidden subgroup problem: the shifted subset problem. The problem is to determine a subset S of some abelian group, given access to quantum states of the form |S+x>, for some…
Almost all of the most successful quantum algorithms discovered to date exploit the ability of the Fourier transform to recover subgroup structure of functions, especially periodicity. The fact that Fourier transforms can also be used to…
Motivated by algorithmic problems arising in quantum field theories whose dynamical variables are geometric in nature, we provide a quantum algorithm that efficiently approximates the colored Jones polynomial. The construction is based on…
The quantum algorithms of Deutsch, Simon and Shor are described in a way which highlights their dependence on the Fourier transform. The general construction of the Fourier transform on an Abelian group is outlined and this provides a…
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this…
We present a quantum algorithm which identifies with certainty a hidden subgroup of an arbitrary finite group G in only a polynomial (in log |G|) number of calls to the oracle. This is exponentially better than the best classical algorithm.…
We report an experimental demonstration of a one-way implementation of a quantum algorithm solving Simon's Problem - a black box period-finding problem which has an exponential gap between the classical and quantum runtime. Using an…
Simon's problem is an essential example demonstrating the faster speed of quantum computers than classical computers for solving some problems. The optimal separation between exact quantum and classical query complexities for Simon's…
Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the…
Simon in his FOCS'94 paper was the first to show an exponential gap between classical and quantum computation. The problem he dealt with is now part of a well-studied class of problems, the hidden subgroup problems. We study Simon's problem…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…