相关论文: An Exact Quantum Polynomial-Time Algorithm for Sim…
We investigate the power of quantum computers when they are required to return an answer that is guaranteed correct after a time that is upper-bounded by a polynomial in the worst case. In an oracle setting, it is shown that such machines…
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 one of the most important problems demonstrating the power of quantum algorithms, as it greatly inspired the proposal of Shor's algorithm. The generalized Simon's problem is a natural extension of Simon's problem, and…
In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing…
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…
In this paper, we give a quantum algorithm which solves collision problem in an expected polynomial time. Especially, when the function is two-to-one, we present a quantum algorithm which can find a collision with certainty in a worst-case…
Simon's problem plays an important role in the history of quantum algorithms, as it inspired Shor to discover the celebrated quantum algorithm solving integer factorization in polynomial time. Besides, the quantum algorithm for Simon's…
In seeking out an algorithm to test out the capability of the IBM Quantum Experience quantum computer, we were given a review paper covering various algorithms for solving the subset-sum problem, including both classical and quantum…
Simon's problem is one of the most important problems demonstrating the power of quantum computing. Recently, an interesting distributed quantum algorithm for Simon's problem was proposed, where a key sorting operator requiring a large…
Combinatorial optimization - a field of research addressing problems that feature strongly in a wealth of scientific and industrial contexts - has been identified as one of the core potential fields of applicability of quantum computers. It…
An efficient quantum algorithm is proposed to solve in polynomial time the parity problem, one of the hardest problems both in conventional quantum computation and in classical computation, on NMR quantum computers. It is based on the…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
We show that a separation between the class of all problems that can efficiently be solved on a quantum computer and those solvable using probabilistic classical algorithms in polynomial time implies the generalized contextuality of quantum…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
Simon's problem is one of the most important problems demonstrating the power of quantum computers, which achieves a large separation between quantum and classical query complexities. However, Simon's discussion on his problem was limited…
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…
Grover's algorithm can solve NP-complete problems on quantum computers faster than all the known algorithms on classical computers. However, Grover's algorithm still needs exponential time. Due to the BBBV theorem, Grover's algorithm is…
The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of…
Conditions on sure-success decidability of weights of Boolean functions are presented for a given number of generalized Grover iterations. It is shown that the decidability problem reduces to a system of algebraic equations of a single…
We consider whether trainable quantum unitaries can be used to discover quantum speed-ups for classical problems. Using methods recently developed for training quantum neural nets, we consider Simon's problem, for which there is a known…