相关论文: A Continuous Variable Shor Algorithm
Shor's algorithm is one of the most promising applications of quantum computers. However, since $\sim 10^6$ physical qubits are believed to be required for established approaches, the algorithm will need to be distributed across many…
We contribute a 2D nearest-neighbor quantum architecture for Shor's algorithm to factor an $n$-bit number in $O(\log^2(n))$ depth. Our implementation uses parallel phase estimation, constant-depth fanout and teleportation, and…
The hidden subgroup problem~(HSP) is one of the most important problems in quantum computation. Many problems for which quantum algorithm achieves exponential speedup over its classical counterparts can be reduced to the Abelian HSP.…
Quantum performance simulators can provide practical metrics for the effectiveness of executing theoretical quantum information processing protocols on physical hardware. In this work we present a scheme to simulate the performance of fault…
Many modern asymmetric encryption methods rely on prime numbers, as they have distinctive properties. For instance, the security of RSA cryptosystem relies on the computational difficulty of factoring a large composite number in its prime…
Shor's factoring algorithm guarantees a success probability of at least one half for any fixed modulus N = pq with distinct primes p and q. We show that this guarantee does not extend to the asymptotic regime. As N -> infinity, the…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
We present a quantum algorithm for the dihedral hidden subgroup problem with time and query complexity $O(\exp(C\sqrt{\log N}))$. In this problem an oracle computes a function $f$ on the dihedral group $D_N$ which is invariant under a…
Consider the following generalized hidden shift problem: given a function f on {0,...,M-1} x Z_N satisfying f(b,x)=f(b+1,x+s) for b=0,1,...,M-2, find the unknown shift s in Z_N. For M=N, this problem is an instance of the abelian hidden…
Characterization of quantum processes is a preliminary step necessary in the development of quantum technology. The conventional method uses standard quantum process tomography, which requires $d^2$ input states and $d^4$ quantum…
A number of elegant approaches have been developed for the identification of quantum circuits which can be efficiently simulated on a classical computer. Recently, these methods have been employed to demonstrate the classical simulability…
As quantum computing progresses steadily from theory into practice, programmers will face a common problem: How can they be sure that their code does what they intend it to do? This paper presents encouraging results in the application of…
Gibbs sampling from continuous real-valued functions is a challenging problem of interest in machine learning. Here we leverage quantum Fourier transforms to build a quantum algorithm for this task when the function is periodic. We use the…
The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the…
In this paper, we consider the hidden subgroup problem (HSP) over the class of semi-direct product groups $\mathbb{Z}_{p^r}\rtimes\mathbb{Z}_q$, for p and q prime. We first present a classification of these groups in five classes. Then, we…
Post Quantum and Quantum Cryptography schemes are feasible quantum computer applications for 7G networks. These schemes could possibly replace existing schemes. These algorithms have been compromised by advances in quantum search algorithms…
Regev recently introduced a quantum factoring algorithm that may be perceived as a $d$-dimensional variation of Shor's factoring algorithm. In this work, we extend Regev's factoring algorithm to an algorithm for computing discrete…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
It is well known that quantum computers can efficiently find a hidden subgroup $H$ of a finite Abelian group $G$. This implies that after only a polynomial (in $\log |G|$) number of calls to the oracle function, the states corresponding to…
The construction of large, coherent quantum systems necessary for quantum computation remains an entreating but elusive goal, due to the ubiquitous nature of decoherence. Recent progress in quantum error correction schemes have given new…