相关论文: Factoring in a Dissipative Quantum Computer
A quantum computer is a multi-particle interferometer that comprises beam splitters at both ends and arms, where the n two-level particles undergo the interactions among them. The arms are designed so that relevant functions required to…
There are two important, and potentially interconnecting, avenues to the realisation of large-scale quantum algorithms: improvement of the hardware, and reduction of resource requirements demanded by algorithm components. In focusing on the…
We show that $n$-bit integers can be factorized by independently running a quantum circuit with $\tilde{O}(n^{3/2})$ gates for $\sqrt{n}+4$ times, and then using polynomial-time classical post-processing. The correctness of the algorithm…
Quantum computers require quantum logic, something fundamentally different to classical Boolean logic. This difference leads to a greater efficiency of quantum computation over its classical counter-part. In this review we explain the basic…
Shor's algorithms for factorization and discrete logarithms on a quantum computer employ Fourier transforms preceding a final measurement. It is shown that such a Fourier transform can be carried out in a semi-classical way in which a…
Dissipation can be used as a resource to control and simulate quantum systems. We discuss a modular model based on fast dissipation capable of performing universal quantum computation, and simulating arbitrary Lindbladian dynamics. The…
As the field of quantum computing grows, novel algorithms which take advantage of quantum phenomena need to be developed. As we are currently in the NISQ (noisy intermediate scale quantum) era, quantum algorithm researchers cannot reliably…
The execution cost of quantum algorithms is typically quantified through asymptotic gate counts and qubit register sizes, yet these metrics do not directly capture which genuinely quantum resources, and in what amount, must be created and…
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 determine the cost of performing Shor's algorithm for integer factorization on a ternary quantum computer, using two natural models of universal fault-tolerant computing: (i) a model based on magic state distillation that assumes the…
Major obstacles remain to the implementation of macroscopic quantum computing: hardware problems of noise, decoherence, and scaling; software problems of error correction; and, most important, algorithm construction. Finding truly quantum…
Each year, the gap between theoretical proposals and experimental endeavours to create quantum computers gets smaller, driven by the promise of fundamentally faster algorithms and quantum simulations. This occurs by the combination of…
The multiplication of superpositions of numbers is a core operation in many quantum algorithms. The standard method for multiplication (both classical and quantum) has a runtime quadratic in the size of the inputs. Quantum circuits with…
The effects of imperfect gate operations in implementation of Shor's prime factorization algorithm are investigated. The gate imperfections may be classified into three categories: the systematic error, the random error, and the one with…
The effects of imperfect gate operations in implementation of Shor's prime factorization algorithm are investigated. The gate imperfections may be classified into three categories: the systematic error, the random error, and the one with…
To see the feasibility of a large-scale quantum computing, it is required to accurately analyze the performance and the quantum resource. However, most of the analysis reported so far have focused on the statistical examination, i.e.,…
It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably…
In theory, quantum computers can efficiently simulate quantum physics, factor large numbers and estimate integrals, thus solving otherwise intractable computational problems. In practice, quantum computers must operate with noisy devices…
We show how the execution time of algorithms on quantum computers depends on the architecture of the quantum computer, the choice of algorithms (including subroutines such as arithmetic), and the ``clock speed'' of the quantum computer. The…
We investigate the time T a quantum computer requires to factorize a given number dependent on the number of bits L required to represent this number. We stress the fact that in most cases one has to take into account that the execution…