相关论文: Multilinear Formulas and Skepticism of Quantum Com…

For quantum computation, we investigate the conjecture that the superposition of macroscopically distinct states is necessary for a large quantum speedup. Although this conjecture was supported for a circuit-based quantum computer…

Since Shor's discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers - the difficulty of…

An efficient quantum modular exponentiation method is indispensible for Shor's factoring algorithm. But we find that all descriptions presented by Shor, Nielsen and Chuang, Markov and Saeedi, et al., are flawed. We also remark that some…

An alternative quantum algorithm for the discrete logarithm problem is presented. The algorithm uses two quantum registers and two Fourier transforms whereas Shor's algorithm requires three registers and four Fourier transforms. A crucial…

Multiparameter quantum estimation theory aims to determine simultaneously the ultimate precision of all parameters contained in the state of a given quantum system. Determining this ultimate precision depends on the quantum Fisher…

Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…

Shor's factoring algorithm uses two quantum registers. By introducing more registers we show that the measured numbers in these registers which are of the same pre-measurement state, should be equal if the original Shor's complexity…

The so-called "threshold" theorem says that, once the error rate per qubit per gate is below a certain value, indefinitely long quantum computation becomes feasible, even if all of the qubits involved are subject to relaxation processes,…

An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is…

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…

The quantum computer is supposed to process information by applying unitary transformations to the complex amplitudes defining the state of N qubits. A useful machine needing N=1000 or more, the number of continuous parameters describing…

We investigate macroscopic entanglement of quantum states in quantum computers, where we say a quantum state is entangled macroscopically if the state has superposition of macroscopically distinct states. The index $p$ of the macroscopic…

Harrow, Hassidim, and Lloyd showed that for a suitably specified $N \times N$ matrix $A$ and $N$-dimensional vector $\vec{b}$, there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of…

In Mod. Phys. Lett. A 9, 3119 (1994), one of us (R.D.S) investigated a formulation of quantum mechanics as a generalized measure theory. Quantum mechanics computes probabilities from the absolute squares of complex amplitudes, and the…

Shor's and Grover's famous quantum algorithms for factoring and searching show that quantum computers can solve certain computational problems significantly faster than any classical computer. We discuss here what quantum computers_cannot_…

Amongst the most remarkable successes of quantum computation are Shor's efficient quantum algorithms for the computational tasks of integer factorisation and the evaluation of discrete logarithms. In this article we review the essential…

Quantum information processing and its associated technologies has reached an interesting and timely stage in their development where many different experiments have been performed establishing the basic building blocks. The challenge…

The notion of state vector is, in quantum mechanics, as central as it is problematic, as illustrates the wealth of publications about the sub- jects, including in particular the many attempts to obtain an acceptable interpretation of…

The preprocessing stage of Shor's algorithm generates a class of quantum states referred to as periodic states, on which the quantum Fourier transform is applied. Such states also play an important role in other quantum algorithms that rely…

Shor's algorithm for factoring in polynomial time on a quantum computer\cite{Shor} gives an enormous advantage over all known classical factoring algorithm. We demonstrate how to factor products of large prime numbers using a compiled…