Related papers: Quantum Computation of Prime Number Functions
Fundamental questions in chemistry and physics may never be answered due to the exponential complexity of the underlying quantum phenomena. A desire to overcome this challenge has sparked a new industry of quantum technologies with the…
The search problem is to find a state satisfying certain properties out of a given set. Grover's algorithm drives a quantum computer from a prepared initial state to the target state and solves the problem quadratically faster than a…
The von Neumann and quantum R\'enyi entropies characterize fundamental properties of quantum systems and lead to theoretical and practical applications in many fields. Quantum algorithms for estimating quantum entropies, using a quantum…
The superpositional wave function oscillations for finite-time implementation of quantum algorithms modifies the desired interference required for quantum computing. We propose a scheme with trapped ultracold ion-pairs being qubits to…
The factorization of a large digit integer in polynomial time is a challenging computational task to decipher. The exponential growth of computation can be alleviated if the factorization problem is changed to an optimization problem with…
A recently introduced classical simulation method for universal quantum computation with magic states operates by repeated sampling from probability functions [M. Zurel et al. PRL 260404 (2020)]. This method is closely related to sampling…
In standard quantum computation, the initial state is pure and the answer is determined by making a measurement of some of the bits in the computational basis. What can be accomplished if the initial state is a highly mixed state and the…
By harnessing the superposition and entanglement of physical states, quantum computers could outperform their classical counterparts in solving problems of technological impact, such as factoring large numbers and searching databases. A…
A simple method is proposed to prepare conveniently the effective pure state |00...0><0...00| with any number of qubits in a quantum ensemble. The preparation is based on the temporal averaging (Knill, Chuang, and Laflamme, Phys.Rev.A 57,…
Distributed computing seems to be a natural approach to overcome size limitations of quantum computers in terms of number of qubits. But one lacks an efficient distribution approach to deal systematically with potential algorithms. This…
A simple criterion is derived in order that a number sequence ${\cal S}_n$ is a permitted spectrum of a quantized system. The sequence of the prime numbers fulfils the criterion and the corresponding one-dimensional quantum potential is…
Quantum computing algorithms require that the quantum register be initially present in a superposition state. To achieve this, we consider the practical problem of creating a coherent superposition state of several qubits. Owing to…
A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The best previous result had shown the…
We discuss a model for quantum computing with initially mixed states. Although such a computer is known to be less powerful than a quantum computer operating with pure (entangled) states, it may efficiently solve some problems for which no…
The quantum permutation algorithm provides computational speed-up over classical algorithms in determining the parity of a given cyclic permutation. For its $n$-qubit implementations, the number of required quantum gates scales…
It is shown that in two-state quantum theory, a generic quantum state can be described by a non-computable real number. In terms of this, the criterion for measurement outcome is simply and deterministically defined. This demonstration is…
We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state $|0\rangle$ computational basis. In addition, we allow the creation of a one-qubit ancilla in a…
We present an efficient quantum algorithm for preparing a pure state on a quantum computer, where the quantum state corresponds to that of a molecular system with a given number $m$ of electrons occupying a given number $n$ of spin…
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…
We present a finite set of projective measurements that, together with quantum memory and preparation of the |0> state, suffice for universal quantum computation. This extends work of Nielsen [quant-ph/0108020], who proposed a scheme in…