相关论文: The Precise Formula in a Sine Function Form of the…
This paper presented two general quantum search algorithms. We derived the iterated formulas and the simpler approximate formulas and the precise formula for the amplitude in the desired state. A mathematical proof of Grover's algorithm…
Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring…
A general consideration on the phase rotations in quantum searching algorithm is taken in this work. As four phase rotations on the initial state, the marked states, and the states orthogonal to them are taken account, we deduce a phase…
A general quantum search algorithm with arbitrary unitary transformations and an arbitrary initial state is considered in this work. To serach a marked state with certainty, we have derived, using an SU(2) representation: (1) the matching…
We present a general phase matching condition for the quantum search algorithm with arbitrary unitary transformation and arbitrary phase rotations. We show by an explicit expression that the phase matching condition depends both on the…
We consider the use of arbitrary phases in quantum amplitude amplification which is a generalization of quantum searching. We prove that the phase condition in amplitude amplification is given by $\tan(\varphi/2) = \tan(\phi/2)(1-2a)$,…
In this paper, we present an algorithm for preparing quantum states of the form $\sum_{i=0}^{n-1} \alpha_i |i\rangle$, where the coefficients $\alpha_i$ are specified by a quantum oracle. Our method achieves this task twice as fast as the…
We consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured. Most quantum…
In [Phys. Rev. Lett. 113, 210501 (2014)], to achieve the optimal fixed-point quantum search in the case of unknown fraction (denoted by $\lambda$) of target items, the analytical multiphase matching (AMPM) condition has been proposed. In…
Based on the standard transfer matrix, a formally exact quantization condition for arbitrary potentials, which outflanks and unifies the historical approaches, is derived. It can be used to find the exact bound-state energy eigenvalues of…
While Quantum phase estimation (QPE) is at the core of many quantum algorithms known to date, its physical implementation (algorithms based on quantum Fourier transform (QFT)) is highly constrained by the requirement of high-precision…
We introduce a versatile method for preparing a quantum state whose amplitudes are given by some known function. Unlike existing approaches, our method does not require handcrafted reversible arithmetic circuits, or quantum table reads, to…
We propose a new method to design adaptation algorithms that guarantee a certain prescribed level of performance and are applicable to systems with nonconvex parameterization. The main idea behind the method is, given the desired…
This paper focuses on the quantum amplitude estimation algorithm, which is a core subroutine in quantum computation for various applications. The conventional approach for amplitude estimation is to use the phase estimation algorithm, which…
Each iteration in Grover's original quantum search algorithm contains 4 steps: two Hadamard-Walsh transformations and two amplitudes inversions. When the inversion of the marked state is replaced by arbitrary phase rotation \theta and the…
Quantum amplitude estimation is a key sub-routine of a number of quantum algorithms with various applications. We propose an adaptive algorithm for interval estimation of amplitudes. The quantum part of the algorithm is based only on…
Using the methods of the "form factor program" exact expressions of all matrix elements are obtained for several operators of the quantum sine Gordon model: all powers of the fundamental bose field, general exponentials of it, the energy…
We show that quantum computation can be performed in a system at thermal equilibrium if a spontaneous symmetry breaking occurs. The computing process is associated to the time evolution of the statistical average of the qubit coherence…
To solve the AC optimal power flow problem, it is proposed in [1,2] that a convex conic approximation to branch flow model (BFM) can be obtained if we first eliminate phase angles of voltages and currents and then relax a set of equality…
Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…