相关论文: How many functions can be distinguished with k qua…
We study four problems: put $n$ distinguishable/non-distinguishable balls into $k$ non-empty distinguishable/non-distinguishable boxes randomly. What is the threshold function $k=k(n) $ to make almost sure that no two boxes contain the same…
We study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x+s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends…
An important theoretical problem in the study of quantum computation, that is also practically relevant in the context of near-term quantum devices, is to understand the computational power of hybrid models, that combine poly-time classical…
The q-Bessel-Macdonald functions of kinds 1, 2 and 3 are considered. Their representations by classical integral are constructed.
QMA is the class of languages that can be decided by an efficient quantum verifier given a quantum witness, whereas QCMA is the class of such languages where the efficient quantum verifier only is given a classical witness. A challenging…
A real-valued function on R^n is k-regulous, where k is a nonnegative integer, if it is of class C^k and can be represented as a quotient of two polynomial functions on R^n. Several interesting results involving such functions have been…
We study a longstanding question of Aaronson and Kuperberg on whether there exists a classical oracle separating $\mathsf{QMA}$ from $\mathsf{QCMA}$. Settling this question in either direction would yield insight into the power of quantum…
We describe an inequality of finite or infinite sequences of real numbers and their quotients. More precisely, we compare the quotient of H\"older functionals of two sequences of numbers with the sum of their quotients. In the last section…
General relativity and quantum mechanics are incompatible at the Planck scale. This contention can be examined if a quantum computer is set to operate at a rate that exceeds the classical limit of one operation per Planck volume-time, or…
The current paper presents a new quantum algorithm for finding multicollisions, often denoted by $\ell$-collisions, where an $\ell$-collision for a function is a set of $\ell$ distinct inputs that are mapped by the function to the same…
We propose an optical implementation of the Deutsch-Jozsa Algorithm using classical light in a binary decision-tree scheme. Our approach uses a ring cavity and linear optical devices in order to efficiently quarry the oracle functional…
While recent work suggests that quantum computers can speed up the solution of semidefinite programs, little is known about the quantum complexity of more general convex optimization. We present a quantum algorithm that can optimize a…
As quantum computers mature, the applicability in practice becomes more important. Many uses of quantum computers will be hybrid, with classical computers still playing an important role in operating and using the quantum computer. The term…
What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field…
Given a unitary representation of a finite group on a finite-dimensional Hilbert space, we show how to find a state whose translates under the group are distinguishable with the highest probability. We apply this to several quantum oracle…
It is shown that a good estimate of the fidelity of an experimentally realized quantum process can be obtained by measuring the outputs for only two complementary sets of input states. The number of measurements required to test a quantum…
How many quantum queries are required to determine the coefficients of a degree-$d$ polynomial in $n$ variables? We present and analyze quantum algorithms for this multivariate polynomial interpolation problem over the fields…
In this paper, for every $n \in \mathbb{N}$, the following relationships between the functions $K_{b}(n)$ and $K_{e}(n)$ and the Bernoulli and Euler numbers are proved: \[ B_{2n} = -\,\frac{(2n)!}{2^{2n}-2}\, K_{b}(n), \qquad E_{2n} =…
Classically, determining the gradient of a black-box function f:R^p->R requires p+1 evaluations. Using the quantum Fourier transform, two evaluations suffice. This is based on the approximate local periodicity of exp(2*pi*i*f(x)). It is…
Given a large dataset of many tuples, it is hard for users to pick out their preferred tuples. Thus, the preference query problem, which is to find the most preferred tuples from a dataset, is widely discussed in the database area. In this…