Related papers: A quantum algorithm for computing the Carmichael f…
We present several new examples of speed-ups obtainable by quantum algorithms in the context of property testing. First, motivated by sampling algorithms, we consider probability distributions given in the form of an oracle $f:[n]\to[m]$.…
We study quantum algorithms for the hidden shift problem of complex scalar- and vector-valued functions on finite abelian groups. Given oracle access to a shifted function and the Fourier transform of the unshifted function, the goal is to…
Many quantum algorithms make use of oracles which evaluate classical functions on a superposition of inputs. In order to facilitate implementation, testing, and resource estimation of such algorithms, we present quantum circuits for…
We prove lower bounds on the error probability of a quantum algorithm for searching through an unordered list of N items, as a function of the number T of queries it makes. In particular, if T=O(sqrt{N}) then the error is lower bounded by a…
Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's…
This paper extends the quantum search class of algorithms to the multiple solution case. It is shown that, like the basic search algorithm, these too can be represented as a rotation in an appropriately defined two dimensional vector space.…
We study algorithms for solving three problems on strings. The first one is the Most Frequently String Search Problem. The problem is the following. Assume that we have a sequence of $n$ strings of length $k$. The problem is finding the…
Quantum sampling, a fundamental subroutine in numerous quantum algorithms, involves encoding a given probability distribution in the amplitudes of a pure state. Given the hefty cost of large-scale quantum storage, we initiate the study of…
A potential approach for demonstrating quantum advantage is using quantum computers to simulate fermionic systems. Quantum algorithms for fermionic system simulation usually involve the Hamiltonian evolution and measurements. However, in…
Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
Many quantum algorithms involve the evaluation of expectation values. Optimal strategies for estimating a single expectation value are known, requiring a number of state preparations that scales with the target error $\varepsilon$ as…
We consider the problem of estimating the partition function $Z(\beta)=\sum_x \exp(-\beta(H(x))$ of a Gibbs distribution with a Hamilton $H(\cdot)$, or more precisely the logarithm of the ratio $q=\ln Z(0)/Z(\beta)$. It has been recently…
Properties of Shor's algorithm and the related period-finding algorithm could serve as benchmarks for the operation of a quantum computer. Distinctive universal behaviour is expected for the probability for success of the period-finding…
The development of tailored materials for specific applications is an active field of research in chemistry, material science and drug discovery. The number of possible molecules that can be obtained from a set of atomic species grow…
This paper explores the problem of quantum measurement complexity. In computability theory, the complexity of a problem is determined by how long it takes an effective algorithm to solve it. This complexity may be compared to the difficulty…
The quantum search algorithm of Chen and Diao, which finds with certainty a single target item in an unsorted database, is modified so as to be capable of searching for an arbitrary specified number of target items. If the number of…
We give an algorithm to compute $N$ steps of a convolution quadrature approximation to a continuous temporal convolution using only $O(N \log N)$ multiplications and $O(\log N)$ active memory. The method does not require evaluations of the…
The Carmichael lambda function $\lambda(n)$ is defined to be the smallest positive integer $m$ such that $a^m \equiv 1 \pmod{n}$ for all $(a,n)=1.$ $\lambda_k(n)$ is defined to be the $k$th iterate of $\lambda(n).$ Let L(n) be the smallest…
We give a technique to reduce the error probability of quantum algorithms that determine whether its input has a specified property of interest. The standard process of reducing this error is statistical processing of the results of…
We demonstrate the implementation of a quantum algorithm for estimating the number of matching items in a search operation using a two qubit nuclear magnetic resonance (NMR) quantum computer.