Related papers: Quantum Algorithm for Distribution-Free Junta Test…
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…
Equivalence testing, a fundamental problem in the field of distribution testing, seeks to infer if two unknown distributions on $[n]$ are the same or far apart in the total variation distance. Conditional sampling has emerged as a powerful…
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…
Given an item and a list of values of size $N$. It is required to decide if such item exists in the list. Classical computer can search for the item in O(N). The best known quantum algorithm can do the job in $O(\sqrt{N})$. In this paper, a…
We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is redundancy in the number of measurements. More precisely, if…
It is a long-standing open question in quantum complexity theory whether the definition of $\textit{non-deterministic}$ quantum computation requires quantum witnesses $(\textsf{QMA})$ or if classical witnesses suffice $(\textsf{QCMA})$. We…
We provide more sample-efficient versions of some basic routines in quantum data analysis, along with simpler proofs. Particularly, we give a quantum "Threshold Search" algorithm that requires only $O((\log^2 m)/\epsilon^2)$ samples of a…
Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this paper, we propose quantum algorithms capable of testing whether a Hamiltonian…
We here present the rate analysis and a proof of principle realization of a device-independent quantum key distribution (QKD) protocol requiring the lowest detection efficiency necessary to achieve a secure key compared to…
The problem of tolerant junta testing is a natural and challenging problem which asks if the property of a function having some specified correlation with a $k$-Junta is testable. In this paper we give an affirmative answer to this…
Device-independent quantum key distribution (QKD) can permit the superior security even with unknown devices. In practice, however, the realization of device-independent QKD is technically challenging because of its low noise tolerance. In…
Limited by today's physical devices, quantum circuits are usually noisy and difficult to be designed deeply. The novel computing architecture of distributed quantum computing is expected to reduce the noise and depth of quantum circuits. In…
We present an optimal quantum algorithm for fidelity estimation between two quantum states when one of them is pure. In particular, the (square root) fidelity of a mixed state to a pure state can be estimated to within additive error…
Uniformity testing is arguably one of the most fundamental distribution testing problems. Given sample access to an unknown distribution $\mathbf{p}$ on $[n]$, one must decide if $\mathbf{p}$ is uniform or $\varepsilon$-far from uniform (in…
This paper gives the first separation of quantum and classical pure (i.e., non-cryptographic) computing abilities with no restriction on the amount of available computing resources, by considering the exact solvability of a celebrated…
We present an algorithm for the generalized search problem (searching $k$ marked items among $N$ items) based on a continuous Hamiltonian and exploiting resonance. This resonant algorithm has the same time complexity $O(\sqrt{N/k})$ as the…
Symmetry is an important and unifying notion in many areas of physics. In quantum mechanics, it is possible to eliminate degrees of freedom from a system by leveraging symmetry to identify the possible physical transitions. This allows us…
In this paper, we consider a quantum algorithm for solving the following problem: ``Suppose $f$ is a function given as a black box (that is also called an oracle) and $f$ is invariant under some AND-mask. Examine a property of $f$ by…
We study efficient quantum certification algorithms for quantum state set and unitary quantum channel. We present an algorithm that uses $O(\varepsilon^{-4}\ln |\mathcal{P}|)$ copies of an unknown state to distinguish whether the unknown…
Measurement-device-independent quantum key distribution (MDI-QKD), which is immune to all detector side-channel attacks, is the most promising solution to the security issues in practical quantum key distribution systems. Though several…