相关论文: Quantum Hidden Subgroup Algorithms: The Devil Is i…
It has recently been shown that quantum computers can efficiently solve the Heisenberg hidden subgroup problem, a problem whose classical query complexity is exponential. This quantum algorithm was discovered within the framework of using…
Quantum cryptography allows one to distribute a secret key between two remote parties using the fundamental principles of quantum mechanics. The well-known established paradigm for the quantum key distribution relies on the actual…
Machine learning algorithms are powerful tools for data driven tasks such as image classification and feature detection, however their vulnerability to adversarial examples - input samples manipulated to fool the algorithm - remains a…
A new LLNL Strategic Initiative is focused on developing improved methods for Bayesian inference when the input data depends on hidden parameters. Part of this effort involves investigating the idea of using an array of quantum oscillators…
The quantum hidden subgroup approach is an actively studied approach to solve combinatorial problems in quantum complexity theory. With the success of the Shor's algorithm, it was hoped that similar approach may be useful to solve the other…
In this paper we consider a generalization of quantum hash functions for arbitrary groups. We show that quantum hash function exists for arbitrary abelian group. We construct a set of "good" automorphisms --- a key component of quantum hash…
We present a novel approach to secret key establishment that appears to be resistant to currently known quantum cryptanalytic algorithms. This quantum resistance arises because the security of our method does not rely on the difficulty of…
We present a polynomial-time quantum algorithm for the Hidden Subgroup Problem over $\mathbb{D}_{2^n}$. The usual approach to the Hidden Subgroup Problem relies on harmonic analysis in the domain of the problem, and the best known algorithm…
We consider an approach to deciding isomorphism of rigid n-vertex graphs (and related isomorphism problems) by solving a nonabelian hidden shift problem on a quantum computer using the standard method. Such an approach is arguably more…
There have been several research works on the hidden shift problem, quantum algorithms for the problem, and their applications. However, all the results have focused on discrete groups with discrete oracle functions. In this paper, we…
Ever since its inception, cryptography has been caught in a vicious circle: Cryptographers keep inventing methods to hide information, and cryptanalysts break them, prompting cryptographers to invent even more sophisticated encryption…
Group homomorphic encryption represents one of the most important building blocks in modern cryptography. It forms the basis of widely-used, more sophisticated primitives, such as CCA2-secure encryption or secure multiparty computation.…
Hidden variables are extra components added to try to banish counterintuitive features of quantum mechanics. We start with a quantum-mechanical model and describe various properties that can be asked of a hidden-variable model. We present…
We study the problem of finding a subgroup of a given order in a finite group, where the group is represented by its Cayley table. We analyze the complexity of the problem in the special case of abelian groups and present an optimal…
Modern programming relies on our ability to treat preprogrammed functions as black boxes - we can invoke them as subroutines without knowing their physical implementation. Here we show it is generally impossible to execute an unknown…
We revisit the finite Abelian hidden subgroup problem (AHSP) from a mathematical perspective and make the following contributions. First, by employing amplitude amplification, we present an exact quantum algorithm for the finite AHSP, our…
This is continuation of the approach to performing quantum algorithms using geometric structures which was presented by Aerts and Czachor. We solve the Simon's problem which, next to the Shor's alghorithm, is a representative of a quantum…
Quantum protocols including quantum key distribution and blind quantum computing often require the preparation of quantum states of known dimensions. Here, we show that, rather surprisingly, hidden multi-dimensional modulation is often…
When the 4-state or the 6-state protocol of quantum cryptography is carried out on a noisy (i.e. realistic) quantum channel, then the raw key has to be processed to reduce the information of an adversary Eve down to an arbitrarily low…
Quantum annealing promises to be an effective heuristic for complex NP-hard problems. However, clear demonstrations of quantum advantage are wanting, primarily constrained by the difficulty of embedding the problem into the quantum…