相关论文: Candidate One-Way Functions and One-Way Permutatio…

Quantum neural networks (QNNs) represent a pioneering intersection of quantum computing and deep learning. In this study, we unveil a fundamental convolution property inherent to QNNs, stemming from the natural parallelism of quantum gate…

Let $I = (i_1, \dots, i_k)$ and $J = (j_1, \dots, j_k)$ be two length $k$ sequences drawn from $\{1, \dots, n \}$. We have the group algebra element $[I,J] := \sum_{w(I) = J} w \in \mathbb{C}[\mathfrak{S}_n]$ where the sum is over…

Our main result here is that the specialization at $t=1/q$ of the $Q_{km,kn}$ operators studied in [4] may be given a very simple plethystic form. This discovery yields elementary and direct derivations of several identities relating these…

We introduce and analyze a novel class of binary operations on finite-dimensional vector spaces over a field K, defined by second-order multilinear expressions with linear shifts. These operations generate polynomials whose degree increases…

One-time programs (Goldwasser, Kalai and Rothblum, CRYPTO 2008) are functions that can be run on any single input of a user's choice, but not on a second input. Classically, they are unachievable without trusted hardware, but the…

Quantum computations promise the ability to solve problems intractable in the classical setting. Restricting the types of computations considered often allows to establish a provable theoretical advantage by quantum computations, and later…

We study 1-way quantum finite automata (QFAs) and compare them with their classical counterparts. We show that 1-way QFAs can be very space efficient. We construct a 1-way QFAs that are quadratically smaller than any equivalent…

Quantum signal processing and quantum singular value transformation are powerful tools to implement polynomial transformations of block-encoded matrices on quantum computers, and has achieved asymptotically optimal complexity in many…

Let $R$ be a finite commutative ring with $1\ne 0$. The set $\mathcal{F}(R)$ of polynomial functions on $R$ is a finite commutative ring with pointwise operations. Its group of units $\mathcal{F}(R)^\times$ is just the set of all…

An interesting classical result due to Jackson allows polynomial-time learning of the function class DNF using membership queries. Since in most practical learning situations access to a membership oracle is unrealistic, this paper explores…

One-way state generators (OWSG) are natural quantum analogs to classical one-way functions. We consider statistically-verifiable OWSGs (sv-OWSG), which are potentially weaker objects than OWSGs. We show that O(n/log(n))-copy sv-OWSGs (n…

We characterize the set of all N-ary quasigroups of order 4: every N-ary quasigroup of order 4 is permutably reducible or semilinear. Permutable reducibility means that an N-ary quasigroup can be represented as a composition of K-ary and…

Quantum Hall effect wave functions corresponding to the filling factors 1/2p+1, 2/2p+1, ..., 2p/2p+1, 1, are shown to form a basis of irreducible cyclic representation of the quantum algebra U_q(sl(2)) at q^{2p+1}=1. Thus, the wave…

Negabent functions were introduced as a generalization of bent functions, which have applications in coding theory and cryptography. In this paper, we have extended the notion of negabent functions to the functions defined from…

We investigate the subclass of reversible functions that are self-inverse and relate them to reversible circuits that are equal to their reverse circuit, which are called palindromic circuits. We precisely determine which self-inverse…

We investigate the question which Q-valued characters and characters of Q-representations of finite groups are Z-linear combinations of permutation characters. This question is known to reduce to that for quasi-elementary groups, and we…

We describe the construction of quantum gates (unitary operators) from boolean functions and give a number of applications. Both non-reversible and reversible boolean functions are considered. The construction of the Hamilton operator for a…

The promise of quantum computation and its consequences for complexity-theoretic cryptography motivates an immediate search for cryptosystems which can be implemented with current technology, but which remain secure even in the presence of…

The Quantum Singular Value Transformation (QSVT) is a technique that provides a unified framework for describing many of the quantum algorithms discovered to date. We implement a noise-free simulation of the technique to investigate how it…

One of the principal obstacles on the way to quantum computers is the lack of distinguished basis in the space of unitary evolutions and thus the lack of the commonly accepted set of basic operations (universal gates). A natural choice,…