Related papers: Quantum Group Actions
We consider actions of quantum groups on lattice spin systems. We show that if an action of a quantum group respects the local structure of a lattice system, it has to be an ordinary group. Even allowing weakly delocalized (quasi-local)…
In the near future, there will likely be special-purpose quantum computers with 40-50 high-quality qubits. This paper lays general theoretical foundations for how to use such devices to demonstrate "quantum supremacy": that is, a clear…
The quantum Fourier transform (QFT) is central to many quantum algorithms, yet its necessity is not always well understood. We re-examine its role in canonical query problems. The Deutsch-Jozsa algorithm requires neither a QFT nor a domain…
Possible contractions of quantum orthogonal groups which correspond to different choices of primitive elements of Hopf algebra are considered and all allowed contractions in Cayley--Klein scheme are obtained. Quantum deformations of…
The earlier proposed Dynamics-Generating Approach (DGA) is reviewed and extended. Starting from an arbitrarily chosen group or semigroup which have structure similar to the structure of Galilei group, DGA allows one to construct…
We demonstrated the detailed construction of the hybrid quantum-classical computer. Based on this architecture, the useful concept of amplitude interception is illustrated. It is then embedded into a combination of Depth-First Search and…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
This paper focuses on the classification of classes of topological equivalence of finite group actions on Riemann surfaces. By the Riemann-Hurwitz bound, there are just finitely many groups that act conformally on a closed orientable…
The notion of quantum hashing formalized by F. Ablayev and A. Vasiliev in 2013. F. Ablayev and M. Ablayev in 2014 introduced the notion of quantum hash generator which is convenient technical tool for constructing quantum hash func- tions.…
One-way functions are fundamental to classical cryptography and their existence remains a longstanding problem in computational complexity theory. Recently, a provable quantum one-way function has been identified, which maintains its…
Universal quantum computation on decoherence-free subspaces and subsystems (DFSs) is examined with particular emphasis on using only physically relevant interactions. A necessary and sufficient condition for the existence of…
The Quantum Skip Gate (QSG) is a unitary circuit primitive that coherently superposes the execution and omission of an expensive quantum subroutine based on the outcome of a cheaper preceding subroutine, without mid-circuit measurement or…
We prove First Fundamental Theorems of Coinvariant Theory for the standard coactions of the quantum general and special linear groups on tensor products of quantum matrix algebras. More precisely, let m,n,t be arbitrary positive integers,…
Cryptographic systems are derived using units in group rings. Combinations of types of units in group rings give units not of any particular type. This includes cases of taking powers of units and products of such powers and adds the…
Secure computation often benefits from the use of correlated randomness to achieve fast, non-cryptographic online protocols. A recent paradigm put forth by Boyle $\textit{et al.}$ (CCS 2018, Crypto 2019) showed how pseudorandom correlation…
Cryptographic hash functions are fundamental primitives widely used in practice. For such a function $f:\{0, 1\}^n\to\{0, 1\}^m$, it is nearly impossible for an adversary to produce the hash $f(x)$ without knowing the secret message…
In this work we present a principle which says that quasimorphisms can be obtained via "local data" of the group action on certain appropriate spaces. In a rough manner the principle says that instead of starting with a given group and try…
Complex cryptographic protocols are often constructed from simpler building-blocks. In order to advance quantum cryptography, it is important to study practical building-blocks that can be used to develop new protocols. An example is…
It is an important question to find constructions of quantum cryptographic protocols which rely on weaker computational assumptions than classical protocols. Recently, it has been shown that oblivious transfer and multi-party computation…
Quantum mechanics provides cryptographic primitives whose security is grounded in hardness assumptions independent of those underlying classical cryptography. However, existing proposals require low-noise quantum communication and…