相关论文: An Explicit Construction of Quantum Expanders
We construct the most general form of our previously proposed nonlinear extension of quantum mechanics that possesses three basic properties. Unlike the simpler model, the new version is not completely integrable, but it has an underlying…
A large class of quantum field theories on 1+1 dimensional Minkowski space, namely, certain integrable models, has recently been constructed rigorously by Lechner. However, the construction is very abstract and the concrete form of local…
Some quantum algebras build from deformed oscillator algebras may be described in terms of a particular case of extended umbral calculus. We give here an example of a specific relation between such certain quantum algebras and generalized…
Making quantum mechanical equations and concepts come to life through interactive simulation and visualization are commonplace for augmenting learning and teaching. However, graphical visualizations nearly always exhibit a set of hard-coded…
Cosystolic expansion is a high-dimensional generalization of the Cheeger constant for simplicial complexes. Originally, this notion was motivated by the fact that it implies the topological overlapping property, but more recently it was…
(Abridged.) Quantum computers promise to solve some problems exponentially faster than traditional computers, but we still do not fully understand why this is the case. While the most studied model of quantum computation uses qubits, which…
We construct a universal code for stationary and memoryless classical-quantum channel as a quantum version of the universal coding by Csisz\'{a}r and K\"{o}rner. Our code is constructed by the combination of irreducible representation, the…
Quantum Transformers integrate the representational power of classical Transformers with the computational advantages of quantum computing. Since 2022, research in this area has rapidly expanded, giving rise to diverse technical paradigms…
In this paper we propose a naive construction of 2-dimensional extended topological quantum field theories (TQFTs), which can be further generalized to the higher-dimension extended TQFTs.
In this short note we partially answer a question of Fukaya and Kato by constructing a $q$-expansion with coefficients in a non-commutative Iwasawa algebra whose constant term is a non-commutative p-adic zeta function.
To obtain the explicit form of evolution operator in the Tavis-Cummings model we must calculate the term ${e}^{-itg(S_{+}\otimes a+S_{-}\otimes a^{\dagger})}$ explicitly which is very hard. In this paper we try to make the quantum matrix…
A general deformation of the Heisenberg algebra is introduced with two deformed operators instead of just one. This is generalised to many variables, and permits the simultaneous existence of coherent states, and the transposition of…
A binary expression in terms of operators is given which satisfies all the quantum counterparts of the algebraic properties of the classical antibracket. This quantum antibracket has therefore the same relation to the classical antibracket…
We construct a ring structure on complex cobordism tensored with the rationals, which is related to the usual ring structure as quantum cohomology is related to ordinary cohomology. The resulting object defines a generalized two-…
Based on the connection between the categorical derivation of classical programs from specifications and the category-theoretic approach to quantum physics, this paper contributes to extending the laws of classical program algebra to…
Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and quantum circuits are naturally interpretable in such structures. We…
Instead of producing quantum languages that are fit for current quantum computers, we build a language from standard classical assembler and augment it with quantum capabilities so that quantum algorithms become a subset of it. This paves…
Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…
In this note, we give a self-contained and elementary proof of the elementary construction of spectral high-dimensional expanders using elementary matrices due to Kaufman and Oppenheim [Proc. 50th ACM Symp. on Theory of Computing (STOC),…