Related papers: A simple algorithm for extending the identities fo…
We describe a bilinear identity satisfied by certain multidimensional q-hypergeometric integrals. The identity can be considered as a deformation of the Riemann bilinear relation for the twisted de Rham (co)homologies. The identity also…
We use Maya diagrams to refine the criterion by Fulton and Woodward for the smallest powers of the quantum parameter $q$ that occur in a product of Schubert classes in the (small) quantum cohomology of partial flags. Our approach using Maya…
We find a $q$-analog of the following symmetrical identity involving binomial coefficients $\binom{n}{m}$ and Eulerian numbers $A_{n,m}$, due to Chung, Graham and Knuth [{\it J. Comb.}, {\bf 1} (2010), 29--38]: {equation*} \sum_{k\geq…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
We give a new proof of the dilogarithm identities, associated to the (2,2n+1) minimal models of the Virasoro algebra.
Information-processing tasks modelled by homomorphisms between relational structures can witness quantum advantage when entanglement is used as a computational resource. We prove that the occurrence of quantum advantage is determined by the…
In this paper we give new identities involving q-Euler polynomials of higher order.
Classical fingerprinting associates with each string a shorter string (its fingerprint), such that, with high probability, any two distinct strings can be distinguished by comparing their fingerprints alone. The fingerprints can be…
We initiate the systematic study of QMA algorithms in the setting of property testing, to which we refer as QMA proofs of proximity (QMAPs). These are quantum query algorithms that receive explicit access to a sublinear-size untrusted proof…
Combining Newton and Lagrange interpolation, we give $q$-identities which generalize results of Van Hamme, Uchimura, Dilcher and Prodinger.
Given two finite posets P and Q, P is a chain minor of Q if there exists a partial function f from the elements of Q to the elements of P such that for every chain in P there is a chain C_Q in Q with the property that f restricted to C_Q is…
First we prove some elementary but useful identities in the group ring of Q/Z. Our identities have potential applications to several unsolved problems which involve sums of Farey fractions. In this paper we use these identities, together…
Quantum coherence plays an important role in quantum information protocols that provide an advantage over classical information processing. The amount of coherence that can exist between two orthogonal subspaces is limited by the positivity…
A quantum generalization of Rogers' five term, or ``pentagon'' dilogarithm identity is suggested. It is shown that the classical limit gives usual Rogers' identity. The case where the quantum identity is realized in finite dimensional space…
In this paper we show that certain special cases of the hidden subgroup problem can be solved in polynomial time by a quantum algorithm. These special cases involve finding hidden normal subgroups of solvable groups and permutation groups,…
It is discussed an opportunity to introduce new class of quantum algorithms based on possibility to express amplitude of transition between two states of quantum system as sum of some function along all possible classical paths. Continuous…
An extension of Quantum Group is described. We propose to unite the quantum groups with parameter q and with parameter modularly dual to q.
We deduce new q-series identities by applying inverse relations to certain identities for basic hypergeometric series. The identities obtained themselves do not belong to the hierarchy of basic hypergeometric series. We extend two of our…
We describe the combinatorics of the multisemigroup with multiplicities for the tensor category of subbimodules of the identity bimodule, for an arbitrary non-uniform orientation of a finite cyclic quiver.
We present a one-parameter family of quantum maps whose spectral statistics are of the same intermediate type as observed in polygonal quantum billiards. Our central result is the evaluation of the spectral two-point correlation form factor…