Search Results

Infrastructures are group-like objects that make their appearance in arithmetic geometry in the study of computational problems related to number fields and function fields over finite fields. The most prominent computational tasks of infrastructures ...

We present an efficient general method for realizing a quantum walk operator corre-sponding to an arbitrary sparse classical random walk. Our approach is based on Groverand Rudolph's method for preparing coherent versions of efficiently integrable ...

We consider the following combinatorial problem. We are given three strings s, t, and t'of length L over some fixed finite alphabet and an integer m that is polylogarithmic inL. We have a symmetric relation on substrings of constant length that ...

Given a verifier circuit for a problem in QMA, we show how to exponentially amplifythe gap between its acceptance probabilities in the 'yes' and 'no' cases, with a methodthat is quadratically faster than the procedure given by Marriott and Watrous [1]. ...

The Jones and HOMFLY polynomials are link invariants with close connections to quan-tum computing. It was recently shown that finding a certain approximation to the Jonespolynomial of the trace closure of a braid at the fifth root of unity is a complete ...

We consider a natural generalization of an abelian Hidden Subgroup Problem where thesubgroups and their cosets correspond to graphs of linear functions over a finite field Fwith d elements. The hidden functions of the generalized problem are not ...

We consider a hypothetical apparatus that implements measurements for arbitrary 4- local quantum observables A on n qubits. The apparatus implements the "measurement algorithm" after receiving a classical description of A. We show that a few precise ...

We analyze relationships between quantum computation and a family of generalizations of the Jones polynomial. Extending recent work by Aharonov et al., we give efficient quantum circuits for implementing the unitary Jones-Wenzl representations of the ...

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 natural than ...

We establish a connection between the problem of constructing maximal collections of mutually unbiased bases (MUBs) and an open problem in the theory of Lie algebras. More precisely, we show that a collection of µ MUBs in n gives rise to a collection of ...

Recently, P. Wocjan and M. Horodecki [Open Syst. Inf. Dyn. 12, 331 (2005)] gave a characterizationof combinatorially independent permutation separability criteria. Combinatorialindependence is a necessary condition for permutations to yield truly ...

We show that k = w + 2 mutually unbiased bases can be constructed in any square dimension d = s² provided that there are w mutually orthogonal Latin squares of order s. The construction combines the design-theoretic objects (s, k)-nets (which can be ...

QMA and QCMA are possible quantum analogues of the complexity class NP. In QMA the proof is a quantum state and the verification is a quantum circuit. In contrast, in QCMA the proof is restricted to be a classical state. It is not known whether QMA ...

Any quantum system with a non-trivial Hamiltonian is able to simulate any other Hamiltonian evolution provided that a sufficiently large group of unitary control operations is available. We show that there exist finite groups with this property and ...

We consider a quantum computer consisting of n spins with an arbitrary but fixed pair-interaction Hamiltonian and describe how to simulate other pair-interactions by interspersing the natural time evolution with fast local transformations. Calculating ...