Alexander Russell

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Recently, it has been shown that one-dimensional quantum walks can mix more quickly than classical random walks, suggesting that quantum Monte Carlo algorithms can outperform their classical counterparts. We study two quantum walks on the n-dimensional hypercube, one in discrete time and one in continuous time. In both cases we show that the quantum walk(More)
The Hidden Subgroup Problem is the foundation of many quantum algorithms. An eÆ ient solution is known for the problem over Abelian groups and this was used in Simon's algorithm and Shor's Fa toring and Dis rete Log algorithms. The non-Abelian ase is open; an eÆ ient solution would give rise to an eÆ ient quantum algorithm for Graph Isomorphism. We fully(More)
In the leader election problem, n players wish to elect a random leader. The difficulty is that some coalition of players may conspire to elect one of its own members. We adopt the perfect information model: all communication is by broadcast, and the bad players have unlimited computational power. Protocols proceed in rounds: though players are synchronized(More)
Many quantum algorithms, including Shor's celebrated factoring and discrete log algorithms, proceed by reduction to a <i>hidden subgroup problem</i>, in which a unknown subgroup <i>H</i> of a group <i>G</i> must be determined from a quantum state &psi; over <i>G</i> that is uniformly supported on a left coset of <i>H</i>. These hidden subgroup problems are(More)
We introduce the natural class ${\bf\,S}^P_2$ containing those languages that may be expressed in terms of two symmetric quantifiers. This class lies between $\Delta^P_2$ and $\Sigma^P_2\,\cap\,\Pi^P_2$ and naturally generates a “symmetric” hierarchy corresponding to the polynomial-time hierarchy. We demonstrate, using the probabilistic method, new(More)
The hidden subgroup problem is the foundation of many quantum algorithms. An efficient solution is known for the problem over abelian groups, employed by both Simon’s algorithm and Shor’s factoring and discrete log algorithms. The nonabelian case, however, remains open; an efficient solution would give rise to an efficient quantum algorithm for graph(More)
The <i>quantum Fourier transform</i> (QFT) is the principal ingredient of most efficient quantum algorithms. We present a generic framework for the construction of efficient quantum circuits for the QFT by "quantizing" the highly successful <i>separation of variables</i> technique for the construction of efficient classical Fourier transforms. Specifically,(More)
A graph G is said to be d-distinguishable if there is a d-coloring of G which no non-trivial automorphism preserves. That is, 9χ : G !f1; : : : ;dg; 8φ 2 Aut(G)nfidg;9v;χ(v) 6= χ(φ(v)): It was conjectured that if jGj> jAut(G)j and the Aut(G) action on G has no singleton orbits, then G is 2-distinguishable. We give an example where this fails. We partially(More)
Neighbor discovery is one of the first steps in configuring and managing a wireless network. Most existing studies on neighbor discovery assume a single-packet reception model where only a single packet can be received successfully at a receiver. In this paper, motivated by the increasing prevalence of multipacket reception (MPR) technologies such as CDMA(More)