Unambiguous Logarithmic Space Bounded Computations

On Equivalence of Nondeterministic and Unambiguous Logarithmic Space Bounded Turing Machines

Unambiguity in Logspace – a Survey

The restriction of nondeterminism to unambiguous computations has been used as an attempt to clarify the relationship between deterministic and nondeterministic models of computation. In this paper we will consider three different, increasingly more restrictive notions of unambiguity. While all of them coincide for polynomial time bounded computation, this does not seem to happen for logarithmi...

Space-Efficient Error Reduction for Unitary Quantum Computations

This paper presents a general space-efficient method for error reduction for unitary quantum computation. Consider a polynomial-time quantum computation with completeness c and soundness s, either with or without a witness (corresponding to QMA and BQP, respectively). To convert this computation into a new computation with error at most 2−p, the most space-efficient method known requires extra ...

Unambiguity and Fewness for Logarithmic Space 3 (preliminary Version, January 1991)

We consider various types of unambiguity for logarithmic space bounded Turing machines and polynomial time bounded log space auxiliary push-down automata. In particular, we introduce the notions of (general), reach, and strong unambiguity. We demonstrate that closure under complement of unambiguous classes implies equivalence of unambiguity and \unambiguous fewness". This, as we will show, appl...

Matchgate and space-bounded quantum computations are equivalent

Matchgates are an especially multiflorous class of two-qubit nearest neighbour quantum gates, defined by a set of algebraic constraints. They occur for example in the theory of perfect matchings of graphs, non-interacting fermions, and one-dimensional spin chains. We show that the computational power of circuits of matchgates is equivalent to that of space-bounded quantum computation with unita...