3,632 research outputs found
Quantum Branching Programs and Space-Bounded Nonuniform Quantum Complexity
In this paper, the space complexity of nonuniform quantum computations is
investigated. The model chosen for this are quantum branching programs, which
provide a graphic description of sequential quantum algorithms. In the first
part of the paper, simulations between quantum branching programs and
nonuniform quantum Turing machines are presented which allow to transfer lower
and upper bound results between the two models. In the second part of the
paper, different variants of quantum OBDDs are compared with their
deterministic and randomized counterparts. In the third part, quantum branching
programs are considered where the performed unitary operation may depend on the
result of a previous measurement. For this model a simulation of randomized
OBDDs and exponential lower bounds are presented.Comment: 45 pages, 3 Postscript figures. Proofs rearranged, typos correcte
Turing machines can be efficiently simulated by the General Purpose Analog Computer
The Church-Turing thesis states that any sufficiently powerful computational
model which captures the notion of algorithm is computationally equivalent to
the Turing machine. This equivalence usually holds both at a computability
level and at a computational complexity level modulo polynomial reductions.
However, the situation is less clear in what concerns models of computation
using real numbers, and no analog of the Church-Turing thesis exists for this
case. Recently it was shown that some models of computation with real numbers
were equivalent from a computability perspective. In particular it was shown
that Shannon's General Purpose Analog Computer (GPAC) is equivalent to
Computable Analysis. However, little is known about what happens at a
computational complexity level. In this paper we shed some light on the
connections between this two models, from a computational complexity level, by
showing that, modulo polynomial reductions, computations of Turing machines can
be simulated by GPACs, without the need of using more (space) resources than
those used in the original Turing computation, as long as we are talking about
bounded computations. In other words, computations done by the GPAC are as
space-efficient as computations done in the context of Computable Analysis
Complexity classification of two-qubit commuting hamiltonians
We classify two-qubit commuting Hamiltonians in terms of their computational
complexity. Suppose one has a two-qubit commuting Hamiltonian H which one can
apply to any pair of qubits, starting in a computational basis state. We prove
a dichotomy theorem: either this model is efficiently classically simulable or
it allows one to sample from probability distributions which cannot be sampled
from classically unless the polynomial hierarchy collapses. Furthermore, the
only simulable Hamiltonians are those which fail to generate entanglement. This
shows that generic two-qubit commuting Hamiltonians can be used to perform
computational tasks which are intractable for classical computers under
plausible assumptions. Our proof makes use of new postselection gadgets and Lie
theory.Comment: 34 page
Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
We consider quantum computations comprising only commuting gates, known as
IQP computations, and provide compelling evidence that the task of sampling
their output probability distributions is unlikely to be achievable by any
efficient classical means. More specifically we introduce the class post-IQP of
languages decided with bounded error by uniform families of IQP circuits with
post-selection, and prove first that post-IQP equals the classical class PP.
Using this result we show that if the output distributions of uniform IQP
circuit families could be classically efficiently sampled, even up to 41%
multiplicative error in the probabilities, then the infinite tower of classical
complexity classes known as the polynomial hierarchy, would collapse to its
third level. We mention some further results on the classical simulation
properties of IQP circuit families, in particular showing that if the output
distribution results from measurements on only O(log n) lines then it may in
fact be classically efficiently sampled.Comment: 13 page
Time and Space Bounds for Reversible Simulation
We prove a general upper bound on the tradeoff between time and space that
suffices for the reversible simulation of irreversible computation. Previously,
only simulations using exponential time or quadratic space were known.
The tradeoff shows for the first time that we can simultaneously achieve
subexponential time and subquadratic space.
The boundary values are the exponential time with hardly any extra space
required by the Lange-McKenzie-Tapp method and the ()th power time with
square space required by the Bennett method. We also give the first general
lower bound on the extra storage space required by general reversible
simulation. This lower bound is optimal in that it is achieved by some
reversible simulations.Comment: 11 pages LaTeX, Proc ICALP 2001, Lecture Notes in Computer Science,
Vol xxx Springer-Verlag, Berlin, 200
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