5,861 research outputs found
Superlinear advantage for exact quantum algorithms
A quantum algorithm is exact if, on any input data, it outputs the correct
answer with certainty (probability 1). A key question is: how big is the
advantage of exact quantum algorithms over their classical counterparts:
deterministic algorithms. For total Boolean functions in the query model, the
biggest known gap was just a factor of 2: PARITY of N inputs bits requires
queries classically but can be computed with N/2 queries by an exact quantum
algorithm.
We present the first example of a Boolean function f(x_1, ..., x_N) for which
exact quantum algorithms have superlinear advantage over the deterministic
algorithms. Any deterministic algorithm that computes our function must use N
queries but an exact quantum algorithm can compute it with O(N^{0.8675...})
queries.Comment: 20 pages, v6: small number of small correction
A Survey of Quantum Learning Theory
This paper surveys quantum learning theory: the theoretical aspects of
machine learning using quantum computers. We describe the main results known
for three models of learning: exact learning from membership queries, and
Probably Approximately Correct (PAC) and agnostic learning from classical or
quantum examples.Comment: 26 pages LaTeX. v2: many small changes to improve the presentation.
This version will appear as Complexity Theory Column in SIGACT News in June
2017. v3: fixed a small ambiguity in the definition of gamma(C) and updated a
referenc
Exact quantum query complexity of
In the exact quantum query model a successful algorithm must always output
the correct function value. We investigate the function that is true if exactly
or of the input bits given by an oracle are 1. We find an optimal
algorithm (for some cases), and a nontrivial general lower and upper bound on
the minimum number of queries to the black box.Comment: 19 pages, fixed some typos and constraint
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