60,456 research outputs found
Analysis of Quantum Entanglement in Quantum Programs using Stabilizer Formalism
Quantum entanglement plays an important role in quantum computation and
communication. It is necessary for many protocols and computations, but causes
unexpected disturbance of computational states. Hence, static analysis of
quantum entanglement in quantum programs is necessary. Several papers studied
the problem. They decided qubits were entangled if multiple qubits unitary
gates are applied to them, and some refined this reasoning using information
about the state of each separated qubit. However, they do not care about the
fact that unitary gate undoes entanglement and that measurement may separate
multiple qubits. In this paper, we extend prior work using stabilizer
formalism. It refines reasoning about separability of quantum variables in
quantum programs.Comment: In Proceedings QPL 2015, arXiv:1511.0118
New Developments in Quantum Algorithms
In this survey, we describe two recent developments in quantum algorithms.
The first new development is a quantum algorithm for evaluating a Boolean
formula consisting of AND and OR gates of size N in time O(\sqrt{N}). This
provides quantum speedups for any problem that can be expressed via Boolean
formulas. This result can be also extended to span problems, a generalization
of Boolean formulas. This provides an optimal quantum algorithm for any Boolean
function in the black-box query model.
The second new development is a quantum algorithm for solving systems of
linear equations. In contrast with traditional algorithms that run in time
O(N^{2.37...}) where N is the size of the system, the quantum algorithm runs in
time O(\log^c N). It outputs a quantum state describing the solution of the
system.Comment: 11 pages, 1 figure, to appear as an invited survey talk at MFCS'201
Shaded Tangles for the Design and Verification of Quantum Programs (Extended Abstract)
We give a scheme for interpreting shaded tangles as quantum programs, with
the property that isotopic tangles yield equivalent programs. We analyze many
known quantum programs in this way -- including entanglement manipulation and
error correction -- and in each case present a fully-topological formal
verification, yielding in several cases substantial new insight into how the
program works. We also use our methods to identify several new or generalized
procedures.Comment: In Proceedings QPL 2017, arXiv:1802.0973
Geometry of abstraction in quantum computation
Quantum algorithms are sequences of abstract operations, performed on
non-existent computers. They are in obvious need of categorical semantics. We
present some steps in this direction, following earlier contributions of
Abramsky, Coecke and Selinger. In particular, we analyze function abstraction
in quantum computation, which turns out to characterize its classical
interfaces. Some quantum algorithms provide feasible solutions of important
hard problems, such as factoring and discrete log (which are the building
blocks of modern cryptography). It is of a great practical interest to
precisely characterize the computational resources needed to execute such
quantum algorithms. There are many ideas how to build a quantum computer. Can
we prove some necessary conditions? Categorical semantics help with such
questions. We show how to implement an important family of quantum algorithms
using just abelian groups and relations.Comment: 29 pages, 42 figures; Clifford Lectures 2008 (main speaker Samson
Abramsky); this version fixes a pstricks problem in a diagra
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