5 research outputs found
Local unitary versus local Clifford equivalence of stabilizer states
We study the relation between local unitary (LU) equivalence and local
Clifford (LC) equivalence of stabilizer states. We introduce a large subclass
of stabilizer states, such that every two LU equivalent states in this class
are necessarily LC equivalent. Together with earlier results, this shows that
LC, LU and SLOCC equivalence are the same notions for this class of stabilizer
states. Moreover, recognizing whether two given stabilizer states in the
present subclass are locally equivalent only requires a polynomial number of
operations in the number of qubits.Comment: 8 pages, replaced with published versio
Edge local complementation for logical cluster states
A method is presented for the implementation of edge local complementation in
graph states, based on the application of two Hadamard operations and a single
controlled-phase (CZ) gate. As an application, we demonstrate an efficient
scheme to construct a one-dimensional logical cluster state based on the
five-qubit quantum error-correcting code, using a sequence of edge local
complementations. A single physical CZ operation, together with local
operations, is sufficient to create a logical CZ operation between two logical
qubits. The same construction can be used to generate any encoded graph state.
This approach in concatenation may allow one to create a hierarchical quantum
network for quantum information tasks.Comment: 15 pages, two figures, IOP styl
Cartoon Computation: Quantum-like computing without quantum mechanics
We present a computational framework based on geometric structures. No
quantum mechanics is involved, and yet the algorithms perform tasks analogous
to quantum computation. Tensor products and entangled states are not needed --
they are replaced by sets of basic shapes. To test the formalism we solve in
geometric terms the Deutsch-Jozsa problem, historically the first example that
demonstrated the potential power of quantum computation. Each step of the
algorithm has a clear geometric interpetation and allows for a cartoon
representation.Comment: version accepted in J. Phys.A (Letter to the Editor