1,628 research outputs found
Transforming graph states to Bell-pairs is NP-Complete
Critical to the construction of large scale quantum networks, i.e. a quantum internet, is the development of fast algorithms for managing entanglement present in the network. One fundamental building block for a quantum internet is the distribution of Bell pairs between distant nodes in the network. Here we focus on the problem of transforming multipartite entangled states into the tensor product of bipartite Bell pairs between specific nodes using only a certain class of local operations and classical communication. In particular we study the problem of deciding whether a given graph state, and in general a stabilizer state, can be transformed into a set of Bell pairs on specific vertices using only single-qubit Clifford operations, single-qubit Pauli measurements and classical communication. We prove that this problem is NP-Complete
Graphical description of the action of Clifford operators on stabilizer states
We introduce a graphical representation of stabilizer states and translate
the action of Clifford operators on stabilizer states into graph operations on
the corresponding stabilizer-state graphs. Our stabilizer graphs are
constructed of solid and hollow nodes, with (undirected) edges between nodes
and with loops and signs attached to individual nodes. We find that local
Clifford transformations are completely described in terms of local
complementation on nodes and along edges, loop complementation, and change of
node type or sign. Additionally, we show that a small set of equivalence rules
generates all graphs corresponding to a given stabilizer state; we do this by
constructing an efficient procedure for testing the equality of any two
stabilizer graphs.Comment: 14 pages, 8 figures. Version 2 contains significant changes.
Submitted to PR
Scheme for constructing graphs associated with stabilizer quantum codes
We propose a systematic scheme for the construction of graphs associated with
binary stabilizer codes. The scheme is characterized by three main steps:
first, the stabilizer code is realized as a codeword-stabilized (CWS) quantum
code; second, the canonical form of the CWS code is uncovered; third, the input
vertices are attached to the graphs. To check the effectiveness of the scheme,
we discuss several graphical constructions of various useful stabilizer codes
characterized by single and multi-qubit encoding operators. In particular, the
error-correcting capabilities of such quantum codes are verified in
graph-theoretic terms as originally advocated by Schlingemann and Werner.
Finally, possible generalizations of our scheme for the graphical construction
of both (stabilizer and nonadditive) nonbinary and continuous-variable quantum
codes are briefly addressed.Comment: 42 pages, 12 figure
Hard limits on the postselectability of optical graph states
Coherent control of large entangled graph states enables a wide variety of
quantum information processing tasks, including error-corrected quantum
computation. The linear optical approach offers excellent control and
coherence, but today most photon sources and entangling gates---required for
the construction of large graph states---are probabilistic and rely on
postselection. In this work, we provide proofs and heuristics to aid
experimental design using postselection. We derive a fundamental limitation on
the generation of photonic qubit states using postselected entangling gates:
experiments which contain a cycle of postselected gates cannot be postselected.
Further, we analyse experiments that use photons from postselected photon pair
sources, and lower bound the number of classes of graph state entanglement that
are accessible in the non-degenerate case---graph state entanglement classes
that contain a tree are are always accessible. Numerical investigation up to
9-qubits shows that the proportion of graph states that are accessible using
postselection diminishes rapidly. We provide tables showing which classes are
accessible for a variety of up to nine qubit resource states and sources. We
also use our methods to evaluate near-term multi-photon experiments, and
provide our algorithms for doing so.Comment: Our manuscript comprises 4843 words, 6 figures, 1 table, 47
references, and a supplementary material of 1741 words, 2 figures, 1 table,
and a Mathematica code listin
Photonic multipartite entanglement conversion using nonlocal operations
We propose a simple setup for the conversion of multipartite entangled states
in a quantum network with restricted access. The scheme uses nonlocal
operations to enable the preparation of states that are inequivalent under
local operations and classical communication, but most importantly does not
require full access to the states. It is based on a flexible linear optical
conversion gate that uses photons, which are ideally suited for distributed
quantum computation and quantum communication in extended networks. In order to
show the basic working principles of the gate, we focus on converting a
four-qubit entangled cluster state to other locally inequivalent four-qubit
states, such as the GHZ and symmetric Dicke state. We also show how the gate
can be incorporated into extended graph state networks, and can be used to
generate variable entanglement and quantum correlations without entanglement
but nonvanishing quantum discord.Comment: 10 pages, 6 figures, correction of reference list, add Journal ref.
and DO
Deterministic construction of arbitrary states with quadratically increasing number of two-qubit gates
We propose a quantum circuit composed of gates and four single-qubit
gates to generate a state of three qubits. This circuit was then enhanced
by integrating two-qubit gates to create a state of four and five qubits.
After a couple of enhancements, we show that an arbitrary state can be
generated depending only on the degree of enhancement. The generalized formula
for the number of two-qubit gates required is given, showing that an -qubit
-state generation can be achieved with quadratically increasing number of
two-qubit gates. Also, the practical feasibility is discussed regarding photon
sources and various applications of gates
Universal MBQC with generalised parity-phase interactions and Pauli measurements
We introduce a new family of models for measurement-based quantum computation
which are deterministic and approximately universal. The resource states which
play the role of graph states are prepared via 2-qubit gates of the form
. When , these are equivalent, up
to local Clifford unitaries, to graph states. However, when , their
behaviour diverges in two important ways. First, multiple applications of the
entangling gate to a single pair of qubits produces non-trivial entanglement,
and hence multiple parallel edges between nodes play an important role in these
generalised graph states. Second, such a state can be used to realise
deterministic, approximately universal computation using only Pauli and
measurements and feed-forward. Even though, for , the relevant resource
states are no longer stabiliser states, they admit a straightforward, graphical
representation using the ZX-calculus. Using this representation, we are able to
provide a simple, graphical proof of universality. We furthermore show that for
every this family is capable of producing all Clifford gates and all
diagonal gates in the -th level of the Clifford hierarchy.Comment: 19 pages, accepted for publication in Quantum (quantum-journal.org).
A previous version of this article had the title: "Universal MBQC with
M{\o}lmer-S{\o}rensen interactions and two measurement bases
- …