27,504 research outputs found
Pauli Measurements are Universal
International audienc
Quantum computational universality of hypergraph states with Pauli-X and Z basis measurements
Measurement-based quantum computing is one of the most promising quantum
computing models. Although various universal resource states have been proposed
so far, it was open whether only two Pauli bases are enough for both of
universal measurement-based quantum computing and its verification. In this
paper, we construct a universal hypergraph state that only requires and
-basis measurements for universal measurement-based quantum computing. We
also show that universal measurement-based quantum computing on our hypergraph
state can be verified in polynomial time using only and -basis
measurements. Furthermore, in order to demonstrate an advantage of our
hypergraph state, we construct a verifiable blind quantum computing protocol
that requires only and -basis measurements for the client.Comment: 12 pages, 8 figures, 1 table, close to published versio
Determinism and Computational Power of Real Measurement-based Quantum Computation
International audienceMeasurement-based quantum computing (MBQC) is a universal model for quantum computation. The combinatorial characterisation of determinism in this model, powered by measurements, and hence, fundamentally probabilistic, is the cornerstone of most of the breakthrough results in this field. The most general known sufficient condition for a deterministic MBQC to be driven is that the underlying graph of the computation has a particular kind of flow called Pauli flow. The necessity of the Pauli flow was an open question. We show that the Pauli flow is necessary for real-MBQC, and not in general providing counterexamples for (complex) MBQC. We explore the consequences of this result for real MBQC and its applications. Real MBQC and more generally real quantum computing is known to be universal for quantum computing. Real MBQC has been used for interactive proofs by McKague. The two-prover case corresponds to real-MBQC on bipartite graphs. While (complex) MBQC on bipartite graphs are universal, the universality of real MBQC on bipartite graphs was an open question. We show that real bipartite MBQC is not universal proving that all measurements of real bipartite MBQC can be parallelised leading to constant depth computations. As a consequence, McKague techniques cannot lead to two-prover interactive proofs
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
Trading classical and quantum computational resources
We propose examples of a hybrid quantum-classical simulation where a
classical computer assisted by a small quantum processor can efficiently
simulate a larger quantum system. First we consider sparse quantum circuits
such that each qubit participates in O(1) two-qubit gates. It is shown that any
sparse circuit on n+k qubits can be simulated by sparse circuits on n qubits
and a classical processing that takes time . Secondly, we
study Pauli-based computation (PBC) where allowed operations are
non-destructive eigenvalue measurements of n-qubit Pauli operators. The
computation begins by initializing each qubit in the so-called magic state.
This model is known to be equivalent to the universal quantum computer. We show
that any PBC on n+k qubits can be simulated by PBCs on n qubits and a classical
processing that takes time . Finally, we propose a purely
classical algorithm that can simulate a PBC on n qubits in a time where . This improves upon the brute-force simulation
method which takes time . Our algorithm exploits the fact that
n-fold tensor products of magic states admit a low-rank decomposition into
n-qubit stabilizer states.Comment: 14 pages, 4 figure
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