550,208 research outputs found
A single-shot measurement of the energy of product states in a translation invariant spin chain can replace any quantum computation
In measurement-based quantum computation, quantum algorithms are implemented
via sequences of measurements. We describe a translationally invariant
finite-range interaction on a one-dimensional qudit chain and prove that a
single-shot measurement of the energy of an appropriate computational basis
state with respect to this Hamiltonian provides the output of any quantum
circuit. The required measurement accuracy scales inverse polynomially with the
size of the simulated quantum circuit. This shows that the implementation of
energy measurements on generic qudit chains is as hard as the realization of
quantum computation. Here a ''measurement'' is any procedure that samples from
the spectral measure induced by the observable and the state under
consideration. As opposed to measurement-based quantum computation, the
post-measurement state is irrelevant.Comment: 19 pages, transition rules for the CA correcte
Unifying Quantum Computation with Projective Measurements only and One-Way Quantum Computation
Quantum measurement is universal for quantum computation. Two models for
performing measurement-based quantum computation exist: the one-way quantum
computer was introduced by Briegel and Raussendorf, and quantum computation via
projective measurements only by Nielsen. The more recent development of this
second model is based on state transfers instead of teleportation. From this
development, a finite but approximate quantum universal family of observables
is exhibited, which includes only one two-qubit observable, while others are
one-qubit observables. In this article, an infinite but exact quantum universal
family of observables is proposed, including also only one two-qubit
observable.
The rest of the paper is dedicated to compare these two models of
measurement-based quantum computation, i.e. one-way quantum computation and
quantum computation via projective measurements only. From this comparison,
which was initiated by Cirac and Verstraete, closer and more natural
connections appear between these two models. These close connections lead to a
unified view of measurement-based quantum computation.Comment: 9 pages, submitted to QI 200
Experimental measurement-based quantum computing beyond the cluster-state model
The paradigm of measurement-based quantum computation opens new experimental
avenues to realize a quantum computer and deepens our understanding of quantum
physics. Measurement-based quantum computation starts from a highly entangled
universal resource state. For years, clusters states have been the only known
universal resources. Surprisingly, a novel framework namely quantum computation
in correlation space has opened new routes to implement measurement-based
quantum computation based on quantum states possessing entanglement properties
different from cluster states. Here we report an experimental demonstration of
every building block of such a model. With a four-qubit and a six-qubit state
as distinct from cluster states, we have realized a universal set of
single-qubit rotations, two-qubit entangling gates and further Deutsch's
algorithm. Besides being of fundamental interest, our experiment proves
in-principle the feasibility of universal measurement-based quantum computation
without using cluster states, which represents a new approach towards the
realization of a quantum computer.Comment: 26 pages, final version, comments welcom
The Measurement Calculus
Measurement-based quantum computation has emerged from the physics community
as a new approach to quantum computation where the notion of measurement is the
main driving force of computation. This is in contrast with the more
traditional circuit model which is based on unitary operations. Among
measurement-based quantum computation methods, the recently introduced one-way
quantum computer stands out as fundamental.
We develop a rigorous mathematical model underlying the one-way quantum
computer and present a concrete syntax and operational semantics for programs,
which we call patterns, and an algebra of these patterns derived from a
denotational semantics. More importantly, we present a calculus for reasoning
locally and compositionally about these patterns.
We present a rewrite theory and prove a general standardization theorem which
allows all patterns to be put in a semantically equivalent standard form.
Standardization has far-reaching consequences: a new physical architecture
based on performing all the entanglement in the beginning, parallelization by
exposing the dependency structure of measurements and expressiveness theorems.
Furthermore we formalize several other measurement-based models:
Teleportation, Phase and Pauli models and present compositional embeddings of
them into and from the one-way model. This allows us to transfer all the theory
we develop for the one-way model to these models. This shows that the framework
we have developed has a general impact on measurement-based computation and is
not just particular to the one-way quantum computer.Comment: 46 pages, 2 figures, Replacement of quant-ph/0412135v1, the new
version also include formalization of several other measurement-based models:
Teleportation, Phase and Pauli models and present compositional embeddings of
them into and from the one-way model. To appear in Journal of AC
Flow Ambiguity: A Path Towards Classically Driven Blind Quantum Computation
Blind quantum computation protocols allow a user to delegate a computation to
a remote quantum computer in such a way that the privacy of their computation
is preserved, even from the device implementing the computation. To date, such
protocols are only known for settings involving at least two quantum devices:
either a user with some quantum capabilities and a remote quantum server or two
or more entangled but noncommunicating servers. In this work, we take the first
step towards the construction of a blind quantum computing protocol with a
completely classical client and single quantum server. Specifically, we show
how a classical client can exploit the ambiguity in the flow of information in
measurement-based quantum computing to construct a protocol for hiding critical
aspects of a computation delegated to a remote quantum computer. This ambiguity
arises due to the fact that, for a fixed graph, there exist multiple choices of
the input and output vertex sets that result in deterministic measurement
patterns consistent with the same fixed total ordering of vertices. This allows
a classical user, computing only measurement angles, to drive a
measurement-based computation performed on a remote device while hiding
critical aspects of the computation.Comment: (v3) 14 pages, 6 figures. expands introduction and definition of
flow, corrects typos to increase readability; contains a new figure to
illustrate example run of CDBQC protocol; minor changes to match the
published version.(v2) 12 pages, 5 figures. Corrects motivation for
quantities used in blindness analysi
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