1,463 research outputs found
Covert Quantum Internet
We apply covert quantum communication based on entanglement generated from
the Minkowski vacuum to the setting of quantum computation and quantum
networks. Our approach hides the generation and distribution of entanglement in
quantum networks by taking advantage of relativistic quantum effects. We devise
a suite of covert quantum teleportation protocols that utilize the shared
entanglement, local operations, and covert classical communication to transfer
or process quantum information in stealth. As an application of our covert
suite, we construct two prominent examples of measurement-based quantum
computation, namely the teleportation-based quantum computer and the one-way
quantum computer. In the latter case we explore the covert generation of graph
states, and subsequently outline a protocol for the covert implementation of
universal blind quantum computation.Comment: 9 pages, 2 figure
Unconditionally verifiable blind computation
Blind Quantum Computing (BQC) allows a client to have a server carry out a
quantum computation for them such that the client's input, output and
computation remain private. A desirable property for any BQC protocol is
verification, whereby the client can verify with high probability whether the
server has followed the instructions of the protocol, or if there has been some
deviation resulting in a corrupted output state. A verifiable BQC protocol can
be viewed as an interactive proof system leading to consequences for complexity
theory. The authors, together with Broadbent, previously proposed a universal
and unconditionally secure BQC scheme where the client only needs to be able to
prepare single qubits in separable states randomly chosen from a finite set and
send them to the server, who has the balance of the required quantum
computational resources. In this paper we extend that protocol with new
functionality allowing blind computational basis measurements, which we use to
construct a new verifiable BQC protocol based on a new class of resource
states. We rigorously prove that the probability of failing to detect an
incorrect output is exponentially small in a security parameter, while resource
overhead remains polynomial in this parameter. The new resource state allows
entangling gates to be performed between arbitrary pairs of logical qubits with
only constant overhead. This is a significant improvement on the original
scheme, which required that all computations to be performed must first be put
into a nearest neighbour form, incurring linear overhead in the number of
qubits. Such an improvement has important consequences for efficiency and
fault-tolerance thresholds.Comment: 46 pages, 10 figures. Additional protocol added which allows
arbitrary circuits to be verified with polynomial securit
Universal blind quantum computation
We present a protocol which allows a client to have a server carry out a
quantum computation for her such that the client's inputs, outputs and
computation remain perfectly private, and where she does not require any
quantum computational power or memory. The client only needs to be able to
prepare single qubits randomly chosen from a finite set and send them to the
server, who has the balance of the required quantum computational resources.
Our protocol is interactive: after the initial preparation of quantum states,
the client and server use two-way classical communication which enables the
client to drive the computation, giving single-qubit measurement instructions
to the server, depending on previous measurement outcomes. Our protocol works
for inputs and outputs that are either classical or quantum. We give an
authentication protocol that allows the client to detect an interfering server;
our scheme can also be made fault-tolerant.
We also generalize our result to the setting of a purely classical client who
communicates classically with two non-communicating entangled servers, in order
to perform a blind quantum computation. By incorporating the authentication
protocol, we show that any problem in BQP has an entangled two-prover
interactive proof with a purely classical verifier.
Our protocol is the first universal scheme which detects a cheating server,
as well as the first protocol which does not require any quantum computation
whatsoever on the client's side. The novelty of our approach is in using the
unique features of measurement-based quantum computing which allows us to
clearly distinguish between the quantum and classical aspects of a quantum
computation.Comment: 20 pages, 7 figures. This version contains detailed proofs of
authentication and fault tolerance. It also contains protocols for quantum
inputs and outputs and appendices not available in the published versio
Qudit versions of the qubit "pi-over-eight" gate
When visualised as an operation on the Bloch sphere, the qubit
"pi-over-eight" gate corresponds to one-eighth of a complete rotation about the
vertical axis. This simple gate often plays an important role in quantum
information theory, typically in situations for which Pauli and Clifford gates
are insufficient. Most notably, when it supplements the set of Clifford gates
then universal quantum computation can be achieved. The "pi-over-eight" gate is
the simplest example of an operation from the third level of the Clifford
hierarchy (i.e., it maps Pauli operations to Clifford operations under
conjugation). Here we derive explicit expressions for all qudit (d-level, where
d is prime) versions of this gate and analyze the resulting group structure
that is generated by these diagonal gates. This group structure differs
depending on whether the dimensionality of the qudit is two, three or greater
than three. We then discuss the geometrical relationship of these gates (and
associated states) with respect to Clifford gates and stabilizer states. We
present evidence that these gates are maximally robust to depolarizing and
phase damping noise, in complete analogy with the qubit case. Motivated by this
and other similarities we conjecture that these gates could be useful for the
task of qudit magic-state distillation and, by extension, fault-tolerant
quantum computing. Very recent, independent work by Campbell, Anwar and Browne
confirms the correctness of this intuition, and we build upon their work to
characterize noise regimes for which noisy implementations of these gates can
(or provably cannot) supplement Clifford gates to enable universal quantum
computation.Comment: Version 2 changed to reflect improved distillation routines in
arXiv:1205.3104v2. Minor typos fixed. 12 Pages,2 Figures,3 Table
What is a quantum computer, and how do we build one?
The DiVincenzo criteria for implementing a quantum computer have been seminal
in focussing both experimental and theoretical research in quantum information
processing. These criteria were formulated specifically for the circuit model
of quantum computing. However, several new models for quantum computing
(paradigms) have been proposed that do not seem to fit the criteria well. The
question is therefore what are the general criteria for implementing quantum
computers. To this end, a formal operational definition of a quantum computer
is introduced. It is then shown that according to this definition a device is a
quantum computer if it obeys the following four criteria: Any quantum computer
must (1) have a quantum memory; (2) facilitate a controlled quantum evolution
of the quantum memory; (3) include a method for cooling the quantum memory; and
(4) provide a readout mechanism for subsets of the quantum memory. The criteria
are met when the device is scalable and operates fault-tolerantly. We discuss
various existing quantum computing paradigms, and how they fit within this
framework. Finally, we lay out a roadmap for selecting an avenue towards
building a quantum computer. This is summarized in a decision tree intended to
help experimentalists determine the most natural paradigm given a particular
physical implementation
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
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