2,977 research outputs found
Continuous-variable blind quantum computation
Blind quantum computation is a secure delegated quantum computing protocol
where Alice who does not have sufficient quantum technology at her disposal
delegates her computation to Bob who has a fully-fledged quantum computer in
such a way that Bob cannot learn anything about Alice's input, output, and
algorithm. Protocols of blind quantum computation have been proposed for
several qubit measurement-based computation models, such as the graph state
model, the Affleck-Kennedy-Lieb-Tasaki model, and the
Raussendorf-Harrington-Goyal topological model. Here, we consider blind quantum
computation for the continuous-variable measurement-based model. We show that
blind quantum computation is possible for the infinite squeezing case. We also
show that the finite squeezing causes no additional problem in the blind setup
apart from the one inherent to the continuous-variable measurement-based
quantum computation.Comment: 20 pages, 8 figure
Quantum computational tensor network on string-net condensate
The string-net condensate is a new class of materials which exhibits the
quantum topological order. In order to answer the important question, "how
useful is the string-net condensate in quantum information processing?", we
consider the most basic example of the string-net condensate, namely the
gauge string-net condensate on the two-dimensional hexagonal lattice, and show
that the universal measurement-based quantum computation (in the sense of the
quantum computational webs) is possible on it by using the framework of the
quantum computational tensor network. This result implies that even the most
basic example of the string-net condensate is equipped with the correlation
space that has the capacity for the universal quantum computation.Comment: 5 pages, 4 figure
Blind quantum computation protocol in which Alice only makes measurements
Blind quantum computation is a new secure quantum computing protocol which
enables Alice who does not have sufficient quantum technology to delegate her
quantum computation to Bob who has a fully-fledged quantum computer in such a
way that Bob cannot learn anything about Alice's input, output, and algorithm.
In previous protocols, Alice needs to have a device which generates quantum
states, such as single-photon states. Here we propose another type of blind
computing protocol where Alice does only measurements, such as the polarization
measurements with a threshold detector. In several experimental setups, such as
optical systems, the measurement of a state is much easier than the generation
of a single-qubit state. Therefore our protocols ease Alice's burden.
Furthermore, the security of our protocol is based on the no-signaling
principle, which is more fundamental than quantum physics. Finally, our
protocols are device independent in the sense that Alice does not need to trust
her measurement device in order to guarantee the security.Comment: 9 pages, 3 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
Quantum Fully Homomorphic Encryption With Verification
Fully-homomorphic encryption (FHE) enables computation on encrypted data
while maintaining secrecy. Recent research has shown that such schemes exist
even for quantum computation. Given the numerous applications of classical FHE
(zero-knowledge proofs, secure two-party computation, obfuscation, etc.) it is
reasonable to hope that quantum FHE (or QFHE) will lead to many new results in
the quantum setting. However, a crucial ingredient in almost all applications
of FHE is circuit verification. Classically, verification is performed by
checking a transcript of the homomorphic computation. Quantumly, this strategy
is impossible due to no-cloning. This leads to an important open question: can
quantum computations be delegated and verified in a non-interactive manner? In
this work, we answer this question in the affirmative, by constructing a scheme
for QFHE with verification (vQFHE). Our scheme provides authenticated
encryption, and enables arbitrary polynomial-time quantum computations without
the need of interaction between client and server. Verification is almost
entirely classical; for computations that start and end with classical states,
it is completely classical. As a first application, we show how to construct
quantum one-time programs from classical one-time programs and vQFHE.Comment: 30 page
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
Unforgeable Quantum Encryption
We study the problem of encrypting and authenticating quantum data in the
presence of adversaries making adaptive chosen plaintext and chosen ciphertext
queries. Classically, security games use string copying and comparison to
detect adversarial cheating in such scenarios. Quantumly, this approach would
violate no-cloning. We develop new techniques to overcome this problem: we use
entanglement to detect cheating, and rely on recent results for characterizing
quantum encryption schemes. We give definitions for (i.) ciphertext
unforgeability , (ii.) indistinguishability under adaptive chosen-ciphertext
attack, and (iii.) authenticated encryption. The restriction of each definition
to the classical setting is at least as strong as the corresponding classical
notion: (i) implies INT-CTXT, (ii) implies IND-CCA2, and (iii) implies AE. All
of our new notions also imply QIND-CPA privacy. Combining one-time
authentication and classical pseudorandomness, we construct schemes for each of
these new quantum security notions, and provide several separation examples.
Along the way, we also give a new definition of one-time quantum authentication
which, unlike all previous approaches, authenticates ciphertexts rather than
plaintexts.Comment: 22+2 pages, 1 figure. v3: error in the definition of QIND-CCA2 fixed,
some proofs related to QIND-CCA2 clarifie
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
Reachability in Higher-Order-Counters
Higher-order counter automata (\HOCS) can be either seen as a restriction of
higher-order pushdown automata (\HOPS) to a unary stack alphabet, or as an
extension of counter automata to higher levels. We distinguish two principal
kinds of \HOCS: those that can test whether the topmost counter value is zero
and those which cannot.
We show that control-state reachability for level \HOCS with -test is
complete for \mbox{}-fold exponential space; leaving out the -test
leads to completeness for \mbox{}-fold exponential time. Restricting
\HOCS (without -test) to level , we prove that global (forward or
backward) reachability analysis is \PTIME-complete. This enhances the known
result for pushdown systems which are subsumed by level \HOCS without
-test.
We transfer our results to the formal language setting. Assuming that \PTIME
\subsetneq \PSPACE \subsetneq \mathbf{EXPTIME}, we apply proof ideas of
Engelfriet and conclude that the hierarchies of languages of \HOPS and of \HOCS
form strictly interleaving hierarchies. Interestingly, Engelfriet's
constructions also allow to conclude immediately that the hierarchy of
collapsible pushdown languages is strict level-by-level due to the existing
complexity results for reachability on collapsible pushdown graphs. This
answers an open question independently asked by Parys and by Kobayashi.Comment: Version with Full Proofs of a paper that appears at MFCS 201
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