51 research outputs found
Generalized Semi-Quantum Secret Sharing Schemes
We investigate quantum secret sharing schemes constructed from
non-binary stabilizer quantum error correcting codes with
carrier qudits of prime dimension . We provide a systematic way of
determining the access structure, which completely determines the forbidden and
intermediate structures. We then show that the information available to the
intermediate structure can be fully described and quantified by what we call
the *information group*, a subgroup of the Pauli group of qudits, and
employ this group structure to construct a method for hiding the information
from the intermediate structure via twirling of the information group and
sharing of classical bits between the dealer and the players. Our scheme allows
the transformation of a ramp (intermediate) quantum secret sharing scheme into
a semi-quantum perfect secret sharing scheme with the same access structure as
the ramp one but without any intermediate subsets, and is optimal in the amount
of classical bits the dealer has to distribute.Comment: Replaced by published version, typos correcte
Accessing quantum secrets via local operations and classical communication
Quantum secret-sharing and quantum error-correction schemes rely on
multipartite decoding protocols, yet the non-local operations involved are
challenging and sometimes infeasible. Here we construct a quantum
secret-sharing protocol with a reduced number of quantum communication channels
between the players. Our scheme is based on embedding a classical linear code
into a quantum error-correcting code. Our work paves the way towards the more
general problem of simplifying the decoding of quantum error-correcting codes.Comment: 5 pages, 2 figures, replaced with the PRA published versio
Construction of Equientangled Bases in Arbitrary Dimensions via Quadratic Gauss Sums and Graph States
Recently [Karimipour and Memarzadeh, Phys. Rev. A 73, 012329 (2006)] studied
the problem of finding a family of orthonormal bases in a bipartite space each
of dimension with the following properties: (i) The family continuously
interpolates between the product basis and the maximally entangled basis as
some parameter is varied, and (ii) for a fixed , all basis states have
the same amount of entanglement. The authors derived a necessary condition and
provided explicit solutions for but the existence of a solution for
arbitrary dimensions remained an open problem. We prove that such families
exist in arbitrary dimensions by providing two simple solutions, one employing
the properties of quadratic Gauss sums and the other using graph states. The
latter can be generalized to multipartite equientangled bases with more than
two parties.Comment: Minor changes, replaced by the published version. Any comments are
welcome
Separable Operations on Pure States
We show that the possible ensembles produced when a separable operation acts
on a single pure bipartite entangled state are completely characterized by a
majorization condition, a collection of inequalities for Schmidt coefficients,
which is identical to that already known for the particular case of local
operations and classical communication (LOCC). As a consequence, various known
results for LOCC, including some involving monotonicity of entanglement, can be
extended to the class of all separable operations.Comment: Typo corrected in the abstrac
Entanglement transformations using separable operations
We study conditions for the deterministic transformation
of a bipartite entangled state by a
separable operation. If the separable operation is a local operation with
classical communication (LOCC), Nielsen's majorization theorem provides
necessary and sufficient conditions. For the general case we derive a necessary
condition in terms of products of Schmidt coefficients, which is equivalent to
the Nielsen condition when either of the two factor spaces is of dimension 2,
but is otherwise weaker. One implication is that no separable operation can
reverse a deterministic map produced by another separable operation, if one
excludes the case where the Schmidt coefficients of and are the
same as those of . The question of sufficient conditions in the
general separable case remains open. When the Schmidt coefficients of
are the same as those of , we show that the Kraus
operators of the separable transformation restricted to the supports of
on the factor spaces are proportional to unitaries. When that
proportionality holds and the factor spaces have equal dimension, we find
conditions for the deterministic transformation of a collection of several full
Schmidt rank pure states to pure states .Comment: Replaced with the published version. Any comments are welcom
Quantum circuit optimizations for NISQ architectures
Currently available quantum computing hardware platforms have limited 2-qubit
connectivity among their addressable qubits. In order to run a generic quantum
algorithm on such a platform, one has to transform the initial logical quantum
circuit describing the algorithm into an equivalent one that obeys the
connectivity restrictions.
In this work we construct a circuit synthesis scheme that takes as input the
qubit connectivity graph and a quantum circuit over the gate set generated by
and outputs a circuit that respects the connectivity of
the device. As a concrete application, we apply our techniques to Google's
Bristlecone 72-qubit quantum chip connectivity, IBM's Tokyo 20-qubit quantum
chip connectivity, and Rigetti's Acorn 19-qubit quantum chip connectivity. In
addition, we also compare the performance of our scheme as a function of
sparseness of randomly generated quantum circuits.
Note: Recently, the authors of arXiv:1904.00633 independently presented a
similar optimization scheme. Our work is independent of arXiv:1904.00633, being
a longer version of the seminar presented by Beatrice Nash at the Dagstuhl
Seminar 18381: Quantum Programming Languages, pg. 120, September 2018,
Dagstuhl, Germany, slide deck available online at
https://materials.dagstuhl.de/files/18/18381/18381.BeatriceNash.Slides.pdf.Comment: Replaced by the published versio
Neural ensemble decoding for topological quantum error-correcting codes
Topological quantum error-correcting codes are a promising candidate for
building fault-tolerant quantum computers. Decoding topological codes
optimally, however, is known to be a computationally hard problem. Various
decoders have been proposed that achieve approximately optimal error
thresholds. Due to practical constraints, it is not known if there exists an
obvious choice for a decoder. In this paper, we introduce a framework which can
combine arbitrary decoders for any given code to significantly reduce the
logical error rates. We rely on the crucial observation that two different
decoding techniques, while possibly having similar logical error rates, can
perform differently on the same error syndrome. We use machine learning
techniques to assign a given error syndrome to the decoder which is likely to
decode it correctly. We apply our framework to an ensemble of Minimum-Weight
Perfect Matching (MWPM) and Hard-Decision Re-normalization Group (HDRG)
decoders for the surface code in the depolarizing noise model. Our simulations
show an improvement of 38.4%, 14.6%, and 7.1% over the pseudo-threshold of MWPM
in the instance of distance 5, 7, and 9 codes, respectively. Lastly, we discuss
the advantages and limitations of our framework and applicability to other
error-correcting codes. Our framework can provide a significant boost to error
correction by combining the strengths of various decoders. In particular, it
may allow for combining very fast decoders with moderate error-correcting
capability to create a very fast ensemble decoder with high error-correcting
capability.Comment: Replaced with the published version, comments welcome
Consistent histories for tunneling molecules subject to collisional decoherence
The decoherence of a two-state tunneling molecule, such as a chiral molecule
or ammonia, due to collisions with a buffer gas is analyzed in terms of a
succession of quantum states of the molecule satisfying the conditions for a
consistent family of histories. With the separation in energy of
the levels in the isolated molecule and a decoherence rate
proportional to the rate of collisions, we find for (strong
decoherence) a consistent family in which the molecule flips randomly back and
forth between the left- and right-handed chiral states in a stationary Markov
process. For there is a family in which the molecule
oscillates continuously between the different chiral states, but with
occasional random changes of phase, at a frequency that goes to zero at a phase
transition . This transition is similar to the behavior of the
inversion frequency of ammonia with increasing pressure, but will be difficult
to observe in chiral molecules such as DS. There are additional
consistent families both for and for . In
addition we relate the speed with which chiral information is transferred to
the environment to the rate of decrease of complementary types of information
(e.g., parity information) remaining in the molecule itself.Comment: 18 pages, 3 figure
staq -- A full-stack quantum processing toolkit
We describe 'staq', a full-stack quantum processing toolkit written in
standard C++. 'staq' is a quantum compiler toolkit, comprising of tools that
range from quantum optimizers and translators to physical mappers for quantum
devices with restricted connectives. The design of 'staq' is inspired from the
UNIX philosophy of "less is more", i.e. 'staq' achieves complex functionality
via combining (piping) small tools, each of which performs a single task using
the most advanced current state-of-the-art methods. We also provide a set of
illustrative benchmarks.Comment: Replaced with the published version, comments are welcom
Benchmarking the quantum cryptanalysis of symmetric, public-key and hash-based cryptographic schemes
Quantum algorithms can break factoring and discrete logarithm based
cryptography and weaken symmetric cryptography and hash functions. In order to
estimate the real-world impact of these attacks, apart from tracking the
development of fault-tolerant quantum computers it is important to have an
estimate of the resources needed to implement these quantum attacks.
For attacking symmetric cryptography and hash functions, generic quantum
attacks are substantially less powerful than they are for today's public-key
cryptography. So security will degrade gradually as quantum computing resources
increase. At present, there is a substantial resource overhead due to the cost
of fault-tolerant quantum error correction. We provide estimates of this
overhead using state-of-the-art methods in quantum fault-tolerance. We use
state-of-the-art optimized circuits, though further improvements in their
implementation would also reduce the resources needed to implement these
attacks. To bound the potential impact of further circuit optimizations we
provide cost estimates assuming trivial-cost implementations of these
functions. These figures indicate the effective bit-strength of the various
symmetric schemes and hash functions based on what we know today (and with
various assumptions on the quantum hardware), and frame the various potential
improvements that should continue to be tracked. As an example, we also look at
the implications for Bitcoin's proof-of-work system.
For many of the currently used asymmetric (public-key) cryptographic schemes
based on RSA and elliptic curve discrete logarithms, we again provide cost
estimates based on the latest advances in cryptanalysis, circuit compilation
and quantum fault-tolerance theory. These allow, for example, a direct
comparison of the quantum vulnerability of RSA and elliptic curve cryptography
for a fixed classical bit strength.Comment: 19 pages, 66 figures, 3 tables, all comments are welcom
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