1,969 research outputs found
Abstract structure of unitary oracles for quantum algorithms
We show that a pair of complementary dagger-Frobenius algebras, equipped with
a self-conjugate comonoid homomorphism onto one of the algebras, produce a
nontrivial unitary morphism on the product of the algebras. This gives an
abstract understanding of the structure of an oracle in a quantum computation,
and we apply this understanding to develop a new algorithm for the
deterministic identification of group homomorphisms into abelian groups. We
also discuss an application to the categorical theory of signal-flow networks.Comment: In Proceedings QPL 2014, arXiv:1412.810
Mermin Non-Locality in Abstract Process Theories
The study of non-locality is fundamental to the understanding of quantum
mechanics. The past 50 years have seen a number of non-locality proofs, but its
fundamental building blocks, and the exact role it plays in quantum protocols,
has remained elusive. In this paper, we focus on a particular flavour of
non-locality, generalising Mermin's argument on the GHZ state. Using strongly
complementary observables, we provide necessary and sufficient conditions for
Mermin non-locality in abstract process theories. We show that the existence of
more phases than classical points (aka eigenstates) is not sufficient, and that
the key to Mermin non-locality lies in the presence of certain algebraically
non-trivial phases. This allows us to show that fRel, a favourite toy model for
categorical quantum mechanics, is Mermin local. We show Mermin non-locality to
be the key resource ensuring the device-independent security of the HBB CQ
(N,N) family of Quantum Secret Sharing protocols. Finally, we challenge the
unspoken assumption that the measurements involved in Mermin-type scenarios
should be complementary (like the pair X,Y), opening the doors to a much wider
class of potential experimental setups than currently employed. In short, we
give conditions for Mermin non-locality tests on any number of systems, where
each party has an arbitrary number of measurement choices, where each
measurement has an arbitrary number of outcomes and further, that works in any
abstract process theory.Comment: In Proceedings QPL 2015, arXiv:1511.0118
Digital zero noise extrapolation for quantum error mitigation
Zero-noise extrapolation (ZNE) is an increasingly popular technique for
mitigating errors in noisy quantum computations without using additional
quantum resources. We review the fundamentals of ZNE and propose several
improvements to noise scaling and extrapolation, the two key components in the
technique. We introduce unitary folding and parameterized noise scaling. These
are digital noise scaling frameworks, i.e. one can apply them using only
gate-level access common to most quantum instruction sets. We also study
different extrapolation methods, including a new adaptive protocol that uses a
statistical inference framework. Benchmarks of our techniques show error
reductions of 18X to 24X over non-mitigated circuits and demonstrate ZNE
effectiveness at larger qubit numbers than have been tested previously. In
addition to presenting new results, this work is a self-contained introduction
to the practical use of ZNE by quantum programmers.Comment: 11 pages, 7 figure
Derivative Pricing using Quantum Signal Processing
Pricing financial derivatives on quantum computers typically includes quantum
arithmetic components which contribute heavily to the quantum resources
required by the corresponding circuits. In this manuscript, we introduce a
method based on Quantum Signal Processing (QSP) to encode financial derivative
payoffs directly into quantum amplitudes, alleviating the quantum circuits from
the burden of costly quantum arithmetic. Compared to current state-of-the-art
approaches in the literature, we find that for derivative contracts of
practical interest, the application of QSP significantly reduces the required
resources across all metrics considered, most notably the total number of
T-gates by x and the number of logical qubits by x.
Additionally, we estimate that the logical clock rate needed for quantum
advantage is also reduced by a factor of x. Overall, we find that
quantum advantage will require k logical qubits, and quantum devices that
can execute T-gates at a rate of MHz. While in this work we focus
specifically on the payoff component of the derivative pricing process where
the method we present is most readily applicable, similar techniques can be
employed to further reduce the resources in other applications, such as state
preparation
Red Blood Cells from Individuals with Abdominal Obesity or Metabolic Abnormalities Exhibit Less Deformability upon Entering a Constriction.
Abdominal obesity and metabolic syndrome (MS) are multifactorial conditions associated with increased risk of cardiovascular disease and type II diabetes mellitus. Previous work has demonstrated that the hemorheological profile is altered in patients with abdominal obesity and MS, as evidenced for example by increased whole blood viscosity. To date, however, no studies have examined red blood cell (RBC) deformability of blood from individuals with obesity or metabolic abnormalities under typical physiological flow conditions. In this study, we pumped RBCs through a constriction in a microfluidic device and used high speed video to visualize and track the mechanical behavior of ~8,000 RBCs obtained from either healthy individuals (n = 5) or obese participants with metabolic abnormalities (OMA) (n = 4). We demonstrate that the OMA+ cells stretched on average about 25% less than the healthy controls. Furthermore, we examined the effects of ingesting a high-fat meal on RBC mechanical dynamics, and found that the postprandial period has only a weak effect on the stretching dynamics exhibited by OMA+ cells. The results suggest that chronic rigidification of RBCs plays a key role in the increased blood pressure and increased whole blood viscosity observed in OMA individuals and was independent of an acute response triggered by consumption of a high-fat meal
Effects of Surface Roughness on the Electrochemical Reduction of CO₂ over Cu
We have investigated the role of surface roughening on the CO₂ reduction reaction (CO₂RR) over Cu. The activity and product selectivity of Cu surfaces roughened by plasma pretreatment in Ar, O₂, or N₂ were compared with that of electrochemically polished Cu samples. Differences in total and product current densities, the ratio of current densities for HER (the hydrogen evolution reaction) to CO₂RR, and the ratio of current densities for C₂₊ to C₁ products depend on the electrochemically active surface and are nearly independent of plasma composition. Theoretical analysis of an electropolished and roughened Cu surface reveals a higher fraction of undercoordinated Cu sites on the roughened surface, sites that bind CO preferentially. Roughened surfaces also contain square sites similar to those on a Cu(100) surface but with neighboring step sites, which adsorb OC–COH, a precursor to C₂₊ products. These findings explain the increases in the formation of oxygenates and hydrocarbons relative to CO and the ratio of oxygenates to hydrocarbons observed with increasing surface roughness
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