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 $\sim 16$x and the number of logical qubits by $\sim 4$x. Additionally, we estimate that the logical clock rate needed for quantum advantage is also reduced by a factor of $\sim 5$x. Overall, we find that quantum advantage will require $4.7$k logical qubits, and quantum devices that can execute $10^9$ T-gates at a rate of $45$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