Scaling issues in ensemble implementations of the Deutsch-Jozsa algorithm

We discuss the ensemble version of the Deutsch-Jozsa (DJ) algorithm which attempts to provide a "scalable" implementation on an expectation-value NMR quantum computer. We show that this ensemble implementation of the DJ algorithm is at best as efficient as the classical random algorithm. As soon as any attempt is made to classify all possible functions with certainty, the implementation requires an exponentially large number of molecules. The discrepancies arise out of the interpretation of mixed state density matrices.Comment: Minor changes, reference added, replaced with publised versio

Implementation of the Five Qubit Error Correction Benchmark

The smallest quantum code that can correct all one-qubit errors is based on five qubits. We experimentally implemented the encoding, decoding and error-correction quantum networks using nuclear magnetic resonance on a five spin subsystem of labeled crotonic acid. The ability to correct each error was verified by tomography of the process. The use of error-correction for benchmarking quantum networks is discussed, and we infer that the fidelity achieved in our experiment is sufficient for preserving entanglement.Comment: 6 pages with figure

Burden of Adverse Metabolic Factors Is Associated With Increased Left Ventricular Concentricity in Adults With Normal-Range Body Mass Index: The Framingham Heart Study

Introduction: Persons with normal-range body mass index (BMI) but adverse metabolic characteristics associated with obesity have been described as metabolically-obese normal weight (MONW). We sought to determine whether adverse metabolic profile is associated with alterations in left ventricular (LV) structure or function among adults with normal BMI. Methods: From the 1794 Framingham Heart Study Offspring cohort adults who underwent cardiac magnetic resonance imaging (CMRI) , we identified 446 free of non-skin cancer and prevalent clinical cardiovascular disease (CVD) who had 18.5≤BMI\u3c25.0 kg/m2 and complete covariates. We calculated a metabolic score (MS) where 1 point was assigned for each of: a) fasting glucose≥100 mg/dL or diabetes; b) SBP≥140 or DBP≥90 mmHg or antihypertensive treatment; c) TG≥150 or HDL_C \u3c40(M)/\u3c50(W) mg/dL or lipid treatment; d) HOMA-IR≥2.5; e) waist circumference ≥102/88cm for M/W. Participants were classified as MS0 (no points), MS1 (exactly 1 point), or MS2+ (≥2 points). LV mass (LVM), end-diastolic volume (EDV), ejection fraction (EF), and concentricity (LVM/EDV) were measured from breathhold cine SSFP CMR scans; we calculated LVM/BSA. Analysis of covariance (ANCOVA) was used to compare MS1 and MS2+ groups to the MS0 group. CMRI variables were adjusted for sex, age, heart rate (HR) and body size (BSA); LVM/BSA was adjusted for sex, age, HR only. We also tested for linear trend across metabolic groups. Results: LV concentricity increased with worsening metabolic status. This was driven by lower LV EDV, not increased LVM. LVM did not differ across (trend) or between MS-groups. LVEDV decreased across groups but only MS2 differed significantly from MS0. LVEF increased slightly but significantly across MS-groups. Conclusions: In a community-dwelling cohort, among participants who were free of cancer and clinical CVD and had normal BMI, worsening metabolic profile was associated with adverse remodeling of the left ventricle, reflected by greater LV concentricity

Classical model for bulk-ensemble NMR quantum computation

We present a classical model for bulk-ensemble NMR quantum computation: the quantum state of the NMR sample is described by a probability distribution over the orientations of classical tops, and quantum gates are described by classical transition probabilities. All NMR quantum computing experiments performed so far with three quantum bits can be accounted for in this classical model. After a few entangling gates, the classical model suffers an exponential decrease of the measured signal, whereas there is no corresponding decrease in the quantum description. We suggest that for small numbers of quantum bits, the quantum nature of NMR quantum computation lies in the ability to avoid an exponential signal decrease.Comment: 14 pages, no figures, revte