Negative Quasi-Probability as a Resource for Quantum Computation

A central problem in quantum information is to determine the minimal physical resources that are required for quantum computational speedup and, in particular, for fault-tolerant quantum computation. We establish a remarkable connection between the potential for quantum speed-up and the onset of negative values in a distinguished quasi-probability representation, a discrete analog of the Wigner function for quantum systems of odd dimension. This connection allows us to resolve an open question on the existence of bound states for magic-state distillation: we prove that there exist mixed states outside the convex hull of stabilizer states that cannot be distilled to non-stabilizer target states using stabilizer operations. We also provide an efficient simulation protocol for Clifford circuits that extends to a large class of mixed states, including bound universal states.Comment: 15 pages v4: This is a major revision. In particular, we have added a new section detailing an explicit extension of the Gottesman-Knill simulation protocol to deal with positively represented states and measurement (even when these are non-stabilizer). This paper also includes significant elaboration on the two main results of the previous versio

Robust Online Hamiltonian Learning

In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer-Rao lower bound, certifying its own performance.Comment: 24 pages, 12 figures; to appear in New Journal of Physic

Quasi-probability representations of quantum theory with applications to quantum information science

This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional quantum theory. We focus on both the characteristics and applications of these representations with an emphasis toward quantum information theory. We discuss the recently proposed unification of the set of possible quasi-probability representations via frame theory and then discuss the practical relevance of negativity in such representations as a criteria for quantumness.Comment: v3: typos fixed, references adde

Framed Hilbert space: hanging the quasi-probability pictures of quantum theory

Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an alternate approach to defining a set of quasi-probability representations, based on a more natural generalization of a classical representation, is equivalent to our earlier approach based on frames, and therefore is also subject to our no-go theorem for a non-negative representation. Furthermore, we clarify the relationship between the contextuality of quantum theory and the necessity of negativity in quasi-probability representations and discuss their relevance as criteria for non-classicality. We also provide a comprehensive overview of known quasi-probability representations and their expression within the frame formalism.Comment: 46 pages, 1 table, contains a review of finite dimensional quasi-probability function

Frame representations of quantum mechanics and the necessity of negativity in quasi-probability representations

Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted dimensions and their physical significance in contexts such as drawing quantum-classical comparisons is limited by the non-uniqueness of the particular representation. Here we show how the mathematical theory of frames provides a unified formalism which accommodates all known quasi-probability representations of finite dimensional quantum systems. Moreover, we show that any quasi-probability representation satisfying two reasonable properties is equivalent to a frame representation and then prove that any such representation of quantum mechanics must exhibit either negativity or a deformed probability calculus.Comment: 13 pages, published versio

Quantum Fourier transform, Heisenberg groups and quasiprobability distributions

This paper aims to explore the inherent connection among Heisenberg groups, quantum Fourier transform and (quasiprobability) distribution functions. Distribution functions for continuous and finite quantum systems are examined first as a semiclassical approach to quantum probability distribution. This leads to studying certain functionals of a pair of "conjugate" observables, connected via the quantum Fourier transform. The Heisenberg groups emerge naturally from this study and we take a rapid look at their representations. The quantum Fourier transform appears as the intertwining operator of two equivalent representation arising out of an automorphism of the group. Distribution functions correspond to certain distinguished sets in the group algebra. The marginal properties of a particular class of distribution functions (Wigner distributions) arise from a class of automorphisms of the group algebra of the Heisenberg group. We then study the reconstruction of Wigner function from the marginal distributions via inverse Radon transform giving explicit formulas. We consider applications of our approach to quantum information processing and quantum process tomography.Comment: 39 page

Wigner formalism for a particle on an infinite lattice: dynamics and spin

The recently proposed Wigner function for a particle in an infinite lattice (Hinarejos M, Banuls MC and Perez A 2012 New J. Phys. 14 103009) is extended here to include an internal degree of freedom as spin. This extension is made by introducing a Wigner matrix. The formalism is developed to account for dynamical processes, with or without decoherence. We show explicit solutions for the case of Hamiltonian evolution under a position-dependent potential, and for evolution governed by a master equation under some simple models of decoherence, for which the Wigner matrix formalism is well suited. Discrete processes are also discussed. Finally, we discuss the possibility of introducing a negativity concept for the Wigner function in the case where the spin degree of freedom is included

Identification of the factors associated with outcomes in a condition management programme

<p>Background: A requirement of the Government’s Pathways to Work (PtW) agenda was to introduce a Condition Management Programme (CMP). The aim of the present study was to identify the differences between those who engaged and made progress in this telephone-based biopsychosocial intervention, in terms of their health, and those who did not and to determine the client and practitioner characteristics and programme elements associated with success in a programme aimed at improving health.</p> <p>Methods: Data were obtained from the CMP electronic spreadsheets and clients paper-based case records. CMP standard practice was that questionnaires were administered during the pre- and post-assessment phases over the telephone. Each client’s record contains their socio-demographic data, their primary health condition, as well as the pre- and post-intervention scores of the health assessment tool administered. Univariate and multivariate statistical analysis was used to investigate the relationships between the database variables. Clients were included in the study if their records were available for analysis from July 2006 to December 2007.</p> <p> Results: On average there were 112 referrals per month, totalling 2016 referrals during the evaluation period. The majority (62.8%) of clients had a mental-health condition. Successful completion of the programme was 28.5% (575 “completers”; 144 “discharges”). Several factors, such as age, health condition, mode of contact, and practitioner characteristics, were significant determinants of participation and completion of the programme. The results showed that completion of the CMP was associated with a better mental-health status, by reducing the number of clients that were either anxious, depressed or both, before undertaking the programme, from 74% to 32.5%.</p> <p>Conclusions: Our findings showed that an individual's characteristics are associated with success in the programme, defined as completing the intervention and demonstrating an improved health status. This study provides some evidence that the systematic evaluation of such programmes and interventions could identify ways in which they could be improved.</p&gt

Induction of androgenesis and production of haploid embryos in anther cultures of borage (Borago officinalis L.)

[EN] Borage (Borago officinalis L.) is an important medicinal plant with different culinary, pharmaceutical and industrial properties. Unfortunately, there are no published reports on the establishment of protocols to produce DHs in this species up to now. In this work, we show for the first time the induction of borage microspores to become embryogenic calli, from which haploid embryos are produced. In addition, we evaluated the effect of using different flower bud sizes, carbon sources, concentrations of 2,4-D and BAP, cold (4 A degrees C) pretreatments and heat shock treatments. Production of total calli, embryogenic calli and callus-derived embryos was differently affected by the different parameters studied. Our results showed that the use of 5-7 mm-long flower buds, a cold (4 A degrees C) pretreatment during 4 days, a 32 A degrees C heat shock for 3 days, and the addition of 3 % maltose and 2 mgl(-1) 2,4-D and 1 mgl(-1) BAP to the culture medium, was beneficial for embryo production. Overall, this work demonstrates that DH technology is possible in borage, and opens the door for future improvements needed to finally obtain borage DH plants.Eshaghi, ZC.; Abdollahi, MR.; Moosavi, SS.; Deljou, A.; Seguí-Simarro, JM. (2015). Induction of androgenesis and production of haploid embryos in anther cultures of borage (Borago officinalis L.). Plant Cell, Tissue and Organ Culture. 122:321-329. doi:10.1007/s11240-015-0768-5S321329122Abdollahi MR, Moieni A, Javaran MJ (2004) Interactive effects of shock and culture density on embryo induction in isolated microspore culture of Brassica napus L. cv. 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The Small Satellite-Based, Imaging X-Ray Polarimeter Explorer (IXPE) Mission

The Imaging X-ray Polarimeter Explorer (IXPE) focuses on high energy astrophysics in the 2—8 keV x-ray band. IXPE is designed to explore general relativistic and quantum physics effects of gravity, energy, electric and magnetic fields at extreme limits. IXPE, a NASA Small Explorer (SMEX) Mission, will add new dimensions to on-orbit x-ray science: polarization degree, polarization angle and extended object polarization imaging. Polarization uniquely probes physical anisotropies that are not otherwise measurable—ordered magnetic fields, aspheric matter distributions, or general relativistic coupling to black-hole spin. Detailed imaging enables the specific properties of extended x-ray sources to be differentiated. The IXPE Observatory consists of spacecraft and payload modules built up in parallel to form the Observatory during system integration and test. The payload includes three polarization-sensitive, x-ray detector arrays paired with three x-ray mirror module assemblies (MMA). A deployable boom provides the correct separation (focal length) between the detector units and MMAs. Currently, the boom has been delivered, all four detectors units (DU) are complete, the detectors service unit (DSU) is complete, instrument system testing has been completed (DSU with 3 DUs), three of four MMAs is built and all spacecraft components except the solar array have been delivered along with the spacecraft and payload structures. Payload and spacecraft integration and test (I&T) started in March 2020. This paper overviews the flight segment (the Observatory, payload, and spacecraft implementation concepts) with emphasis on the build status and summarizes the launch segment. Launch is planned to occur on a Falcon 9 launch vehicle during Summer 2021. The paper summarizes the impacts of switching from the ‘design-to baseline’ of Pegasus XL to the selected launch vehicle for flight, Falcon 9. COVID-19 impacts to the Project are also summarized. The paper will close with a summary of the mission development status. The Project is firmly into the build phase for both the spacecraft and payload and rapidly approaching Observatory I&T