Simulating quantum computation with magic states: how many "bits" for "it"?

A recently introduced classical simulation method for universal quantum computation with magic states operates by repeated sampling from probability functions [M. Zurel et al. PRL 260404 (2020)]. This method is closely related to sampling algorithms based on Wigner functions, with the important distinction that Wigner functions can take negative values obstructing the sampling. Indeed, negativity in Wigner functions has been identified as a precondition for a quantum speed-up. However, in the present method of classical simulation, negativity of quasiprobability functions never arises. This model remains probabilistic for all quantum computations. In this paper, we analyze the amount of classical data that the simulation procedure must track. We find that this amount is small. Specifically, for any number $n$ of magic states, the number of bits that describe the quantum system at any given time is $2n^2+O(n)$.Comment: 10 pages, 2 figure

The role of cohomology in quantum computation with magic states

A web of cohomological facts relates quantum error correction, measurement-based quantum computation, symmetry protected topological order and contextuality. Here we extend this web to quantum computation with magic states. In this computational scheme, the negativity of certain quasiprobability functions is an indicator for quantumness. However, when constructing quasiprobability functions to which this statement applies, a marked difference arises between the cases of even and odd local Hilbert space dimension. At a technical level, establishing negativity as an indicator of quantumness in quantum computation with magic states relies on two properties of the Wigner function: their covariance with respect to the Clifford group and positive representation of Pauli measurements. In odd dimension, Gross' Wigner function -- an adaptation of the original Wigner function to odd-finite-dimensional Hilbert spaces -- possesses these properties. In even dimension, Gross' Wigner function doesn't exist. Here we discuss the broader class of Wigner functions that, like Gross', are obtained from operator bases. We find that such Clifford-covariant Wigner functions do not exist in any even dimension, and furthermore, Pauli measurements cannot be positively represented by them in any even dimension whenever the number of qudits is n>=2. We establish that the obstructions to the existence of such Wigner functions are cohomological.Comment: 33 page

The role of cohomology in quantum computation with magic states

A web of cohomological facts relates quantum error correction, measurement-based quantum computation, symmetry protected topological order and contextuality. Here we extend this web to quantum computation with magic states. In this computational scheme, the negativity of certain quasiprobability functions is an indicator for quantumness. However, when constructing quasiprobability functions to which this statement applies, a marked difference arises between the cases of even and odd local Hilbert space dimension. At a technical level, establishing negativity as an indicator of quantumness in quantum computation with magic states relies on two properties of the Wigner function: their covariance with respect to the Clifford group and positive representation of Pauli measurements. In odd dimension, Gross' Wigner function – an adaptation of the original Wigner function to odd-finite-dimensional Hilbert spaces – possesses these properties. In even dimension, Gross' Wigner function doesn't exist. Here we discuss the broader class of Wigner functions that, like Gross', are obtained from operator bases. We find that such Clifford-covariant Wigner functions do not exist in any even dimension, and furthermore, Pauli measurements cannot be positively represented by them in any even dimension whenever the number of qudits is n$\geq$2. We establish that the obstructions to the existence of such Wigner functions are cohomological

Meeting of the Ecosystem Approach Correspondence Group on on Pollution Monitoring (CorMon Pollution)

In accordance with the UNEP/MAP Programme of Work adopted by COP 21 for the biennium 2020-2021, the United Nations Environment Programme/Mediterranean Action Plan-Barcelona Convention Secretariat (UNEP/MAP) and its Programme for the Assessment and Control of Marine Pollution in the Mediterranean (MED POL) organized the Meeting of the Ecosystem Approach Correspondence Group on Pollution Monitoring (CorMon on Pollution Monitoring). The Meeting was held via videoconference on 26-27 April 2021. 2. The main objectives of the Meeting were to: a) Review the Monitoring Guidelines/Protocols for IMAP Common Indicator 18, as well as the Monitoring Guidelines/Protocols for Analytical Quality Assurance and Reporting of Monitoring Data for IMAP Common Indicators 13, 14, 17, 18 and 20; b) Take stock of the state of play of inter-laboratory testing and good laboratory practice related to IMAP Ecological Objectives 5 and 9; c) Analyze the proposal for the integration and aggregation rules for IMAP Ecological Objectives 5, 9 and 10 and assessment criteria for contaminants and nutrients; d) Recommend the ways and means to strengthen implementation of IMAP Pollution Cluster towards preparation of the 2023 MED Quality Status Report

Hidden variable models and classical simulation algorithms for quantum computation with magic states on qubits

An important problem in quantum computation is to characterize the resources required for a computational speedup over classical computation. Veitch et al. showed that one necessary condition for a computational speedup in the model of quantum computation with magic states is that the discrete Wigner function representing the input state of the quantum circuit must take negative values. The amount of negativity in the discrete Wigner function quantifies the complexity of classical simulation of a quantum computation with simulation being efficient if the Wigner function is nonnegative everywhere. In this sense, negativity of the Wigner quasiprobability representation serves as an indicator of quantumness from a computational perspective. However, this result only holds for systems of qudits where the local Hilbert space dimension is odd. The first main result discussed in this thesis relates to a discrete Wigner function suitable for describing quantum computation with magic states defined for any local Hilbert space dimension. When the local Hilbert space dimension is odd it subsumes the standard discrete Wigner function. When the local Hilbert space dimension is even, as a result of state-independent proofs of contextuality among multiqubit (or multi-even-dimensional-qudit) Pauli observables, the phase space over which the Wigner function is defined becomes much larger. However, for systems of qubits, the properties required for simulation of quantum computation with magic states remain. This simulation method effectively extends the result described above for odd-dimensional qudits to qubits. Although in the even-dimensional case the phase space is much larger, points in multiqubit phase space can be characterized and classified and some structure can be imparted on the phase space. The second main result discussed here is a hidden variable model for quantum computation with magic states on qubits. This model is similar in structure to quasiprobability representations like the discrete Wigner function, but unlike those representations the model is capable of representing all elements of any quantum computation---states, operations, and measurements---using only classical probabilities. No negativity is required. This calls into question the role of negativity in quasiprobability representations as an indicator of quantumness for models of quantum computation.Science, Faculty ofPhysics and Astronomy, Department ofGraduat

The Newfoundland and Labrador mosaic founder population descends from an Irish and British diaspora from 300 years ago

Abstract The founder population of Newfoundland and Labrador (NL) is a unique genetic resource, in part due to its geographic and cultural isolation, where historical records describe a migration of European settlers, primarily from Ireland and England, to NL in the 18th and 19th centuries. Whilst its historical isolation, and increased prevalence of certain monogenic disorders are well appreciated, details of the fine-scale genetic structure and ancestry of the population are lacking. Understanding the genetic origins and background of functional, disease causing, genetic variants would aid genetic mapping efforts in the Province. Here, we leverage dense genome-wide SNP data on 1,807 NL individuals to reveal fine-scale genetic structure in NL that is clustered around coastal communities and correlated with Christian denomination. We show that the majority of NL European ancestry can be traced back to the south-east and south-west of Ireland and England, respectively. We date a substantial population size bottleneck approximately 10-15 generations ago in NL, associated with increased haplotype sharing and autozygosity. Our results reveal insights into the population history of NL and demonstrate evidence of a population conducive to further genetic studies and biomarker discovery

Newfoundland and Labrador: a mosaic founder population of an Irish and British diaspora from 300 years ago.

The founder population of Newfoundland and Labrador (NL) is a unique genetic resource, in part due to geographic and cultural isolation, where historical records describe a migration of European settlers to NL in the 18th and 19th centuries. However, the fine-scale genetic structure and ancestry of the population has not been well described. Here, we leverage dense genome-wide SNP data on 1,807 NL individuals to reveal fine-scale genetic structure in NL that is clustered around coastal communities and correlated with Christian denomination. We show that the majority of NL European ancestry can be traced back to the south-east and south-west of Ireland and England. We date a substantial population size bottleneck approximately 10-15 generations ago in NL, associated with increased haplotype sharing and autozygosity. Our results elucidate novel insights into the population history of NL and demonstrate evidence of a population conducive to further genetic studies and biomarker discovery</p

The Newfoundland and Labrador mosaic founder population descends from an Irish and British diaspora from 300 years ago

The founder population of Newfoundland and Labrador (NL) is a unique genetic resource, in part due to its geographic and cultural isolation, where historical records describe a migration of European settlers, primarily from Ireland and England, to NL in the 18th and 19th centuries. Whilst its historical isolation, and increased prevalence of certain monogenic disorders are well appreciated, details of the fine-scale genetic structure and ancestry of the population are lacking. Understanding the genetic origins and background of functional, disease causing, genetic variants would aid genetic mapping efforts in the Province. Here, we leverage dense genome-wide SNP data on 1,807 NL individuals to reveal fine-scale genetic structure in NL that is clustered around coastal communities and correlated with Christian denomination. We show that the majority of NL European ancestry can be traced back to the south-east and south-west of Ireland and England, respectively. We date a substantial population size bottleneck approximately 10-15 generations ago in NL, associated with increased haplotype sharing and autozygosity. Our results reveal insights into the population history of NL and demonstrate evidence of a population conducive to further genetic studies and biomarker discovery. </p

Characterization of the Y chromosome in Newfoundland and Labrador: evidence of a founder effect

The population of Newfoundland and Labrador (NL) is largely derived from settlers who migrated primarily from England and Ireland in the 1700-1800s. Previously described as an isolated founder population, based on historical and demographic studies, data on the genetic ancestry of this population remains fragmentary. Here we describe the largest investigation of patrilineal ancestry in NL. To determine the paternal genetic structure of the population, 1,110 Y chromosomes from an NL based cohort were analyzed using 5,761 Y-specific markers. We identified 160 distinct paternal haplotypes, the majority of which (71.4%) belong to the R1b haplogroup. When NL is compared with global reference populations, the haplotype composition and frequencies of the NL paternal lineages primarily resemble the English and Irish ancestral source populations. There is also evidence for genetic contributions from Basque, French, Portuguese, and Spanish fishermen and early settlers that frequented NL. The population structure shows geographical and religious clustering that can be associated with the settlement of ancestral source populations from England and Ireland. For example, the R1b-M222 haplotype, seen in people of Irish descent, is found clustered in the Irish-settled Southeast region of NL. The clustering and expansion of Y haplotypes in conjunction with the geographical and religious clusters illustrate that limited subsequent in migration, geographic isolation and societal factors have contributed to the genetic substructure of the NL population and its designation as a founder population.</p