Partition regularity without the columns property

A finite or infinite matrix A with rational entries is called partition regular if whenever the natural numbers are finitely coloured there is a monochromatic vector x with Ax=0. Many of the classical theorems of Ramsey Theory may naturally be interpreted as assertions that particular matrices are partition regular. In the finite case, Rado proved that a matrix is partition regular if and only it satisfies a computable condition known as the columns property. The first requirement of the columns property is that some set of columns sums to zero. In the infinite case, much less is known. There are many examples of matrices with the columns property that are not partition regular, but until now all known examples of partition regular matrices did have the columns property. Our main aim in this paper is to show that, perhaps surprisingly, there are infinite partition regular matrices without the columns property --- in fact, having no set of columns summing to zero. We also make a conjecture that if a partition regular matrix (say with integer coefficients) has bounded row sums then it must have the columns property, and prove a first step towards this.Comment: 13 page

Distinguishing subgroups of the rationals by their Ramsey properties

A system of linear equations with integer coefficients is partition regular over a subset S of the reals if, whenever S\{0} is finitely coloured, there is a solution to the system contained in one colour class. It has been known for some time that there is an infinite system of linear equations that is partition regular over R but not over Q, and it was recently shown (answering a long-standing open question) that one can also distinguish Q from Z in this way. Our aim is to show that the transition from Z to Q is not sharp: there is an infinite chain of subgroups of Q, each of which has a system that is partition regular over it but not over its predecessors. We actually prove something stronger: our main result is that if R and S are subrings of Q with R not contained in S, then there is a system that is partition regular over R but not over S. This implies, for example, that the chain above may be taken to be uncountable.Comment: 14 page

Post-selection-free preparation of high-quality physical qubits

Rapidly improving gate fidelities for coherent operations mean that errors in state preparation and measurement (SPAM) may become a dominant source of error for fault-tolerant operation of quantum computers. This is particularly acute in superconducting systems, where tradeoffs in measurement fidelity and qubit lifetimes have limited overall performance. Fortunately, the essentially classical nature of preparation and measurement enables a wide variety of techniques for improving quality using auxiliary qubits combined with classical control and post-selection. In practice, however, post-selection greatly complicates the scheduling of processes such as syndrome extraction. Here we present a family of quantum circuits that prepare high-quality |0> states without post-selection, instead using CNOT and Toffoli gates to non-linearly permute the computational basis. We find meaningful performance enhancements when two-qubit gate fidelities errors go below 0.2%, and even better performance when native Toffoli gates are available.Comment: Source code and data behind this paper can be found at https://github.com/riverlane/purification-without-post-selectio

The Continuing Story of the Cost-Effectiveness of Photoselective Vaporization of the Prostate versus Transuretheral Resection of the Prostate for the Treatment of Symptomatic Benign Prostatic Obstruction

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LUVMI: an innovative payload for the sampling of volatiles at the Lunar poles

The ISECG identifies one of the first exploration steps as in situ investigations of the moon or asteroids. Europe is developing payload concepts for drilling and sample analysis, a contribution to a 250kg rover as well as for sample return. To achieve these missions, ESA depends on international partnerships. Such missions will be seldom, expensive and the drill/sample site selected will be based on observations from orbit not calibrated with ground truth data. Many of the international science community’s objectives can be met at lower cost, or the chances of mission success improved and the quality of the science increased by making use of an innovative, low mass, mobile robotic payload following the LEAG recommendations. LUVMI provides a smart, low mass, innovative, modular mobile payload comprising surface and subsurface sensing with an in-situ sampling technology capable of depth-resolved extraction of volatiles, combined with a volatile analyser (mass spectrometer) capable of identifying the chemical composition of the most important volatiles. This will allow LUVMI to: traverse the lunar surface prospecting for volatiles; sample subsurface up to a depth of 10 cm (with a goal of 20 cm); extract water and other loosely bound volatiles; identify the chemical species extracted; access and sample permanently shadowed regions (PSR). The main innovation of LUVMI is to develop an in situ sampling technology capable of depth-resolved extraction of volatiles, and then to package within this tool, the analyser itself, so as to maximise transfer efficiency and minimise sample handling and its attendant mass requirements and risk of sample alteration. By building on national, EC and ESA funded research and developments, this project will develop to TRL6 instruments that together form a smart modular mobile payload that could be flight ready in 2020. The LUVMI sampling instrument will be tested in a highly representative environment including thermal, vacuum and regolith simulant and the integrated payload demonstrated in a representative environment

Assessment of the performance and radiation damage effects under cryogenic temperatures of a P-channel CCD204s

CCDs continue to be the detector of choice for high resolution and high performance space applications. One perceived drawback is their susceptibility to radiation damage, in particular the formation of trap sites leading to a decrease in charge transfer efficiency. To that end, ESA has started a programme to investigate a new generation of devices based upon p-channel technology. The expectation is that once mature, p-channel devices may offer a significant increase in tolerance to proton radiation over traditional n-type buried channel CCDs. Early studies of e2v devices to assess the radiation hardness of p-channel devices were limited by the quality of devices available, however more recently, good quality p-channel CCD204s have been manufactured and studied. A more detailed evaluation of p-channel CCDs is now underway to realise the full potential of the technology for use in future high radiation environment space missions. A key aspect is the development of a cryogenic test rig that will allow for the first time a direct comparison of the radiation damage effects when the irradiation is performed both traditionally unbiased at room temperature and cryogenically with the device operational. Subsequent characterisations will also be performed on the cryogenic device after periods of storage at room temperature to investigate the potential annealing effects upon the lattice damage. Here we describe and present early results from an extensive programme of testing which will address all key performance parameters for p-channel CCDs, such as full electro-optical characterisation, assessment of radiation hardness and investigation of trap species

A real-time, scalable, fast and highly resource efficient decoder for a quantum computer

Quantum computers promise to solve computing problems that are currently intractable using traditional approaches. This can only be achieved if the noise inevitably present in quantum computers can be efficiently managed at scale. A key component in this process is a classical decoder, which diagnoses the errors occurring in the system. If the decoder does not operate fast enough, an exponential slowdown in the logical clock rate of the quantum computer occurs. Additionally, the decoder must be resource efficient to enable scaling to larger systems and potentially operate in cryogenic environments. Here we introduce the Collision Clustering decoder, which overcomes both challenges. We implement our decoder on both an FPGA and ASIC, the latter ultimately being necessary for any cost-effective scalable solution. We simulate a logical memory experiment on large instances of the leading quantum error correction scheme, the surface code, assuming a circuit-level noise model. The FPGA decoding frequency is above a megahertz, a stringent requirement on decoders needed for e.g. superconducting quantum computers. To decode an 881 qubit surface code it uses only $4.5\%$ of the available logical computation elements. The ASIC decoding frequency is also above a megahertz on a 1057 qubit surface code, and occupies 0.06 mm$^2$ area and consumes 8 mW of power. Our decoder is optimised to be both highly performant and resource efficient, while its implementation on hardware constitutes a viable path to practically realising fault-tolerant quantum computers.Comment: 11 pages, 4 figure