Quantum Hypothesis Testing with Group Structure

The problem of discriminating between many quantum channels with certainty is analyzed under the assumption of prior knowledge of algebraic relations among possible channels. It is shown, by explicit construction of a novel family of quantum algorithms, that when the set of possible channels faithfully represents a finite subgroup of SU(2) (e.g., $C_n, D_{2n}, A_4, S_4, A_5$) the recently-developed techniques of quantum signal processing can be modified to constitute subroutines for quantum hypothesis testing. These algorithms, for group quantum hypothesis testing (G-QHT), intuitively encode discrete properties of the channel set in SU(2) and improve query complexity at least quadratically in $n$, the size of the channel set and group, compared to na\"ive repetition of binary hypothesis testing. Intriguingly, performance is completely defined by explicit group homomorphisms; these in turn inform simple constraints on polynomials embedded in unitary matrices. These constructions demonstrate a flexible technique for mapping questions in quantum inference to the well-understood subfields of functional approximation and discrete algebra. Extensions to larger groups and noisy settings are discussed, as well as paths by which improved protocols for quantum hypothesis testing against structured channel sets have application in the transmission of reference frames, proofs of security in quantum cryptography, and algorithms for property testing.Comment: 22 pages + 9 figures + 3 table

Multivariable quantum signal processing (M-QSP): prophecies of the two-headed oracle

Recent work shows that quantum signal processing (QSP) and its multi-qubit lifted version, quantum singular value transformation (QSVT), unify and improve the presentation of most quantum algorithms. QSP/QSVT characterize the ability, by alternating ans\"atze, to obliviously transform the singular values of subsystems of unitary matrices by polynomial functions; these algorithms are numerically stable and analytically well-understood. That said, QSP/QSVT require consistent access to a single oracle, saying nothing about computing joint properties of two or more oracles; these can be far cheaper to determine given an ability to pit oracles against one another coherently. This work introduces a corresponding theory of QSP over multiple variables: M-QSP. Surprisingly, despite the non-existence of the fundamental theorem of algebra for multivariable polynomials, there exist necessary and sufficient conditions under which a desired stable multivariable polynomial transformation is possible. Moreover, the classical subroutines used by QSP protocols survive in the multivariable setting for non-obvious reasons, and remain numerically stable and efficient. Up to a well-defined conjecture, we give proof that the family of achievable multivariable transforms is as loosely constrained as could be expected. The unique ability of M-QSP to obliviously approximate joint functions of multiple variables coherently leads to novel speedups incommensurate with those of other quantum algorithms, and provides a bridge from quantum algorithms to algebraic geometry.Comment: 23 pages + 4 figures + 10 page appendix (added background information on algebraic geometry; publication in Quantum

Optimized Compilation of Aggregated Instructions for Realistic Quantum Computers

Recent developments in engineering and algorithms have made real-world applications in quantum computing possible in the near future. Existing quantum programming languages and compilers use a quantum assembly language composed of 1- and 2-qubit (quantum bit) gates. Quantum compiler frameworks translate this quantum assembly to electric signals (called control pulses) that implement the specified computation on specific physical devices. However, there is a mismatch between the operations defined by the 1- and 2-qubit logical ISA and their underlying physical implementation, so the current practice of directly translating logical instructions into control pulses results in inefficient, high-latency programs. To address this inefficiency, we propose a universal quantum compilation methodology that aggregates multiple logical operations into larger units that manipulate up to 10 qubits at a time. Our methodology then optimizes these aggregates by (1) finding commutative intermediate operations that result in more efficient schedules and (2) creating custom control pulses optimized for the aggregate (instead of individual 1- and 2-qubit operations). Compared to the standard gate-based compilation, the proposed approach realizes a deeper vertical integration of high-level quantum software and low-level, physical quantum hardware. We evaluate our approach on important near-term quantum applications on simulations of superconducting quantum architectures. Our proposed approach provides a mean speedup of $5\times$, with a maximum of $10\times$. Because latency directly affects the feasibility of quantum computation, our results not only improve performance but also have the potential to enable quantum computation sooner than otherwise possible.Comment: 13 pages, to apper in ASPLO

Modular quantum signal processing in many variables

Despite significant advances in quantum algorithms, quantum programs in practice are often expressed at the circuit level, forgoing helpful structural abstractions common to their classical counterparts. Consequently, as many quantum algorithms have been unified with the advent of quantum signal processing (QSP) and quantum singular value transformation (QSVT), an opportunity has appeared to cast these algorithms as modules that can be combined to constitute complex programs. Complicating this, however, is that while QSP/QSVT are often described by the polynomial transforms they apply to the singular values of large linear operators, and the algebraic manipulation of polynomials is simple, the QSP/QSVT protocols realizing analogous manipulations of their embedded polynomials are non-obvious. Here we provide a theory of modular multi-input-output QSP-based superoperators, the basic unit of which we call a gadget, and show they can be snapped together with LEGO-like ease at the level of the functions they apply. To demonstrate this ease, we also provide a Python package for assembling gadgets and compiling them to circuits. Viewed alternately, gadgets both enable the efficient block encoding of large families of useful multivariable functions, and substantiate a functional-programming approach to quantum algorithm design in recasting QSP and QSVT as monadic types.Comment: 15 pages + 9 figures + 4 tables + 45 pages supplement. For codebase, see https://github.com/ichuang/pyqsp/tree/bet

A Grand Unification of Quantum Algorithms

Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian simulation, which appear as subroutines for large families of composite quantum algorithms. A number of these quantum algorithms were recently tied together by a novel technique known as the quantum singular value transformation (QSVT), which enables one to perform a polynomial transformation of the singular values of a linear operator embedded in a unitary matrix. In the seminal GSLW'19 paper on QSVT [Gily\'en, Su, Low, and Wiebe, ACM STOC 2019], many algorithms are encompassed, including amplitude amplification, methods for the quantum linear systems problem, and quantum simulation. Here, we provide a pedagogical tutorial through these developments, first illustrating how quantum signal processing may be generalized to the quantum eigenvalue transform, from which QSVT naturally emerges. Paralleling GSLW'19, we then employ QSVT to construct intuitive quantum algorithms for search, phase estimation, and Hamiltonian simulation, and also showcase algorithms for the eigenvalue threshold problem and matrix inversion. This overview illustrates how QSVT is a single framework comprising the three major quantum algorithms, thus suggesting a grand unification of quantum algorithms

Cerebellar ataxia, neuropathy, vestibular areflexia syndrome due to RFC1 repeat expansion.

Ataxia, causing imbalance, dizziness and falls, is a leading cause of neurological disability. We have recently identified a biallelic intronic AAGGG repeat expansion in replication factor complex subunit 1 (RFC1) as the cause of cerebellar ataxia, neuropathy, vestibular areflexia syndrome (CANVAS) and a major cause of late onset ataxia. Here we describe the full spectrum of the disease phenotype in our first 100 genetically confirmed carriers of biallelic repeat expansions in RFC1 and identify the sensory neuropathy as a common feature in all cases to date. All patients were Caucasian and half were sporadic. Patients typically reported progressive unsteadiness starting in the sixth decade. A dry spasmodic cough was also frequently associated and often preceded by decades the onset of walking difficulty. Sensory symptoms, oscillopsia, dysautonomia and dysarthria were also variably associated. The disease seems to follow a pattern of spatial progression from the early involvement of sensory neurons, to the later appearance of vestibular and cerebellar dysfunction. Half of the patients needed walking aids after 10 years of disease duration and a quarter were wheelchair dependent after 15 years. Overall, two-thirds of cases had full CANVAS. Sensory neuropathy was the only manifestation in 15 patients. Sixteen patients additionally showed cerebellar involvement, and six showed vestibular involvement. The disease is very likely to be underdiagnosed. Repeat expansion in RFC1 should be considered in all cases of sensory ataxic neuropathy, particularly, but not only, if cerebellar dysfunction, vestibular involvement and cough coexist

An electrogenic redox loop in sulfate reduction reveals a likely widespread mechanism of energy conservation

The bioenergetics of anaerobic metabolism frequently relies on redox loops performed by membrane complexes with substrate- and quinone-binding sites on opposite sides of the membrane. However, in sulfate respiration (a key process in the biogeochemical sulfur cycle), the substrate- and quinone-binding sites of the QrcABCD complex are periplasmic, and their role in energy conservation has not been elucidated. Here we show that the QrcABCD complex of Desulfovibrio vulgaris is electrogenic, as protons and electrons required for quinone reduction are extracted from opposite sides of the membrane, with a H+/e− ratio of 1. Although the complex does not act as a H+-pump, QrcD may include a conserved proton channel leading from the N-side to the P-side menaquinone pocket. Our work provides evidence of how energy is conserved during dissimilatory sulfate reduction, and suggests mechanisms behind the functions of related bacterial respiratory complexes in other bioenergetic contexts

The Large Observatory For X-ray Timing: LOFT

LOFT, the Large Observatory for X-ray Timing, is a new space mission concept devoted to observations of Galactic and extra-Galactic sources in the X-ray domain with the main goals of probing gravity theory in the very strong field environment of black holes and other compact objects, and investigating the state of matter at supra-nuclear densities in neutron stars. The instruments on-board LOFT, the Large area detector and the Wide Field Monitor combine for the first time an unprecedented large effective area (~10 m2 at 8 keV) sensitive to X-ray photons mainly in the 2-30 keV energy range and a spectral resolution approaching that of CCD-based telescopes (down to 200 eV at 6 keV). LOFT is currently competing for a launch of opportunity in 2022 together with the other M3 mission candidates of the ESA Cosmic Vision Progra

Competence Centre ICDI per Open Science, FAIR, ed EOSC - Mission, Strategia e piano d'azione

This document presents the mission and strategy of the Italian Competence Centre on Open Science, FAIR, and EOSC. The Competence Centre is an initiative born within the Italian Computing and Data Infrastructure (ICDI), a forum created by representatives of major Italian Research Infrastructures and e-Infrastructures, with the aim of promoting sinergies at the national level, and optimising the Italian participation to European and global challenges in this field, including the European Open Science Cloud (EOSC), the European Data Infrastructure (EDI) and HPC. This working paper depicts the mission and objectives of the ICDI Competence Centre, a network of experts with various skills and competences that are supporting the national stakeholders on topics related to Open Science, FAIR principles application and participation to the EOSC. The different actors and roles are described in the document as well as the activities and services offered, and the added value each stakeholder can find the in Competence Centre. The tools and services provided, in particular the concept for the portal, though which the Centre will connect to the national landscape and users, are also presented

The Large Observatory for x-ray timing

The Large Observatory For x-ray Timing (LOFT) was studied within ESA M3 Cosmic Vision framework and participated in the final down-selection for a launch slot in 2022-2024. Thanks to the unprecedented combination of effective area and spectral resolution of its main instrument, LOFT will study the behaviour of matter under extreme conditions, such as the strong gravitational field in the innermost regions of accretion flows close to black holes and neutron stars, and the supra-nuclear densities in the interior of neutron stars. The science payload is based on a Large Area Detector (LAD, 10 m2 effective area, 2-30 keV, 240 eV spectral resolution, 1° collimated field of view) and a WideField Monitor (WFM, 2-50 keV, 4 steradian field of view, 1 arcmin source location accuracy, 300 eV spectral resolution). The WFM is equipped with an on-board system for bright events (e.g. GRB) localization. The trigger time and position of these events are broadcast to the ground within 30 s from discovery. In this paper we present the status of the mission at the end of its Phase A study