A Stabilizer Framework for the Contextual Subspace Variational Quantum Eigensolver and the Noncontextual Projection Ansatz

Quantum chemistry is a promising application for noisy intermediate-scale quantum (NISQ) devices. However, quantum computers have thus far not succeeded in providing solutions to problems of real scientific significance, with algorithmic advances being necessary to fully utilize even the modest NISQ machines available today. We discuss a method of ground state energy estimation predicated on a partitioning of the molecular Hamiltonian into two parts: one that is noncontextual and can be solved classically, supplemented by a contextual component that yields quantum corrections obtained via a Variational Quantum Eigensolver (VQE) routine. This approach has been termed Contextual Subspace VQE (CS-VQE); however, there are obstacles to overcome before it can be deployed on NISQ devices. The problem we address here is that of the ansatz, a parametrized quantum state over which we optimize during VQE; it is not initially clear how a splitting of the Hamiltonian should be reflected in the CS-VQE ansätze. We propose a "noncontextual projection" approach that is illuminated by a reformulation of CS-VQE in the stabilizer formalism. This defines an ansatz restriction from the full electronic structure problem to the contextual subspace and facilitates an implementation of CS-VQE that may be deployed on NISQ devices. We validate the noncontextual projection ansatz using a quantum simulator and demonstrate chemically precise ground state energy calculations for a suite of small molecules at a significant reduction in the required qubit count and circuit depth

A stabilizer framework for Contextual Subspace VQE and the noncontextual projection ansatz

Quantum chemistry is a promising application for noisy intermediate-scale quantum (NISQ) devices. However, quantum computers have thus far not succeeded in providing solutions to problems of real scientific significance, with algorithmic advances being necessary to fully utilise even the modest NISQ machines available today. We discuss a method of ground state energy estimation predicated on a partitioning the molecular Hamiltonian into two parts: one that is noncontextual and can be solved classically, supplemented by a contextual component that yields quantum corrections obtained via a Variational Quantum Eigensolver (VQE) routine. This approach has been termed Contextual Subspace VQE (CS-VQE), but there are obstacles to overcome before it can be deployed on NISQ devices. The problem we address here is that of the ansatz - a parametrized quantum state over which we optimize during VQE. It is not initially clear how a splitting of the Hamiltonian should be reflected in our CS-VQE ans\"atze. We propose a 'noncontextual projection' approach that is illuminated by a reformulation of CS-VQE in the stabilizer formalism. This defines an ansatz restriction from the full electronic structure problem to the contextual subspace and facilitates an implementation of CS-VQE that may be deployed on NISQ devices. We validate the noncontextual projection ansatz using a quantum simulator, with results obtained herein for a suite of trial molecules.Comment: 42 pages, 4 figure

Modernretro : Hidup dengan gaya mid-century modern

143 p. : il.; 18 cm

Living With Mid-Century Modern Style: Modern Retro

Pada pertengahan abad 20, furnitur modern keramik, kaca dan tekstil telah menjadi sangat populer di kalangan orang-orang yang menghargai kontribusi pada gaya-gaya retro modern. Buku ini menampilkan desain-desain interior yang dapat menginspirasi untuk menciptakan tampilan yang menggabungkan gaya klasik dengan visioner seperti Eameses, Bertoia dan Aalto. Buku ini bukan sekedar menciptakan nuansa melainkan juga menunjukkan bagaimana untuk mengambil desain terbaik dari tahun 1920-an hingga 1970-an

A global perspective on collision and non-collision match characteristics in male rugby union: Comparisons by age and playing standard

This study quantified and compared the collision and non-collision match characteristics across age categories (i.e. U12, U14, U16, U18, Senior) for both amateur and elite playing standards from Tier 1 rugby union nations (i.e. England, South Africa, New Zealand). Two-hundred and one male matches (5911 min ball-in-play) were coded using computerised notational analysis, including 193,708 match characteristics (e.g. 83,688 collisions, 33,052 tackles, 13,299 rucks, 1006 mauls, 2681 scrums, 2923 lineouts, 44,879 passes, 5568 kicks). Generalised linear mixed models with post-hoc comparisons and cluster analysis compared the match characteristics by age category and playing standard. Overall significant differences (p < 0.001) between age category and playing standard were found for the frequency of match characteristics, and tackle and ruck activity. The frequency of characteristics increased with age category and playing standard except for scrums and tries that were the lowest at the senior level. For the tackle, the percentage of successful tackles, frequency of active shoulder, sequential and simultaneous tackles increased with age and playing standard. For ruck activity, the number of attackers and defenders were lower in U18 and senior than younger age categories. Cluster analysis demonstrated clear differences in all and collision match characteristics and activity by age category and playing standard. These findings provide the most comprehensive quantification and comparison of collision and non-collision activity in rugby union demonstrating increased frequency and type of collision activity with increasing age and playing standard. These findings have implications for policy to ensure the safe development of rugby union players throughout the world