Reducing resources for verification of quantum computations

We present two verification protocols where the correctness of a "target" computation is checked by means of "trap" computations that can be efficiently simulated on a classical computer. Our protocols rely on a minimal set of noise-free operations (preparation of eight single-qubit states or measurement of four observables, both on a single plane of the Bloch sphere) and achieve linear overhead. To the best of our knowledge, our protocols are the least demanding techniques able to achieve linear overhead. They represent a step towards further reducing the quantum requirements for verification.Comment: Accepted versio

A Method to Evaluate the Field-Shape Multipoles Induced by Coil Deformations

A semi-analytical method to evaluate the effect of coil de-formations on the field-shape imperfections of the LHC dipole is presented. The deformation induced by the collaring procedure and by the thermal stresses is evaluated numerically with a finite element code. The vector field of mechanical displacements is approximated with truncated Taylor and Fourier series. The fitting function agrees with the numerical data to within less that 10 mm. The decom-position in modes of the truncated series permits identification of displacements which are dangerous for the multi-polar content and how they could be cured. An application to compare two designs of the LHC dipole is given

Modelization of the Thermo-Mechanical Structure of the LHC Main Dipole and Influence on Field Quality

The mechanical structure of the main LHC dipole is analysed. A finite element model is used to estimate the loads and the deformations at cryogenic temperature. The correct setting of the model parameters is crucial to obtain a reliable model to forecast the influence of design and tolerances on field quality. We discuss how the prestress loss from room to cryogenic temperature experimentally observed in the prototypes can be predicted using the finite element model. An estimate of the influence on field quality of deformations and tolerances due to manufacturing is given

Thermomechanical properties of the coil of the superconducting magnets for the Large Hadron Collider

The correct definition and measurement of the thermomechanical properties of the superconducting cable used in high-field magnets is crucial to study and model the behavior of the magnet coil from assembly to the operational conditions. In this paper, the authors analyze the superconducting coil of the main dipoles for the Large Hadron Collider. They describe an experimental setup for measuring the elastic modulus at room and at liquid nitrogen temperature and for evaluating the thermal contraction coefficient. The coils exhibit strong nonlinear stress-strain behavior characterized by hysteresis phenomena, which decreases from warm to cold temperature, and a thermal contraction coefficient, which depends on the stress applied to the cable during cooldown. (35 refs)

Control of field quality for the production of the main LHC dipoles

We review the warm magnetic measurements of the first four main dipole prototypes (8 apertures) and their agreement with nominal design. We then estimate the order of magnitude of the corrections that may be needed to re-center the low-order normal harmonics around the nominal values for the forthcoming series production. Correction strategies that provide the minumum impact on production schedule and costs are analysed. For the case of b3 and b5 two possibilities are considered: a variation of the shims to optimize the azimuthal length of the two coil layers, and a variation of the copper wedges of the inner layer, leaving unchanged the azimuthal coil size. For optimizing b2 and b4, we consider modifications of the shape of the ferromagnetic insert, that is placed between the collars and the yoke. Comparison between measurements and simulations of the implemented insert modifications are given and a final design is proposed. Intrinsic limits to the control of field quality during the production are discussed

Analysis of Conductor Displacements in the Coil of the LHC Main Dipole by Speckle Interferometry

Magnetic field quality in superconducting magnets mostly depends on conductor position in operational conditions (under pressure, at 1.9 K). For the case of the LHC main magnets, the conductor layout must agree with the nominal design within less than 0.05 mm to met the field quality specifications. Finite element models are a numerical tool to forecast loads and deformations of mechanical structures, and can be used to evaluate conductor displacements. To verify the FEM response at room temperature, we made displacement measurements using speckle interferometer on a short sample of the dipole coils. Experimental results are compared with the numerical calculations, allowing a stringent test of the most critical features of the FEM (interfaces between different materials and coil properties)

Modeling of Coil Pre-stress Loss During Cool-down in the Main Dipoles of the Large Hadron Collider

We describe a finite element mechanical model of the main LHC dipole, based on the geometry and on the properties of its components; coil characteristics are derived from measurements on stacks of conductors. We show how to define equivalent properties of cable blocks that take into account the collaring procedure when it is not explicitly modelled. Numerical results are then compared to experimental measurements of loads and deformations in dipole prototypes. At cryogenic temperature, equivalent properties are used to implement in the model a pressure- dependent thermal contraction factor observed in stack measurements. This allows to forecast the large pre-stress loss during the cool-down observed in the LHC dipole prototypes

Impact of Coil Deformations on Field Quality in the Large Hadron Collider Main Dipole

In superconducting accelerator magnets the coils are usually pre-stressed in order to avoid conductor movements induced by electro-magnetic forces. In this paper we use a finite element mechanical model of the main LHC dipole to evaluate the coil deformations determined by the pre-stress and their impact on magnetic field quality. The model explains the origin of the offsets between the nominal multipole values and those measured at room temperature in prototype and pre-series dipole magnets. We also present an experiment carried out to analyse the impact on field quality and coil stresses of coil azimuthal spacers (pole shims). A 1 m long dipole collared coil has been re-assembled several times with pole shims of different thickness and the field components have been measured each time. Experimental data are compared to numerical computations based on the mechanical model.One finds that variations of shim thickness induce not only a change of the azimuthal coil length, but also a different pattern in coil deformations. A good agreement is found between measurements and simulations