Effect of ancilla's structure on quantum error correction using the 7-qubit Calderbank-Shor-Steane code

In this work we discuss the ability of different types of ancillas to control the decoherence of a qubit interacting with an environment. The error is introduced into the numerical simulation via a depolarizing isotropic channel. After the correction we calculate the fidelity as a quality criterion for the qubit recovered. We observe that a recovery method with a three-qubit ancilla provides reasonable good results bearing in mind its economy. If we want to go further, we have to use fault-tolerant ancillas with a high degree of parallelism, even if this condition implies introducing new ancilla verification qubits.Comment: 24 pages, 10 Figures included. Accepted in Phys. Rev. A 200

Reform and Representation: A New Method Applied to Recent Electoral Changes

Can electoral reforms such as an independent redistricting commission and the top-two primary create conditions that lead to better legislative representation? We explore this question by presenting a new method for measuring a key indicator of representation - the congruence between a legislator's ideological position and the average position of her district's voters. Our novel approach combines two methods: the joint classification of voters and political candidates on the same ideological scale, along with multilevel regression and post-stratification to estimate the position of the average voter across many districts in multiple elections. After validating our approach, we use it to study the recent impact of reforms in California, showing that they did not bring their hoped-for effects

Towards practical classical processing for the surface code: timing analysis

Topological quantum error correction codes have high thresholds and are well suited to physical implementation. The minimum weight perfect matching algorithm can be used to efficiently handle errors in such codes. We perform a timing analysis of our current implementation of the minimum weight perfect matching algorithm. Our implementation performs the classical processing associated with an nxn lattice of qubits realizing a square surface code storing a single logical qubit of information in a fault-tolerant manner. We empirically demonstrate that our implementation requires only O(n^2) average time per round of error correction for code distances ranging from 4 to 512 and a range of depolarizing error rates. We also describe tests we have performed to verify that it always obtains a true minimum weight perfect matching.Comment: 13 pages, 13 figures, version accepted for publicatio

Optimum Quantum Error Recovery using Semidefinite Programming

Quantum error correction (QEC) is an essential element of physical quantum information processing systems. Most QEC efforts focus on extending classical error correction schemes to the quantum regime. The input to a noisy system is embedded in a coded subspace, and error recovery is performed via an operation designed to perfectly correct for a set of errors, presumably a large subset of the physical noise process. In this paper, we examine the choice of recovery operation. Rather than seeking perfect correction on a subset of errors, we seek a recovery operation to maximize the entanglement fidelity for a given input state and noise model. In this way, the recovery operation is optimum for the given encoding and noise process. This optimization is shown to be calculable via a semidefinite program (SDP), a well-established form of convex optimization with efficient algorithms for its solution. The error recovery operation may also be interpreted as a combining operation following a quantum spreading channel, thus providing a quantum analogy to the classical diversity combining operation.Comment: 7 pages, 3 figure

Modeling proppant flow in fractures using LIGGGHTS, a scalable granular simulator

textProppant flowback in fractures under confining pressures is not well understood and difficult to reproduce in a laboratory setting. Improper management of proppant flowback leads to flow restrictions near the well bore, poor fracture conductivity and costly production equipment damage. A simple, scalable model is developed using a discrete element method (DEM) particle simulator, to simulate representative cubic volumes consisting of fracture openings, fracture walls and the confining formation. The effects of fracture width, confining stress, fluid flow velocity and proppant cohesion are studied for a variety of conditions. Fracture width is found to be dependent on confining stress and fluid flow velocity while proppant production is also dependent on cohesion. Three regimes are observed, with complete fracture evacuation occurring at high flow rates and low confining stresses, fully packed fractures occurring at high confining stresses and open but mostly evacuated fractures occurring in-between. From these observations, a recommended flowback rate can be estimated for a given set of conditions. A slow and controlled well flowback is recommended to improve proppant pack stability. The rate ramp-up time is dependent on the leak-off coefficient.Petroleum and Geosystems Engineerin

The effect of well path, tortuosity and drillstring design on the transmission of axial and torsional vibrations from the bit and mitigation control strategies

As well designs become increasingly complicated, a complete understanding of drillstring vibrations is key to maximize drilling efficiency, to reduce drillstring dysfunction and to minimize drillstring, tool, and borehole damage. Torque and drag models exist that seek to quantify the effects of borehole inclination and tortuosity on static friction along the drillstring; however, the effects on dynamic friction remains poorly understood. This dissertation begins with a review of the past fifty years of work on drillstring dynamics models, an overview of the proposed control strategies and a summary deployed vibration mitigation applications within the drilling industry. Derivations from first principles of a series of computationally efficient axial and torsional drillstring models in both the frequency and time domains are then presented and verified with field data. The transfer matrix approach is used to predict the severity of axial vibrations along the drillstring and is verified using a series of case studies using field data. Harmonic axial vibrations within drillstrings are either induced intentionally, in the case of axial oscillation tools midway along the drillstring, or unintentional, in the case of bit bounce. Two case studies of bit bounce are first evaluated to ensure model validity for a harmonic excitation at a the bit and the model is found to accurately predict bit bounce based on surface rotation rates. Induced axial oscillations, generated by axial oscillation tools, are then investigated to quantify friction reduction and drilling efficiency improvements. Optimal placement is found to depend on wellbore geometry, but is usually restricted to periodic regions of the drillstring. These optimizations are then verified using field trials and suggest that improved placement can result in 20% or more reduction in friction along the drillstring. Two applications of torsional drillstring vibrations are then investigated -- stick slip mitigation and drillstring imaging. The time domain form of the torsional drillstring model is used first to evaluate the effectiveness of three types of top drive controllers -- stiff controllers, tuned PI controllers and impedance matching controllers -- in mitigating stick slip oscillations. Then, the transfer matrix method is applied to evaluate the effect of wellbore geometry on drillstring mobility to conclude that higher order modes of stick slip may become dominant in non-vertical wellbores. The feasibility of drillstring imaging using torsional signals from surface is then investigated to identify inputs and methods that show promise in three setups of varying complexity -- a hanging beam, a laboratory drillstring model and a drilling rig. Two techniques show promise -- white noise injection and model fitting of a step response -- in identifying larger features, including drillstring length and BHA location. However, low sampling frequencies and low bandwidth inputs reduce the ability to image small features such as friction points along the wellpath.Petroleum and Geosystems Engineerin

Classical Rules in Quantum Games

We consider two aspects of quantum game theory: the extent to which the quantum solution solves the original classical game, and to what extent the new solution can be obtained in a classical model.Comment: The previous title, "Quantum games are no fun (yet)", was too whimsical for Physical Review. This is a comment on most, but not all, papers on quantum game theor

Magnetic qubits as hardware for quantum computers

We propose two potential realisations for quantum bits based on nanometre scale magnetic particles of large spin S and high anisotropy molecular clusters. In case (1) the bit-value basis states |0> and |1> are the ground and first excited spin states Sz = S and S-1, separated by an energy gap given by the ferromagnetic resonance (FMR) frequency. In case (2), when there is significant tunnelling through the anisotropy barrier, the qubit states correspond to the symmetric, |0>, and antisymmetric, |1>, combinations of the two-fold degenerate ground state Sz = +- S. In each case the temperature of operation must be low compared to the energy gap, \Delta, between the states |0> and |1>. The gap \Delta in case (2) can be controlled with an external magnetic field perpendicular to the easy axis of the molecular cluster. The states of different molecular clusters and magnetic particles may be entangled by connecting them by superconducting lines with Josephson switches, leading to the potential for quantum computing hardware.Comment: 17 pages, 3 figure