Precision tomography of a three-qubit donor quantum processor in silicon.

Nuclear spins were among the first physical platforms to be considered for quantum information processing1,2, because of their exceptional quantum coherence3 and atomic-scale footprint. However, their full potential for quantum computing has not yet been realized, owing to the lack of methods with which to link nuclear qubits within a scalable device combined with multi-qubit operations with sufficient fidelity to sustain fault-tolerant quantum computation. Here we demonstrate universal quantum logic operations using a pair of ion-implanted 31P donor nuclei in a silicon nanoelectronic device. A nuclear two-qubit controlled-Z gate is obtained by imparting a geometric phase to a shared electron spin4, and used to prepare entangled Bell states with fidelities up to 94.2(2.7)%. The quantum operations are precisely characterized using gate set tomography (GST)5, yielding one-qubit average gate fidelities up to 99.95(2)%, two-qubit average gate fidelity of 99.37(11)% and two-qubit preparation/measurement fidelities of 98.95(4)%. These three metrics indicate that nuclear spins in silicon are approaching the performance demanded in fault-tolerant quantum processors6. We then demonstrate entanglement between the two nuclei and the shared electron by producing a Greenberger-Horne-Zeilinger three-qubit state with 92.5(1.0)% fidelity. Because electron spin qubits in semiconductors can be further coupled to other electrons7-9 or physically shuttled across different locations10,11, these results establish a viable route for scalable quantum information processing using donor nuclear and electron spins.

Direct Randomized Benchmarking for Multiqubit Devices.

Benchmarking methods that can be adapted to multiqubit systems are essential for assessing the overall or "holistic" performance of nascent quantum processors. The current industry standard is Clifford randomized benchmarking (RB), which measures a single error rate that quantifies overall performance. But, scaling Clifford RB to many qubits is surprisingly hard. It has only been performed on one, two, and three qubits as of this writing. This reflects a fundamental inefficiency in Clifford RB: the n-qubit Clifford gates at its core have to be compiled into large circuits over the one- and two-qubit gates native to a device. As n grows, the quality of these Clifford gates quickly degrades, making Clifford RB impractical at relatively low n. In this Letter, we propose a direct RB protocol that mostly avoids compiling. Instead, it uses random circuits over the native gates in a device, which are seeded by an initial layer of Clifford-like randomization. We demonstrate this protocol experimentally on two to five qubits using the publicly available ibmqx5. We believe this to be the greatest number of qubits holistically benchmarked, and this was achieved on a freely available device without any special tuning up. Our protocol retains the simplicity and convenient properties of Clifford RB: it estimates an error rate from an exponential decay. But, it can be extended to processors with more qubits-we present simulations on 10+ qubits-and it reports a more directly informative and flexible error rate than the one reported by Clifford RB. We show how to use this flexibility to measure separate error rates for distinct sets of gates, and we use this method to estimate the average error rate of a set of cnot gates.

Multiparameter Estimation in Networked Quantum Sensors.

We introduce a general model for a network of quantum sensors, and we use this model to consider the following question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a set of unknown parameters? We rigorously answer this question by presenting precise theorems proving that for a broad class of problems there is, at most, a very limited intrinsic advantage to using entangled states or global measurements. Moreover, for many estimation problems separable states and local measurements are optimal, and can achieve the ultimate quantum limit on the estimation uncertainty. This immediately implies that there are broad conditions under which simultaneous estimation of multiple parameters cannot outperform individual, independent estimations. Our results apply to any situation in which spatially localized sensors are unitarily encoded with independent parameters, such as when estimating multiple linear or nonlinear optical phase shifts in quantum imaging, or when mapping out the spatial profile of an unknown magnetic field. We conclude by showing that entangling the sensors can enhance the estimation precision when the parameters of interest are global properties of the entire network.

Unremitting health-care-utilization outcomes of tertiary rehabilitation of patients with chronic musculoskeletal disorders.

BACKGROUND: Unremitting health-care-seeking behaviors have only infrequently been addressed in the literature as an outcome of treatment for chronic disabling work-related musculoskeletal disorders. The limited research has never focused on the patient as the "driver" of health-care utilization, to our knowledge. As a result, little attention has been paid to the differences between treated patients who seek additional health care from a new provider and those who do not. The purpose of this project was to examine the demographic and socioeconomic outcome variables that characterize patients with a chronic disabling work-related musculoskeletal disorder who pursue additional health-care services from a new provider following the completion of a tertiary rehabilitation treatment program. A prospective comparison cohort design was employed to assess characteristics and outcomes of these patients, all of whom were treated with the same interdisciplinary protocol. METHODS: A cohort of 1316 patients who had been consecutively treated with a rehabilitation program for functional restoration was divided into two groups on the basis of whether they had sought treatment from a new health-care provider in the year following completion of treatment. Group 0 (966 patients) did not visit a new health-care provider for treatment of their original occupational injury, and Group 1 (350 patients) visited a new provider on at least one occasion. A structured clinical interview to assess socioeconomic outcomes was carried out one year after discharge from the treatment program; this interview addressed pain, health-care utilization, work status, recurrent injury, and whether the Workers' Compensation case had been closed. RESULTS: The percentage of Group-0 patients who had undergone pre-rehabilitation surgery was significantly lower than the percentage of Group-1 patients who had done so (12% compared with 21%, odds ratio = 1.9 [95% confidence interval = 1.3, 2.7]; p < 0.001). One year after treatment, 90% of the Group-0 patients had returned to work compared with only 78% of the Group-1 patients (odds ratio = 2.6 [95% confidence interval, 1.9, 3.6]; p < 0.001). Similarly, 88% of the Group-0 patients were still working at one year compared with only 62% of the patients in Group 1 (odds ratio = 4.5 [95% confidence interval, 3.3, 6.0]; p < 0.001). Whereas 96% of the Group-0 patients had resolved all related legal and/or financial disputes by one year, only 77% of the Group-1 patients had done so (odds ratio = 6.9 [95% confidence interval, 4.5, 10.5]; p < 0.001). Only a negligible percentage (0.4%) of the patients in Group 0 had undergone a new operation at the site of the original injury, whereas 12% of the Group-1 patients had done so (odds ratio = 31.0 [95% confidence interval, 11.0, 87.3]; p < 0.001). When the above outcome variables were analyzed by dividing Group 1 according to the number of visits to a new service provider, there was a trend for poorer socioeconomic outcomes to be associated with an increasing number of health-care visits. CONCLUSIONS: To our knowledge, the present study represents the first large-scale examination of patients with a chronic disabling work-related musculoskeletal disorder who persist in seeking health-care following the completion of tertiary rehabilitation. The results demonstrate that about 25% of patients with a chronic disabling work-related musculoskeletal disorder pursue new health-care services after completing a course of treatment, and this subgroup accounts for a significant proportion of lost worker productivity, unremitting disability payments, and excess health-care consumption. LEVEL OF EVIDENCE: Prognostic study, Level I-1 (prospective study). See Instructions to Authors for a complete description of levels of evidence.

Gender-related differences in treatment outcomes for patients with musculoskeletal disorders.

BACKGROUND CONTEXT: Clinicians have long hypothesized that gender may be a risk factor in treatment outcomes of patients with chronic disability associated with musculoskeletal disorders. Although the scientific literature shows a higher prevalence of occupational low back injury in men, and a higher rate of repetitive motion and neck injuries in women, few studies have comprehensively investigated the role of gender regarding cost-related outcome variables of significance after work-related injuries. PURPOSE: This study was designed to examine the relationship between gender and biopsychosocial treatment outcomes in a predominately chronically disabled spinal disorder (CDSD) workers' compensation cohort undergoing a tertiary functional restoration program. STUDY DESIGN: A prospective comparison cohort study investigating the effect of gender on biopsychosocial treatment outcomes as risk factors for rehabilitation failure. PATIENT SAMPLE: A cohort of 1,827 consecutively treated patients with CDSD were placed into two gender-based groups: men (n=1,158, average age 40.7+/-10 years) and women (n=669, average age 42.5+/-10 years). OUTCOME MEASURES: Before the start of the program, and again upon completion of the program, all patients received a standard psychosocial assessment and were assessed on a variety of physical factors (leading to a cumulative score, calculated on the basis of the aggregates and averages of these physical measures). A structured clinical interview examining socioeconomic outcomes was conducted at 1 year after program completion, and at least partial information was obtained from this interview on all patients in the present study. METHODS: All patients underwent a medically directed functional restoration program combining quantitatively guided exercise progression with a multimodal disability management approach using psychological and case management techniques. RESULTS: Men had a significantly higher rate of lumbar injury than women, whereas women had a significantly higher rate of cervical injury. Men returned to work and retained work at a 40 hours/week job at a higher rate at 1-year follow-up. Women evidenced a higher rate of health care-seeking behaviors from new providers. On physical testing immediately after treatment, men had a significantly higher cumulative physical score (gender normalized), both before and after treatment. On depression and disability questionnaires, men showed fewer pre- and posttreatment depressive symptoms with lower pretreatment disability scores. CONCLUSIONS: The present study represents the first large-scale examination of the relationship between gender and treatment outcomes for a population with CDSD after work injuries. There was a pattern of moderately better 1-year posttreatment socioeconomic outcome for men. On psychosocial measures, men showed lower disability and depression scores than women, with higher levels of physical functioning both before and after treatment. Overall, male patients with CDSD appeared to show somewhat better biopsychosocial outcomes. This leaves the question of identifying gender-specific risk factors to explain these differences.

Failure to complete a functional restoration program for chronic musculoskeletal disorders: a prospective 1-year outcome study.

OBJECTIVE: To compare comprehensively the likelihood of various socioeconomically relevant outcomes between functional restoration completers and noncompleters, while simultaneously identifying risk factors for noncompletion. DESIGN: A prospective cohort study of patients with chronic disabling occupational musculoskeletal disorders (CDOMD). SETTING: Chronic pain management facility. PARTICIPANTS: A total of 1440 patients with CDOMD were consecutively divided into 2 groups-one with 303 patients who did not complete the prescribed treatment program (noncompleters [NC]) and a second with 1137 patients who did (completers). INTERVENTION: The Interdisciplinary Functional Restoration: Rehabilitation program. MAIN OUTCOME MEASURES: Validated questionnaires about pain, disability, and depression were added to results of a structured 1-year posttreatment telephone interview on socioeconomic outcomes covering work status, health utilization, recurrent injury claims, and resolution of financial disputes. RESULTS: The 1-year posttreatment socioeconomic outcomes were most striking. The NC group was 7 times more likely to have postrehabilitation surgery in the same area, and nearly 7 times more likely to have more than 30 visits to a new health provider in persistent health care-seeking efforts. The NC group also had only half the rates of work return and work retention, being 9.7 times less likely to have returned to any type of work, and 7 times less likely to have retained work at the end of the year. Regression analysis also revealed that work return, surgery in a compensable injured area, more health care utilization from a new provider, and more overall health care utilization (>30 visits) were most reliably predicted by whether the rehabilitation program was completed. CONCLUSIONS: This large prospective study determined that noncompleters of interdisciplinary tertiary rehabilitation for CDOMDs had comparatively poor socioeconomic outcomes in the year after discharge from treatment, especially on work status and health utilization outcomes. These outcomes are of great relevance to societal, medical, and indemnity costs and future worker productivity. Several risk factors of possible importance in identifying potential noncompleters early in the treatment program were identified that may yield more effective interventions tailored to maintain compliance and decrease the percentage of drop-outs.

The million visual analog scale: its utility for predicting tertiary rehabilitation outcomes.

STUDY DESIGN: A longitudinal cohort study involving 1749 patients with chronically disabling spine disorder (CDSD) who underwent tertiary rehabilitation investigated the relation between the Million Visual Analog Scale (MVAS) score and treatment outcome. OBJECTIVES: To determine whether the pretreatment MVAS rating of disability severity is associated with the ability to complete functional restoration rehabilitation, and to determine whether pre- or posttreatment MVAS disability perception is associated with 1-year posttreatment socioeconomic outcomes. The relation of the MVAS to pre- and posttreatment psychosocial measures and physical performance levels also was evaluated. SUMMARY OF BACKGROUND DATA: The MVAS yields a total functional disability score ranging from 0 to 150. Like other "disability inventories," the MVAS differs from a "pain inventory" in that the focus is on disability and function, as opposed to self-reported pain. The MVAS may currently be the most powerful functional rating scale because all its questions relate to the patient's ability to perform activities of daily living. It also has the advantage of a visual analog format, which typically is considered more effective than other commonly used self-report formats. METHODS: A large cohort of 1749 patients with CDSD who underwent tertiary rehabilitation was divided into groups by their severity of disability, rated on the MVAS, both at pre- and posttreatment assessment. The patients were divided into groups ranging from "no reported disability" (MVAS = 0) to "extreme disability" (MVAS = 131-150). The distribution into the six groups was assessed on both pre- and posttreatment MVAS ratings. The patients underwent a 3-week functional restoration program consisting of daily quantitatively directed exercise progression and multimodal disability management. Physical capacity and psychosocial assessments, performed before and after treatment, were correlated with the MVAS scores. A 1-year posttreatment clinical interview obtained information on socioeconomic outcomes, which also were correlated with the MVAS ratings. RESULTS: Mantel-Haenszel linear analyses showed a number of relations between demographic variables and both pre- and posttreatment MVAS scores. Most importantly, the findings showed that severe pretreatment MVAS scores were associated with a lower program completion rate (94% vs 89%; P < 0.001) and a higher rate of postrehabilitation health care use from a new provider (12% vs 41%; P < 0.001). Prerehabilitation scores also were linearly related to lower levels of pretreatment physical performance and higher rates of pretreatment depression. More severe posttreatment MVAS scores were associated linearly with a drop in the work return rate from 93% to 63%, a drop in the work retention rate 1 year after rehabilitation from 86% to 44%, and a drop in the financial settlement rate from 94% to 79% (P < 0.001). A linear trend also was found in the rate of postrehabilitation surgeries, with the percentages rising from 0% in the group with no reported disabilities to 12% in the group with extreme disabilities (P < 0.001). CONCLUSIONS: The current study represents the first large-scale examination of the relation between MVAS ratings and treatment outcomes in a CDSD population. These results demonstrate the effectiveness of a simple disability rating scale, such as the MVAS, for systematic disability assessment in potentially predicting treatment outcomes in patients with CDSD. Despite the popularity of other questionnaires, the MVAS is the first disability inventory with demonstrated effectiveness for this purpose in a large CDSD population.