Spectral thresholding quantum tomography for low rank states

The estimation of high dimensional quantum states is an important statistical problem arising in current quantum technology applications. A key example is the tomography of multiple ions states, employed in the validation of state preparation in ion trap experiments (Häffner et al 2005 Nature 438 643). Since full tomography becomes unfeasible even for a small number of ions, there is a need to investigate lower dimensional statistical models which capture prior information about the state, and to devise estimation methods tailored to such models. In this paper we propose several new methods aimed at the efficient estimation of low rank states and analyse their performance for multiple ions tomography. All methods consist in first computing the least squares estimator, followed by its truncation to an appropriately chosen smaller rank. The latter is done by setting eigenvalues below a certain 'noise level' to zero, while keeping the rest unchanged, or normalizing them appropriately. We show that (up to logarithmic factors in the space dimension) the mean square error of the resulting estimators scales as where r is the rank, is the dimension of the Hilbert space, and N is the number of quantum samples. Furthermore we establish a lower bound for the asymptotic minimax risk which shows that the above scaling is optimal. The performance of the estimators is analysed in an extensive simulations study, with emphasis on the dependence on the state rank, and the number of measurement repetitions. We find that all estimators perform significantly better than the least squares, with the 'physical estimator' (which is a bona fide density matrix) slightly outperforming the other estimators

Kitaev's quantum double model from a local quantum physics point of view

A prominent example of a topologically ordered system is Kitaev's quantum double model $\mathcal{D}(G)$ for finite groups $G$ (which in particular includes $G = \mathbb{Z}_2$, the toric code). We will look at these models from the point of view of local quantum physics. In particular, we will review how in the abelian case, one can do a Doplicher-Haag-Roberts analysis to study the different superselection sectors of the model. In this way one finds that the charges are in one-to-one correspondence with the representations of $\mathcal{D}(G)$, and that they are in fact anyons. Interchanging two of such anyons gives a non-trivial phase, not just a possible sign change. The case of non-abelian groups $G$ is more complicated. We outline how one could use amplimorphisms, that is, morphisms $A \to M_n(A)$ to study the superselection structure in that case. Finally, we give a brief overview of applications of topologically ordered systems to the field of quantum computation.Comment: Chapter contributed to R. Brunetti, C. Dappiaggi, K. Fredenhagen, J. Yngvason (eds), Advances in Algebraic Quantum Field Theory (Springer 2015). Mainly revie

Rank-based model selection for multiple ions quantum tomography

The statistical analysis of measurement data has become a key component of many quantum engineering experiments. As standard full state tomography becomes unfeasible for large dimensional quantum systems, one needs to exploit prior information and the "sparsity" properties of the experimental state in order to reduce the dimensionality of the estimation problem. In this paper we propose model selection as a general principle for finding the simplest, or most parsimonious explanation of the data, by fitting different models and choosing the estimator with the best trade-off between likelihood fit and model complexity. We apply two well established model selection methods -- the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) -- to models consising of states of fixed rank and datasets such as are currently produced in multiple ions experiments. We test the performance of AIC and BIC on randomly chosen low rank states of 4 ions, and study the dependence of the selected rank with the number of measurement repetitions for one ion states. We then apply the methods to real data from a 4 ions experiment aimed at creating a Smolin state of rank 4. The two methods indicate that the optimal model for describing the data lies between ranks 6 and 9, and the Pearson $\chi^{2}$ test is applied to validate this conclusion. Additionally we find that the mean square error of the maximum likelihood estimator for pure states is close to that of the optimal over all possible measurements.Comment: 24 pages, 6 figures, 3 table

Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators

Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition. First, we show that a low-rank density matrix can be estimated using fewer copies of the state, i.e., the sample complexity of tomography decreases with the rank. Second, we show that unknown low-rank states can be reconstructed from an incomplete set of measurements, using techniques from compressed sensing and matrix completion. These techniques use simple Pauli measurements, and their output can be certified without making any assumptions about the unknown state. We give a new theoretical analysis of compressed tomography, based on the restricted isometry property (RIP) for low-rank matrices. Using these tools, we obtain near-optimal error bounds, for the realistic situation where the data contains noise due to finite statistics, and the density matrix is full-rank with decaying eigenvalues. We also obtain upper-bounds on the sample complexity of compressed tomography, and almost-matching lower bounds on the sample complexity of any procedure using adaptive sequences of Pauli measurements. Using numerical simulations, we compare the performance of two compressed sensing estimators with standard maximum-likelihood estimation (MLE). We find that, given comparable experimental resources, the compressed sensing estimators consistently produce higher-fidelity state reconstructions than MLE. In addition, the use of an incomplete set of measurements leads to faster classical processing with no loss of accuracy. Finally, we show how to certify the accuracy of a low rank estimate using direct fidelity estimation and we describe a method for compressed quantum process tomography that works for processes with small Kraus rank.Comment: 16 pages, 3 figures. Matlab code included with the source file

Permutationally invariant state reconstruction

Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, also an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a non-linear large-scale optimization problem, this is a major challenge in the design of scalable tomography schemes. Here we present an efficient state reconstruction scheme for permutationally invariant quantum state tomography. It works for all common state-of-the-art reconstruction principles, including, in particular, maximum likelihood and least squares methods, which are the preferred choices in today's experiments. This high efficiency is achieved by greatly reducing the dimensionality of the problem employing a particular representation of permutationally invariant states known from spin coupling combined with convex optimization, which has clear advantages regarding speed, control and accuracy in comparison to commonly employed numerical routines. First prototype implementations easily allow reconstruction of a state of 20 qubits in a few minutes on a standard computer.Comment: 25 pages, 4 figues, 2 table

High fatigue scores in patients with idiopathic inflammatory myopathies: a multigroup comparative study from the COVAD e-survey

Idiopathic inflammatory myopathies (IIMs) confer a significant risk of disability and poor quality of life, though fatigue, an important contributing factor, remains under-reported in these individuals. We aimed to compare and analyze differences in visual analog scale (VAS) scores (0–10 cm) for fatigue (VAS-F) in patients with IIMs, non-IIM systemic autoimmune diseases (SAIDs), and healthy controls (HCs). We performed a cross-sectional analysis of the data from the COVID-19 Vaccination in Autoimmune Diseases (COVAD) international patient self-reported e-survey. The COVAD survey was circulated from December 2020 to August 2021, and details including demographics, COVID-19 history, vaccination details, SAID details, global health, and functional status were collected from adult patients having received at least one COVID-19 vaccine dose. Fatigue experienced 1 week prior to survey completion was assessed using a single-item 10 cm VAS. Determinants of fatigue were analyzed in regression models. Six thousand nine hundred and eighty-eight respondents (mean age 43.8 years, 72% female; 55% White) were included in the analysis. The overall VAS-F score was 3 (IQR 1–6). Patients with IIMs had similar fatigue scores (5, IQR 3–7) to non-IIM SAIDs [5 (IQR 2–7)], but higher compared to HCs (2, IQR 1–5; P < 0.001), regardless of disease activity. In adjusted analysis, higher VAS-F scores were seen in females (reference female; coefficient −0.17; 95%CI −0.21 to −13; P < 0.001) and Caucasians (reference Caucasians; coefficient −0.22; 95%CI −0.30 to −0.14; P < 0.001 for Asians and coefficient −0.08; 95%CI −0.13 to 0.30; P = 0.003 for Hispanics) in our cohort. Our study found that patients with IIMs exhibit considerable fatigue, similar to other SAIDs and higher than healthy individuals. Women and Caucasians experience greater fatigue scores, allowing identification of stratified groups for optimized multidisciplinary care and improve outcomes such as quality of life

COVAD survey 2 long-term outcomes: unmet need and protocol

Vaccine hesitancy is considered a major barrier to achieving herd immunity against COVID-19. While multiple alternative and synergistic approaches including heterologous vaccination, booster doses, and antiviral drugs have been developed, equitable vaccine uptake remains the foremost strategy to manage pandemic. Although none of the currently approved vaccines are live-attenuated, several reports of disease flares, waning protection, and acute-onset syndromes have emerged as short-term adverse events after vaccination. Hence, scientific literature falls short when discussing potential long-term effects in vulnerable cohorts. The COVAD-2 survey follows on from the baseline COVAD-1 survey with the aim to collect patient-reported data on the long-term safety and tolerability of COVID-19 vaccines in immune modulation. The e-survey has been extensively pilot-tested and validated with translations into multiple languages. Anticipated results will help improve vaccination efforts and reduce the imminent risks of COVID-19 infection, especially in understudied vulnerable groups

JAAD-D-21-03349-SupplementalMaterial

SUPPLEMENTAL MATERIALSupplemental Figure 1. FlowchartFlowchart reporting the clinical profile of DM patients included in the study and the number of patients analyzed at last follow-up.Supplemental Figure 2. Cutaneous improvement to JAK inhibitor in a patient at follow-upIllustrative case (patient 4) with skin refractory dermatomyositis demonstrating a cutaneous response to ruxolitinib. CDASI at baseline was 49 and significantly decreased to 30 at 3-month. Clinical improvement was sustained (CDASI of 26) at 6-month follow-up. Prednisone was decreased from 10 to 7 mg/day over this period of time. Supplemental Figure 3. Manual muscle testing evolution following JAK inhibitor treatmentMean±SD manual MMT8 of 120±31, 121±29, 128±26 and 132±124 at baseline (M0), 3-month, 6-month and last follow-up, respectively.M0: baseline; M3: 3-month; M6: 6-month; FU: follow-up; MMT: manual muscle testing.Data shown as mean±SDSupplemental Figure 4. Treatment burden evolution following JAK inhibitor treatmentPercentage of patients remaining with IVIg and/or prednisone 5mg/day at follow-up. IVIg was stopped in 1 patient at 6-month and in 4 patients at last follow-up. Prednisone decrease to ≤5 mg/day was achieved in 1, 2 and 10 patients at 3-month, 6-month and last follow-up, respectively.IVIg: intravenous immunoglobulin; Pred: prednisone; M0: baseline; M3: 3-month; M6: 6-month; FU: follow-up.Data shown as percentageSupplemental Figure 5. IFN alpha at 3 monthsNon-significant trend of IFN alpha decrease from mean±SD 1612±4316 fg/mL to 1352±3722 fg/mL between baseline and 3-month.IFN: interferonTHIS DATASET IS ARCHIVED AT DANS/EASY, BUT NOT ACCESSIBLE HERE. TO VIEW A LIST OF FILES AND ACCESS THE FILES IN THIS DATASET CLICK ON THE DOI-LINK ABOV

Une solution nouvelle pour l’évaluation des myosites : la mesure de l’activité physique quotidienne par accéléromètrie

International audienc

Dermatomyosites (DM) à anticorps anti-Mi2 revisitées : DM pure avec nécrose musculaire et haut risque de malignité associée

International audienc