Precision Bounds on Continuous-Variable State Tomography using Classical Shadows

Shadow tomography is a framework for constructing succinct descriptions of quantum states using randomized measurement bases, called classical shadows, with powerful methods to bound the estimators used. We recast existing experimental protocols for continuous-variable quantum state tomography in the classical-shadow framework, obtaining rigorous bounds on the number of independent measurements needed for estimating density matrices from these protocols. We analyze the efficiency of homodyne, heterodyne, photon number resolving (PNR), and photon-parity protocols. To reach a desired precision on the classical shadow of an $N$-photon density matrix with a high probability, we show that homodyne detection requires an order $\mathcal{O}(N^{4+1/3})$ measurements in the worst case, whereas PNR and photon-parity detection require $\mathcal{O}(N^4)$ measurements in the worst case (both up to logarithmic corrections). We benchmark these results against numerical simulation as well as experimental data from optical homodyne experiments. We find that numerical and experimental homodyne tomography significantly outperforms our bounds, exhibiting a more typical scaling of the number of measurements that is close to linear in $N$. We extend our single-mode results to an efficient construction of multimode shadows based on local measurements.Comment: Title changed; added new corollary, references and additional explanation

Subspace Correction for Constraints

We demonstrate that it is possible to construct operators that stabilize the constraint-satisfying subspaces of computational problems in their Ising representations. We provide an explicit recipe to construct unitaries and associated measurements for some such constraints. The stabilizer measurements allow the detection of constraint violations, and provide a route to recovery back into the constrained subspace. We call this technique ``subspace correction". As an example, we explicitly investigate the stabilizers using the simplest local constraint subspace: Independent Set. We find an algorithm that is guaranteed to produce a perfect uniform or weighted distribution over all constraint-satisfying states when paired with a stopping condition: a quantum analogue of partial rejection sampling. The stopping condition can be modified for sub-graph approximations. We show that it can prepare exact Gibbs distributions on $d-$regular graphs below a critical hardness $\lambda_d^*$ in sub-linear time. Finally, we look at a potential use of subspace correction for fault-tolerant depth-reduction. In particular we investigate how the technique detects and recovers errors induced by Trotterization in preparing maximum independent set using an adiabatic state preparation algorithm.Comment: 12 + 4 pages, 6 figure

GLP-1-mediated delivery of tesaglitazar improves obesity and glucose metabolism in male mice

Dual agonists activating the peroxisome proliferator-activated receptors alpha and gamma (PPARɑ/ɣ) have beneficial effects on glucose and lipid metabolism in patients with type 2 diabetes, but their development was discontinued due to potential adverse effects. Here we report the design and preclinical evaluation of a molecule that covalently links the PPARɑ/ɣ dual-agonist tesaglitazar to a GLP-1 receptor agonist (GLP-1RA) to allow for GLP-1R-dependent cellular delivery of tesaglitazar. GLP-1RA/tesaglitazar does not differ from the pharmacokinetically matched GLP-1RA in GLP-1R signalling, but shows GLP-1R-dependent PPARɣ-retinoic acid receptor heterodimerization and enhanced improvements of body weight, food intake and glucose metabolism relative to the GLP-1RA or tesaglitazar alone in obese male mice. The conjugate fails to affect body weight and glucose metabolism in GLP-1R knockout mice and shows preserved effects in obese mice at subthreshold doses for the GLP-1RA and tesaglitazar. Liquid chromatography–mass spectrometry-based proteomics identified PPAR regulated proteins in the hypothalamus that are acutely upregulated by GLP-1RA/tesaglitazar. Our data show that GLP-1RA/tesaglitazar improves glucose control with superior efficacy to the GLP-1RA or tesaglitazar alone and suggest that this conjugate might hold therapeutic value to acutely treat hyperglycaemia and insulin resistance

Key signalling nodes in mammary gland development and cancer. Mitogen-activated protein kinase signalling in experimental models of breast cancer progression and in mammary gland development

Seven classes of mitogen-activated protein kinase (MAPK) intracellular signalling cascades exist, four of which are implicated in breast disease and function in mammary epithelial cells. These are the extracellular regulated kinase (ERK)1/2 pathway, the ERK5 pathway, the p38 pathway and the c-Jun N-terminal kinase (JNK) pathway. In some forms of human breast cancer and in many experimental models of breast cancer progression, signalling through the ERK1/2 pathway, in particular, has been implicated as being important. We review the influence of ERK1/2 activity on the organised three-dimensional association of mammary epithelial cells, and in models of breast cancer cell invasion. We assess the importance of epidermal growth factor receptor family signalling through ERK1/2 in models of breast cancer progression and the influence of ERK1/2 on its substrate, the oestrogen receptor, in this context. In parallel, we consider the importance of these MAPK-centred signalling cascades during the cycle of mammary gland development. Although less extensively studied, we highlight the instances of signalling through the p38, JNK and ERK5 pathways involved in breast cancer progression and mammary gland development

COVID-19 Proactive Disease Management Using COVID Virtual Hospital in a Rural Community

Purpose: A community teaching hospital serving a rural population established an intensive “hospital at home” program for patients with COVID-19 utilizing disease risk stratification and pulse oximeter readings to dictate nurse and clinician contact. Herein, we report patient outcomes and provider experiences resulting from this “virtual” approach to triaging pandemic care. Methods: COVID-19-positive patients appropriate for outpatient management were enrolled in our COVID Virtual Hospital (CVH). Patients received pulse oximeters and instructions for home monitoring of vital signs. CVH nurses contacted the patient within 12–48 hours. The primary care provider was alerted of the patient’s diagnosis and held a virtual visit with patient within 2–3 days. Nurses completed a triage form during each patient call; the resulting risk score determined timing of subsequent calls. CVH-relevant patient outcomes included emergency department (ED) visits, mortality, and disease-related hospitalization. Additionally, a survey of providers was conducted to assess CVH experience. Results: From April 22, 2020, to December 21, 2020, 1916 patients were enrolled in the CVH, of which 195 (10.2%) had subsequent visits to the ED. Among those 195 ED visits, 102 (52.3%) were nurse-directed while 93 (47.7%) were patient self-directed; 88 (86.3%) nurse-directed ED visits were subsequently admitted to inpatient care and 14 were discharged home. Of the 93 self-directed ED visits, 3 (3.2%) were admitted. A total of 91 CVH patients (4.7%) were ultimately admitted to inpatient care. Seven deaths occurred among CVH patients, 5 of whom had been admitted for inpatient care. Among 71 providers (23%) who responded to the survey, 94% and 93% agreed that the CVH was beneficial to providers and patients, respectively. Conclusions: Proactive in-home triage of patients with COVID-19 utilizing a virtual hospital model minimized unnecessary presentations to ED and likely prevented our rural hospital from becoming overwhelmed during year one of the pandemic