Simulating Quantum Mean Values in Noisy Variational Quantum Algorithms: A Polynomial-Scale Approach

Large-scale variational quantum algorithms possess an expressive capacity that is beyond the reach of classical computers and is widely regarded as a potential pathway to achieving practical quantum advantages. However, the presence of quantum noise might suppress and undermine these advantages, which blurs the boundaries of classical simulability. To gain further clarity on this matter, we present a novel polynomial-scale method that efficiently approximates quantum mean values in variational quantum algorithms with bounded truncation error in the presence of independent single-qubit depolarizing noise. Our method is based on path integrals in the Pauli basis. We have rigorously proved that, for a fixed noise rate $\lambda$, our method's time and space complexity exhibits a polynomial relationship with the number of qubits $n$, the circuit depth $L$, the inverse truncation error $\frac{1}{\varepsilon}$, and the inverse success probability $\frac{1}{\delta}$. Furthermore, We also prove that computational complexity becomes $\mathrm{Poly}\left(n,L\right)$ when the noise rate $\lambda$ exceeds $\frac{1}{\log{L}}$ and it becomes exponential with $L$ when the noise rate $\lambda$ falls below $\frac{1}{L}$

A simple and scalable hydrogel-based system for culturing protein-producing cells

Recombinant protein therapeutics have become important components of the modern medicine. Majority of them are produced with mammalian cells that are cultured either through adherent culturing, in which cells are cultured on substrates, or suspension culturing, in which cells are suspended and cultured in agitated cell culture medium in a culture vessel. The adherent cell culturing method is limited by its low yield. In suspension culturing, cells need extensive genetic manipulation to grow as single cells at high density, which is time and labor-consuming. Here, we report a new method, which utilizes a thermoreversible hydrogel as the scaffold for culturing protein-expressing cells. The hydrogel scaffolds not only provide 3D spaces for the cells, but also act as physical barriers to prevent excessive cellular agglomeration and protect cells from the hydrodynamic stresses. As a result, cells can grow at high viability, high growth rate, and extremely high yield even without genetic manipulations. The cell yield in the hydrogels is around 20 times of the suspension culturing. In addition, the protein productivity per cell per day in the hydrogel is higher than the adherent culturing method. This new method is simple, scalable and defined. It will be of great value for both the research laboratories and pharmaceutical industry for producing proteins

Altered insular functional connectivity correlates to impaired vigilant attention after sleep deprivation: A resting-state functional magnetic resonance imaging study

ObjectivesThis study used resting-state functional magnetic resonance imaging (rs-fMRI) scans to assess the dominant effects of 36 h total sleep deprivation (TSD) on vigilant attention and changes in the resting-state network.Materials and methodsTwenty-two healthy college students were enrolled in this study. Participants underwent two rs-fMRI scans, once in rested wakefulness (RW) and once after 36 h of TSD. We used psychomotor vigilance tasks (PVT) to measure vigilant attention. The region-of-interest to region-of-interest correlation was employed to analyze the relationship within the salience network (SN) and between other networks after 36 h of TSD. Furthermore, Pearson’s correlation analysis investigated the relationship between altered insular functional connectivity and PVT performance.ResultsAfter 36 h of TSD, participants showed significantly decreased vigilant attention. Additionally, TSD induced decreased functional connectivity between the visual and parietal regions, whereas, a significant increase was observed between the anterior cingulate cortex and insula. Moreover, changes in functional connectivity in the anterior cingulate cortex and insula showed a significant positive correlation with the response time to PVT.ConclusionOur results suggest that 36 h of TSD impaired vigilant visual attention, resulting in slower reaction times. The decrease in visual-parietal functional connectivity may be related to the decrease in the reception of information in the brain. Enhanced functional connectivity of the anterior cingulate cortex with the insula revealed that the brain network compensation occurs mainly in executive function

A simple and scalable hydrogel-based system for culturing protein-producing cells

Recombinant protein therapeutics have become important components of the modern medicine. Majority of them are produced with mammalian cells that are cultured either through adherent culturing, in which cells are cultured on substrates, or suspension culturing, in which cells are suspended and cultured in agitated cell culture medium in a culture vessel. The adherent cell culturing method is limited by its low yield. In suspension culturing, cells need extensive genetic manipulation to grow as single cells at high density, which is time and labor-consuming. Here, we report a new method, which utilizes a thermoreversible hydrogel as the scaffold for culturing protein-expressing cells. The hydrogel scaffolds not only provide 3D spaces for the cells, but also act as physical barriers to prevent excessive cellular agglomeration and protect cells from the hydrodynamic stresses. As a result, cells can grow at high viability, high growth rate, and extremely high yield even without genetic manipulations. The cell yield in the hydrogels is around 20 times of the suspension culturing. In addition, the protein productivity per cell per day in the hydrogel is higher than the adherent culturing method. This new method is simple, scalable and defined. It will be of great value for both the research laboratories and pharmaceutical industry for producing proteins

Efficient quantum imaginary time evolution by drifting real time evolution: an approach with low gate and measurement complexity

Quantum imaginary time evolution (QITE) is one of the promising candidates for finding eigenvalues and eigenstates of a Hamiltonian. However, the original QITE proposal [Nat. Phys. 16, 205-210 (2020)], which approximates the imaginary time evolution by real time evolution, suffers from large circuit depth and measurements due to the size of the Pauli operator pool and Trotterization. To alleviate the requirement for deep circuits, we propose a time-dependent drifting scheme inspired by the qDRIFT algorithm [Phys. Rev. Lett 123, 070503 (2019)], which randomly draws a Pauli term out of the approximated unitary operation generators of QITE according to the strength and rescales that term by the total strength of the Pauli terms. We show that this drifting scheme removes the depth dependency on size of the operator pool and converges inverse linearly to the number of steps. We further propose a deterministic algorithm that selects the dominant Pauli term to reduce the fluctuation for the ground state preparation. Meanwhile, we introduce an efficient measurement reduction scheme across Trotter steps, which removes its cost dependence on the number of iterations, and a measurement distribution protocol for different observables within each time step. We also analyze the main source of error for our scheme both theoretically and numerically. We numerically test the validity of depth reduction, convergence performance, and faithfulness of measurement reduction approximation of our algorithms on LiH, BeH$_2$ and N$_2$ molecules. In particular, the results on LiH molecule give circuit depths comparable to that of the advanced adaptive variational quantum eigensolver~(VQE) methods while requiring much fewer measurements

3D suspension culture of L-Wnt-3a-cells.

<p>L-Wnt-3a-cells were suspended in the low-attachment 6-well plate that was placed on a shaker at 60 rotations per minute (rpm) at low density (5x10⁴ cells/mL) and high density (1x10⁶ cells/mL). (A, B) Phase images of cells on day 0, day 4 and day 8. (C, D, E) The expansion fold, volumetric yield, and cell viability from day 1 to day 8 of the culture. Error bars represent the standard deviation (n = 3). #: P<0.05.</p

Overview of culturing protein-producing cells in three dimensional (3D) thermoreversible PNIPAAm-PEG hydrogels.

<p>(A) The PNIPAAm-PEG polymers are soluble in water at low temperature (e.g. 4°C). They associate to form a network at high temperature (e.g. 37°C), resulting in a hydrogel. When the temperature is reduced (e.g. to 4°C), the polymers become soluble again and the hydrogel is liquefied. (B) To culture cells, single cells are mixed with 10% PNIPAAm-PEG solution at low temperature and casted onto a tissue culture plate, and then incubated at room temperature or 37°C for 5 minutes to form an elastic hydrogel before adding the warm medium. The single cells clonally expand into uniform spheroids within days. Proteins secreted from the cells can diffuse through the hydrogel into the medium. The conditioned medium is collected for purifying the proteins.</p

Culture L-Wnt-3a-cells in 3D PNIPAAm-PEG hydrogels (Passage 1).

<p>L-Wnt-3a-cells were cultured in the hydrogels with three seeding densities: low (5x10⁵ cells/mL), medium (1x10⁶ cells/mL), and high density (2x10⁶ cells/mL). (A) Phase images of the passage 1 cells in the hydrogels on day 2, 4, 6 and 8 of the culture. (B) Live (green) dead (red) staining of day 9 cells in the hydrogels in passage 1. (C) The expansion fold, volumetric yield and cell viability along a 9-day culture in passage 1. Error bars represent the standard deviation (n = 3).</p