Quantum Approximation of Normalized Schatten Norms and Applications to Learning

Efficient measures to determine similarity of quantum states, such as the fidelity metric, have been widely studied. In this paper, we address the problem of defining a similarity measure for quantum operations that can be \textit{efficiently estimated}. Given two quantum operations, $U_1$ and $U_2$, represented in their circuit forms, we first develop a quantum sampling circuit to estimate the normalized Schatten 2-norm of their difference ($\| U_1-U_2 \|_{S_2}$) with precision $\epsilon$, using only one clean qubit and one classical random variable. We prove a Poly$(\frac{1}{\epsilon})$ upper bound on the sample complexity, which is independent of the size of the quantum system. We then show that such a similarity metric is directly related to a functional definition of similarity of unitary operations using the conventional fidelity metric of quantum states ($F$): If $\| U_1-U_2 \|_{S_2}$ is sufficiently small (e.g. $\leq \frac{\epsilon}{1+\sqrt{2(1/\delta - 1)}}$) then the fidelity of states obtained by processing the same randomly and uniformly picked pure state, $|\psi \rangle$, is as high as needed ($F({U}_1 |\psi \rangle, {U}_2 |\psi \rangle)\geq 1-\epsilon$) with probability exceeding $1-\delta$. We provide example applications of this efficient similarity metric estimation framework to quantum circuit learning tasks, such as finding the square root of a given unitary operation.Comment: 25 pages, 4 figures, 6 tables, 1 algorith

Global Existence and Large Time Behavior of Solutions to the Bipolar Nonisentropic Euler-Poisson Equations

We study the one-dimensional bipolar nonisentropic Euler-Poisson equations which can model various physical phenomena, such as the propagation of electron and hole in submicron semiconductor devices, the propagation of positive ion and negative ion in plasmas, and the biological transport of ions for channel proteins. We show the existence and large time behavior of global smooth solutions for the initial value problem, when the difference of two particles’ initial mass is nonzero, and the far field of two particles’ initial temperatures is not the ambient device temperature. This result improves that of Y.-P. Li, for the case that the difference of two particles’ initial mass is zero, and the far field of the initial temperature is the ambient device temperature

Linear-depth quantum circuits for loading Fourier approximations of arbitrary functions

The ability to efficiently load functions on quantum computers with high fidelity is essential for many quantum algorithms. We introduce the Fourier Series Loader (FSL) method for preparing quantum states that exactly encode multi-dimensional Fourier series using linear-depth quantum circuits. The FSL method prepares a ($Dn$)-qubit state encoding the $2^{Dn}$-point uniform discretization of a $D$-dimensional function specified by a $D$-dimensional Fourier series. A free parameter $m < n$ determines the number of Fourier coefficients, $2^{D(m+1)}$, used to represent the function. The FSL method uses a quantum circuit of depth at most $2(n-2)+\lceil \log_{2}(n-m) \rceil + 2^{D(m+1)+2} -2D(m+1)$, which is linear in the number of Fourier coefficients, and linear in the number of qubits ($Dn$) despite the fact that the loaded function's discretization is over exponentially many ($2^{Dn}$) points. We present a classical compilation algorithm with runtime $O(2^{3D(m+1)})$ to determine the FSL circuit for a given Fourier series. The FSL method allows for the highly accurate loading of complex-valued functions that are well-approximated by a Fourier series with finitely many terms. We report results from noiseless quantum circuit simulations, illustrating the capability of the FSL method to load various continuous 1D functions, and a discontinuous 1D function, on 20 qubits with infidelities of less than $10^{-6}$ and $10^{-3}$, respectively. We also demonstrate the practicality of the FSL method for near-term quantum computers by presenting experiments performed on the Quantinuum H$1$-$1$ and H$1$-$2$ trapped-ion quantum computers: we loaded a complex-valued function on 3 qubits with a fidelity of over $95\%$, as well as various 1D real-valued functions on up to 6 qubits with classical fidelities $\approx 99\%$, and a 2D function on 10 qubits with a classical fidelity $\approx 94\%$.Comment: V2: published versio

Activation of the IL-23/Th17 Axis

The aim of this paper is to determine the modulatory effects of Lactobacillus acidophilus on the IL-23/Th17 immune axis in experimental colitis. DSS-induced mouse models of UC were to be saline, hormones, and different concentrations of Lactobacillus acidophilus intervention. The expression of interleukin-(IL-) 17, tumor necrosis factor (TNF ), IL-23, transforming growth factor 1 (TGF 1), signal transducer and activator of transcription 3 (STAT3), and phosphorylated (p)-STAT3 was examined by RT-PCR, Western blotting, and immunohistochemical analysis. And the results showed that administration of L. acidophilus suppressed Th17 cell-mediated secretion of proinflammatory cytokine IL-17 through downregulation of IL-23 and TGF 1 expression and downstream phosphorylation of p-STAT3

On the Quantum Approximation of Normalized Schatten Norms

The similarity of quantum states has long been studied and some good measures such as Fidelity were developed. In this paper, we aim to come up with a similarity measure for quantum operations based on a metric called normalized Schatten 2-norm. Given two quantum operations in circuit forms, we show a quantum sampling circuit that estimates their normalized Schatten 2-norm using one clean qubit and one classical random variable. We prove a $Poly(1/\epsilon)$ upper bound on the sample complexity which is independent of the size of the quantum system. We then extend this sampling method to mixed quantum operations, i.e. a linear combination of unitary quantum operations. In addition, we build a connection between the normalized Schatten 2-norm and the similarity measure of two quantum operations. Inspired by the connection, we then develop an algorithm for quantum circuit learning

PhD

dissertationThe mast cell is one of die major cellular mediators in allergic responses. There are two different types of tissue mast cells in the mouse, the mucosal mast cell and the connective tissue mast cell. With an in vitro culturing system, murine bone marrow mast cells were analyzed for the expression of cytokines, transcription factors, and novel genes. IL-3 derived mast cells (MMC) preferentially express IL-4, IL-10, and EL-13, whereas c-kit ligand derived mast cells (CTMC) do not express these transcripts on a constitutive basis. However, when CTMC were either treated with IL-3 or stimulated by IgE-mediated crosslinking, they were able to upregulate the transcription of these genes. Furthermore, IL-10 protein was shown stored in mast cell granules in preformed state. A lymphoid lineage specific transcription factor, Ikaros, was shown to be constitutively expressed by cultured mast cells. Unlike the T cells which express up to six different forms of Ikaros protein, mast cells only express the protein for form V and VI. However, nuclear extracts from these cells failed to show DNA binding activity when incubated with a DNA binding site from CD3 delta promoter. One the other hand, when increasing mast cell extracts were added to suboptimal amount of T cell nuclear extracts, a DNA binding activity was evident, suggesting that other T cell factors may be required for the complex formation. A differential screening experiment based on rapid PCR amplification was set up to identify genes that are differentially expressed during mast cell differentiation. One gene, Pactolus, was found to be preferentially expressed by CTMC. Two forms of transcripts have been identified, which are generated through alternative splicing. The Pactolus gene is highly homologous to murine P2 integrin subunit. The two isoforms predict two different proteins, with the shorter one encoding a soluble protein and the longer one encoding a transmembrane protein. Polyclonal antisera against a peptide in the cytoplasmic tail of the full length Pactolus protein, but not the preimmune serum, recognized a prominent protein band about 95kD. This band was not present in the spleen despite prolonged exposure. Interestingly, no associating protein could be identified through co-immunoprecipitation, raising the possibility that Pactolus may function alone instead of forming heteroduplex with other adhesion molecules

Preparation and Characterization of a Type of Green Vacuum Insulation Panel Prepared with Straw Core Material

The Vacuum Insulation Panel (VIP), regarded as the most promising high-performance thermal insulation material, still has application limitations because of its high cost. In this paper, VIPs using natural straw as the core material are prepared. The fiber saturation point (FSP) is important in order to determine the optimum for the use of renewable straw materials as a potential VIP core. The microstructure of straw core material, together with the relationship between the moisture content, the diametral compression strength, and the thermal conductivity of as-prepared straw VIPs are investigated. Compression characteristics of straw core material and heat insulation mechanism within the straw VIP envelope enclosure are analyzed. Total thermal conductivity of a straw VIP is sensitive to both the inner pressure and the moisture content of straw core material. The optimum drying process for straw VIPs is heating the straw core material at a temperature of 120 ℃ for 60 min, with its center-of-panel value being about 3.8 mW/(m&middot;K)

Pitting Corrosion Resistance on Annealing Treated Super Duplex Stainless Steel S32750

The pitting corrosion resistance of S32750 super duplex stainless steel, annealing treated at temperatures of 950–1200 °C for 20–60 min, was investigated using potentiodynamic polarization tests. The results show that the volume fractions of ferrite in the S32750 duplex stainless steel increased from 48.9% to 68.4% as annealing temperatures increased from 950 to 1200 °C. The pitting potential of the sample increased first and then decreased from an annealing temperature of 950 to 1050 °C, and the highest pitting potential was observed after annealing at 1050 °C for 35 min. The pitting corrosion resistance of S32750 stainless steel is due to the combination of pitting resistance equivalent number (PREN) value, phase fraction and grain boundary area fraction, and the imbalance of corrosion potential

Lactobacillus acidophilus Suppresses Colitis-Associated Activation of the IL-23/Th17 Axis

The aim of this paper is to determine the modulatory effects of Lactobacillus acidophilus on the IL-23/Th17 immune axis in experimental colitis. DSS-induced mouse models of UC were to be saline, hormones, and different concentrations of Lactobacillus acidophilus intervention. The expression of interleukin- (IL-) 17, tumor necrosis factor α (TNFα), IL-23, transforming growth factor β1 (TGFβ1), signal transducer and activator of transcription 3 (STAT3), and phosphorylated (p)-STAT3 was examined by RT-PCR, Western blotting, and immunohistochemical analysis. And the results showed that administration of L. acidophilus suppressed Th17 cell-mediated secretion of proinflammatory cytokine IL-17 through downregulation of IL-23 and TGFβ1 expression and downstream phosphorylation of p-STAT3