BCS thermal vacuum of fermionic superfluids and its perturbation theory

The thermal field theory is applied to fermionic superfluids by doubling the degrees of freedom of the BCS theory. We construct the two-mode states and the corresponding Bogoliubov transformation to obtain the BCS thermal vacuum. The expectation values with respect to the BCS thermal vacuum produce the statistical average of the thermodynamic quantities. The BCS thermal vacuum allows a quantum-mechanical perturbation theory with the BCS theory serving as the unperturbed state. We evaluate the leading-order corrections to the order parameter and other physical quantities from the perturbation theory. A direct evaluation of the pairing correlation as a function of temperature shows the pseudogap phenomenon results from the perturbation theory. The BCS thermal vacuum is shown to be a generalized coherent and squeezed state. The correspondence between the thermal vacuum and purification of the density matrix allows a unitary transformation, and we found the geometric phase in the parameter space associated with the transformation.Comment: 14 pages, 2 figure

Engineering Dynamical Sweet Spots to Protect Qubits from 1/ff Noise

Protecting superconducting qubits from low-frequency noise is essential for advancing superconducting quantum computation. Based on the application of a periodic drive field, we develop a protocol for engineering dynamical sweet spots which reduce the susceptibility of a qubit to low-frequency noise. Using the framework of Floquet theory, we prove rigorously that there are manifolds of dynamical sweet spots marked by extrema in the quasi-energy differences of the driven qubit. In particular, for the example of fluxonium biased slightly away from half a flux quantum, we predict an enhancement of pure-dephasing by three orders of magnitude. Employing the Floquet eigenstates as the computational basis, we show that high-fidelity single- and two-qubit gates can be implemented while maintaining dynamical sweet-spot operation. We further confirm that qubit readout can be performed by adiabatically mapping the Floquet states back to the static qubit states, and subsequently applying standard measurement techniques. Our work provides an intuitive tool to encode quantum information in robust, time-dependent states, and may be extended to alternative architectures for quantum information processing

The Prognostic Significance of Apoptosis-Related Biological Markers in Chinese Gastric Cancer Patients

BACKGROUND AND OBJECTIVE: The prognosis varied among the patients with the same stage, therefore there was a need for new prognostic and predictive factors. The aim of this study was to evaluate the relationship of apoptosis-related biological markers such as p53, bcl-2, bax, and c-myc, and clinicopathological features and their prognostic value. METHODS: From 1996 to 2007, 4426 patients had undergone curative D2 gastrectomy for gastric cancer at Fudan University Shanghai Cancer Center. Among 501 patients, the expression levels of p53, bcl-2, bax, and c-myc were examined by immunohistochemistry. The prognostic value of biological markers and the correlation between biological markers and other clinicopathological factors were investigated. RESULTS: There were 339 males and 162 females with a mean age of 57. The percentages of positive expression of p53, bcl-2, bax, and c-myc were 65%, 22%, 43%, and 58%, respectively. There was a strong correlation between p53, bax, and c-myc expression (P=0.00). There was significant association between bcl-2, and bax expression (P<0.05). p53 expression correlated with histological grade (P=0.01); bcl-2 expression with pathological stage (P=0.00); bax expression with male (P=0.02), histological grade (P=0.01), Borrmann type (P=0.01), tumor location (P=0.00), lymph node metastasis (P=0.03), and pathological stage (P=0.03); c-myc expression with Borrmann type (P=0.00). bcl-2 expression was related with good survival in univariate analysis (P=0.01). Multivariate analysis showed that bcl-2 expression and pathological stage were defined as independent prognostic factors. There were significant differences of overall 5-year survival rates according to bcl-2 expression or not in stage IIB (P=0.03). CONCLUSION: The expression of bcl-2 was an independent prognostic factor for patients with gastric cancer; it might be a candidate for the gastric cancer staging system

Floquet-engineered enhancement of coherence times in a driven fluxonium qubit

We use the quasienergy structure that emerges when a fluxonium superconducting circuit is driven periodically to encode quantum information with dynamically induced flux-insensitive sweet spots. The framework of Floquet theory provides an intuitive description of these high-coherence working points located away from the half-flux symmetry point of the undriven qubit. This approach offers flexibility in choosing the flux bias point and the energy of the logical qubit states as shown in [\textit{Huang et al., 2020}]. We characterize the response of the system to noise in the modulation amplitude and DC flux bias, and experimentally demonstrate an optimal working point which is simultaneously insensitive against fluctuations in both. We observe a 40-fold enhancement of the qubit coherence times measured with Ramsey-type interferometry at the dynamical sweet spot compared with static operation at the same bias point.Comment: 12 pages, 7 figure

Fast ZZ-Free Entangling Gates for Superconducting Qubits Assisted by a Driven Resonator

Engineering high-fidelity two-qubit gates is an indispensable step toward practical quantum computing. For superconducting quantum platforms, one important setback is the stray interaction between qubits, which causes significant coherent errors. For transmon qubits, protocols for mitigating such errors usually involve fine-tuning the hardware parameters or introducing usually noisy flux-tunable couplers. In this work, we propose a simple scheme to cancel these stray interactions. The coupler used for such cancellation is a driven high-coherence resonator, where the amplitude and frequency of the drive serve as control knobs. Through the resonator-induced-phase (RIP) interaction, the static ZZ coupling can be entirely neutralized. We numerically show that such a scheme can enable short and high-fidelity entangling gates, including cross-resonance CNOT gates within 40 ns and adiabatic CZ gates within 140 ns. Our architecture is not only ZZ free but also contains no extra noisy components, such that it preserves the coherence times of fixed-frequency transmon qubits. With the state-of-the-art coherence times, the error of our cross-resonance CNOT gate can be reduced to below 1e-4