A formally certified end-to-end implementation of Shor's factorization algorithm.

Quantum computing technology may soon deliver revolutionary improvements in algorithmic performance, but it is useful only if computed answers are correct. While hardware-level decoherence errors have garnered significant attention, a less recognized obstacle to correctness is that of human programming errors-"bugs." Techniques familiar to most programmers from the classical domain for avoiding, discovering, and diagnosing bugs do not easily transfer, at scale, to the quantum domain because of its unique characteristics. To address this problem, we have been working to adapt formal methods to quantum programming. With such methods, a programmer writes a mathematical specification alongside the program and semiautomatically proves the program correct with respect to it. The proof's validity is automatically confirmed-certified-by a "proof assistant." Formal methods have successfully yielded high-assurance classical software artifacts, and the underlying technology has produced certified proofs of major mathematical theorems. As a demonstration of the feasibility of applying formal methods to quantum programming, we present a formally certified end-to-end implementation of Shor's prime factorization algorithm, developed as part of a framework for applying the certified approach to general applications. By leveraging our framework, one can significantly reduce the effects of human errors and obtain a high-assurance implementation of large-scale quantum applications in a principled way.

Tunable optical differential operation based on graphene at a telecommunication wavelength.

Optical differential operation based on the photonic spin Hall effect(SHE) has attracted extensive attention in image processing of edge detection, which has advantages of high speed, parallelism, and low power consumption. Here, we theoretically demonstrate tunable optical differential operation in a four-layered nanostructure of prism-graphene-air gap-substrate. It is shown that the spatial differentiation arises inherently from the photonic SHE. Furthermore, we find that the transverse spin-Hall shift induced by the photonic SHE changes dramatically near the Brewster angle with the incident angle increases at a telecommunication wavelength. Meanwhile, the Fermi energy of graphene and the thickness of the air gap can affect the transverse spin shift. Interestingly, we can easily adjust the Fermi energy of graphene in real time through external electrostatic field biasing, enabling fast edge imaging switching at a telecommunication wavelength. This may provide a potential way for future tunable spin-photonic devices, and open up more possible applications for artificial intelligence, such as target recognition, biomedical imaging, and edge detection.

Optical bistability modulation based on graphene sandwich structure with topological interface modes.

In this paper, we have investigated optical bistability modulation of transmitted beam that can be achieved by graphene sandwich structure with topological interface modes at terahertz frequency. Graphene with strong nonlinear optical effect was combined with sandwich photonic crystal to form a new sandwich structure with topological interface modes. The light-limiting properties of the topological interface modes, as well as its high unidirectionality and high transmission efficiency, all contribute positively to the reduction of the optical bistability threshold. In addition, the topological interface modes can effectively ensure the stability of the two steady state switching in the case of external interference. Moreover, optical bistability is closely related to the incident angle, the Fermi energy, the relaxation time, and the number of layers of graphene. Through parameter optimization, optical bistability with threshold of 105 V/m can be obtained, which has reached or is close to the range of the weak field.

Optical bistability in a heterodimer composed of a quantum dot and a metallic nanoshell.

We theoretically explore the conditions for generating optical bistability (OB) in a heterodimer comprised of a semiconductor quantum dot (SQD) and a metallic nanoshell (MNS). The MNS is made of a metallic nanosphere as a core and a dielectric material as a shell. For the specific hybrid system considered, the bistable effect appears only if the frequency of the pump field is equal to (or slightly less than) the exciton frequency for a proper shell thickness. Bistability phase diagrams, when plotted, show that the dipole-induced bistable region can be greatly broadened by changing the shell thickness of the MNS in a strong exciton-plasmon coupling regime. In particular, we demonstrate that the multipole polarization not only narrows the bistable zone but also enlarges the corresponding thresholds for a given intermediate scaled pumping intensity. On the other hand, when the SQD couples strongly with the MNS, the multipole polarization can also significantly broaden the bistable region and induce a great suppression of the FWM (four-wave mixing) signal for a fixed shell thickness. These interesting findings offer a fresh understanding of the bistability conditions in an SQD/MNS heterodimer, and may be useful in the fabrication of high-performance and low-threshold optical bistable nanodevices.

Nonlinear optical bistability based on epsilon-near-zero mode in near-infrared band.

We propose a simple thin-layer structure based on epsilon-near-zero mode field enhancement to achieve optical bistability in the near-infrared band. The high transmittance provided by the thin-layer structure and the electric field energy limited in the ultra-thin epsilon-near-zero material means that the interaction between the input light and the epsilon-near-zero material can be greatly enhanced, creating favorable conditions for the realization of optical bistability in near-infrared band. The optical bistability hysteresis curve is closely related to the incident angle of light and the thickness of epsilon-near-zero material. This structure is relatively simple and easy to prepare, so we believe that this scheme will have a positive effect on the practicality of optical bistability devices in all-optical devices and networks.

Optical bistability modulation based on the photonic crystal Fabry-Perot cavity with graphene.

We investigate the low-threshold optical bistability of transmitted beams at the terahertz range based on the photonic crystal Fabry-Perot cavity with graphene. Graphene with strong nonlinear conductivity is placed in the middle of the Fabry-Perot cavity and the resonance of the cavity plays a positive role in promoting the low-threshold optical bistability. The optical bistability curve is closely related to the incident angle of light, the parameters of graphene, and the structural parameters of the Fabry-Perot cavity. Through parameter optimization, optical bistability with threshold of 105 V/m can be obtained, which has reached or is close to the range of the weak field.

Enhancement and manipulation of group delay based on topological edge state in one-dimensional photonic crystal with graphene.

In this paper, the reflected and transmitted group delay from a one-dimensional photonic crystal heterostructure with graphene at communication band are investigated theoretically. It is shown that the negative reflected group delay of the beam in this structure can be significantly enhanced and can be switched to positive. The large reflected group delay originates from the sharp phase change caused by the excitation of topological edge state at the interface between the two one-dimensional photonic crystals. Besides, the introduction of graphene provides an effective approach for the dynamic control of the group delay. It is clear that the positive and negative group delay can be actively manipulated through the Fermi energy and the relaxation time of the graphene. In addition, we also investigate the transmitted group delay of the structure, which is much less than the reflected one. The enhanced and tunable delay scheme is promising for fabricating optical delay devices like optical buffer, all-optical delays and other applications at optical communication band.

Experimental Realization of Device-Independent Quantum Randomness Expansion.

Randomness expansion where one generates a longer sequence of random numbers from a short one is viable in quantum mechanics but not allowed classically. Device-independent quantum randomness expansion provides a randomness resource of the highest security level. Here, we report the first experimental realization of device-independent quantum randomness expansion secure against quantum side information established through quantum probability estimation. We generate 5.47×10^{8} quantum-proof random bits while consuming 4.39×10^{8} bits of entropy, expanding our store of randomness by 1.08×10^{8} bits at a latency of about 13.1 h, with a total soundness error 4.6×10^{-10}. Device-independent quantum randomness expansion not only enriches our understanding of randomness but also sets a solid base to bring quantum-certifiable random bits into realistic applications.

Characterization of two kcnk3 genes in Nile tilapia (Oreochromis niloticus): Molecular cloning, tissue distribution, and transcriptional changes in various salinity of seawater.

As one important member of the two-pore-domain potassium channel (K2P) family, potassium channel subfamily K member 3 (KCNK3) has been reported for thermogenesis regulation, energy homeostasis, membrane potential conduction, and pulmonary hypertension in mammals. However, its roles in fishes are far less examined and published. In the present study, we identified two kcnk3 genes (kcnk3a and kcnk3b) in an euryhaline fish, Nile tilapia (Oreochromis niloticus), by molecular cloning, genomic survey and laboratory experiments to investigate their potential roles for osmoregulation. We obtained full-length coding sequences of the kcnk3a and kcnk3b genes (1209 and 1173 bp), which encode 402 and 390 amino acids, respectively. Subsequent multiple sequence alignments, putative 3D-structure model prediction, genomic survey and phylogenetic analysis confirmed that two kcnk3 paralogs are widely presented in fish genomes. Interestingly, a DNA fragment inversion of a kcnk3a cluster was found in Cypriniforme in comparison with other fishes. Quantitative real-time PCRs demonstrated that both the tilapia kcnk3 genes were detected in all the examined tissues with a similar distribution pattern, and the highest transcriptions were observed in the heart. Meanwhile, both kcnk3 genes in the gill were proved to have a similar transcriptional change pattern in response to various salinity of seawater, implying that they might be involved in osmoregulation. Furthermore, three predicted transcription factors (arid3a, arid3b, and arid5a) of both kcnk3 genes also showed a similar pattern as their target genes in response to the various salinity, suggesting their potential positive regulatory roles. In summary, we for the first time characterized the two kcnk3 genes in Nile tilapia, and demonstrated their potential involvement in osmoregulation for this economically important fish.

Graphene-based low-threshold and tunable optical bistability in one-dimensional photonic crystal Fano resonance heterostructure at optical communication band.

In this paper, the one-dimensional photonic crystal Fano resonance heterostructure is used to achieve low-threshold and tunable graphene-based optical bistability of the transmitted and reflected light beam at optical communication band. The low-threshold of optical bistability (OB) originates from the local field enhancement owing to the Fano resonance excited by topological edge states mode and Fabry-Perot cavity mode. The study found that it is feasible to continuously adjust the hysteresis behavior and optical bistable thresholds by altering the Fermi energy of the left and right graphene respectively. Furthermore, the OB can also be controlled by changing the number of graphene layers or the angle of incident beam, which makes this structure a feasible object of experimental research at optical communication band in the future.

Molecular cloning of two kcnk3 genes from the Northern snakehead (Channa argus) for quantification of their transcriptions in response to fasting and refeeding.

Potassium channel subfamily K member 3 (KCNK3) has been reported to play important roles in membrane potential conduction, pulmonary hypertension and thermogenesis regulation in mammals. However, its roles remain largely unknown and scarce reports were seen in fish. In the present study, we for the first time identified two kcnk3 genes (kcnk3a and kcnk3b) from the carnivorous Northern snakehead (Channa argus) by molecular cloning and a genomic survey. Subsequently, their transcription changes in response to different feeding status were investigated. Full-length coding sequences of the kcnk3a and kcnk3b genes are 1203 and 1176 bp, encoding 400 and 391 amino acids, respectively. Multiple alignments, 3D-structure prediction and phylogenetic analysis further suggested that these kcnk3 genes may be highly conserved in vertebrates. Tissue distribution analysis by real-time PCR demonstrated that both the snakehead kcnk3s were widely transcribed in majority of the examined tissues but with different distribution patterns. In a short-term (24-h) fasting experiment, we observed that brain kcnk3a and kcnk3b genes showed totally opposite transcription patterns. In a long-term (2-week) fasting and refeeding experiment, we also observed differential change patterns for the brain kcnk3 genes. In summary, our findings suggest that the two kcnk3 genes are close while present different transcription responses to fasting and refeeding. They therefore can be potentially selected as novel target genes for improvement of production and quality of this economically important fish.

Four-wave mixing signal enhancement and optical bistability of a hybrid metal nanoparticle-quantum dot molecule in a nanomechanical resonator.

We investigate theoretically four-wave mixing (FWM) response and optical bistability (OB) in a hybrid nanosystem composed of a metal nanoparticle (MNP) and a semiconductor quantum dot (SQD) coupled to a nanomechanical resonator (NR). It is shown that the FWM signal is enhanced by more than three orders of magnitude as compared to that of the system without exciton-phonon interaction, and the FWM signal can also be suppressed significantly and broadened due to the exciton-plasmon interaction. As the MNP couples strongly with the SQD, the bistable FWM response can be achieved by adjusting the SQD-MNP distance and the pumping intensity. For a given pumping constant and a fixed SQD-MNP distance, the enhanced exciton-phonon interaction can promote the occurrence of bistability. Our findings not only present a feasible way to detect the spacing between two nanoparticles, but also hold promise for developing quantum switches and nanoscale rulers.

VCP maintains nuclear size by regulating the DNA damage-associated MDC1-p53-autophagy axis in Drosophila.

The maintenance of constant karyoplasmic ratios suggests that nuclear size has physiological significance. Nuclear size anomalies have been linked to malignant transformation, although the mechanism remains unclear. By expressing dominant-negative TER94 mutants in Drosophila photoreceptors, here we show disruption of VCP (valosin-containing protein, human TER94 ortholog), a ubiquitin-dependent segregase, causes progressive nuclear size increase. Loss of VCP function leads to accumulations of MDC1 (mediator of DNA damage checkpoint protein 1), connecting DNA damage or associated responses to enlarged nuclei. TER94 can interact with MDC1 and decreases MDC1 levels, suggesting that MDC1 is a VCP substrate. Our evidence indicates that MDC1 accumulation stabilizes p53A, leading to TER94K2A-associated nuclear size increase. Together with a previous report that p53A disrupts autophagic flux, we propose that the stabilization of p53A in TER94K2A-expressing cells likely hinders the removal of nuclear content, resulting in aberrant nuclear size increase.