Beating the break-even point with a discrete-variable-encoded logical qubit.

Quantum error correction (QEC) aims to protect logical qubits from noises by using the redundancy of a large Hilbert space, which allows errors to be detected and corrected in real time1. In most QEC codes2-8, a logical qubit is encoded in some discrete variables, for example photon numbers, so that the encoded quantum information can be unambiguously extracted after processing. Over the past decade, repetitive QEC has been demonstrated with various discrete-variable-encoded scenarios9-17. However, extending the lifetimes of thus-encoded logical qubits beyond the best available physical qubit still remains elusive, which represents a break-even point for judging the practical usefulness of QEC. Here we demonstrate a QEC procedure in a circuit quantum electrodynamics architecture18, where the logical qubit is binomially encoded in photon-number states of a microwave cavity8, dispersively coupled to an auxiliary superconducting qubit. By applying a pulse featuring a tailored frequency comb to the auxiliary qubit, we can repetitively extract the error syndrome with high fidelity and perform error correction with feedback control accordingly, thereby exceeding the break-even point by about 16% lifetime enhancement. Our work illustrates the potential of hardware-efficient discrete-variable encodings for fault-tolerant quantum computation19.

Effective protocol for generating NOON states of resonator modes.

We propose a protocol for the generation of NOON states of resonator modes. The physical model is composed of two Kerr-nonlinear resonators and a four-level qudit. Using the off-resonant couplings between the resonators and the qudit, qudit-level-dependent frequency shifts on the two resonators are induced. The frequency shifts allow us to drive different resonators to the N-photon state when the qudit is in different intermediate levels. Consequently, the generation of NOON states with arbitrary photon number N can be completed in only three steps, i.e., driving the qudit to a superposition state of the two intermediate levels, driving one of the resonators to its N-photon state, and driving the qudit back to its ground level. Numerical simulations show that, in the regime of strong Kerr nonlinearity and coupling strengths, the protocol can produce the NOON state with high fidelity in the cases of different photon numbers. In addition, it is possible for the protocol to produce acceptable fidelity in the presence of systematic errors and decoherence factors. Therefore, the protocol may provide some useful perspectives for effective generation of photonic NOON states.

Quantum metric and metrology with parametrically-driven Tavis-Cummings models.

We study the quantum metric in a driven Tavis-Cummings model, comprised of multiple qubits interacting with a quantized photonic field. The parametrical driving of the photonic field breaks the system's U(1) symmetry down to a Z2 symmetry, whose spontaneous breaking initiates a superradiant phase transition. We analytically solved the eigenenergies and eigenstates, and numerically simulated the system behaviors near the critical point. The critical behaviors near the superradiant phase transition are characterized by the quantum metric, defined in terms of the response of the quantum state to variation of the control parameter. In addition, a quantum metrological protocol based on the critical behaviors of the quantum metric near the superradiant phase transition is proposed, which enables greatly the achievable measurement precision.

Exceptional Entanglement Phenomena: Non-Hermiticity Meeting Nonclassicality.

Non-Hermitian (NH) extension of quantum-mechanical Hamiltonians represents one of the most significant advancements in physics. During the past two decades, numerous captivating NH phenomena have been revealed and demonstrated, but all of which can appear in both quantum and classical systems. This leads to the fundamental question: what NH signature presents a radical departure from classical physics? The solution of this problem is indispensable for exploring genuine NH quantum mechanics, but remains experimentally untouched so far. Here, we resolve this basic issue by unveiling distinct exceptional entanglement phenomena, exemplified by an entanglement transition, occurring at the exceptional point of NH interacting quantum systems. We illustrate and demonstrate such purely quantum-mechanical NH effects with a naturally dissipative light-matter system, engineered in a circuit quantum electrodynamics architecture. Our results lay the foundation for studies of genuinely quantum-mechanical NH physics, signified by exceptional-point-enabled entanglement behaviors.

Observation of a Superradiant Phase Transition with Emergent Cat States.

Superradiant phase transitions (SPTs) are important for understanding light-matter interactions at the quantum level, and play a central role in criticality-enhanced quantum sensing. So far, SPTs have been observed in driven-dissipative systems, but the emergent light fields did not show any nonclassical characteristic due to the presence of strong dissipation. Here we report an experimental demonstration of the SPT featuring the emergence of a highly nonclassical photonic field, realized with a resonator coupled to a superconducting qubit, implementing the quantum Rabi model. We fully characterize the light-matter state by Wigner matrix tomography. The measured matrix elements exhibit quantum interference intrinsic of a photonic mesoscopic superposition, and reveal light-matter entanglement.

Manipulating Complex Hybrid Entanglement and Testing Multipartite Bell Inequalities in a Superconducting Circuit.

Quantum correlations in observables of multiple systems not only are of fundamental interest, but also play a key role in quantum information processing. As a signature of these correlations, the violation of Bell inequalities has not been demonstrated with multipartite hybrid entanglement involving both continuous and discrete variables. Here we create a five-partite entangled state with three superconducting transmon qubits and two photonic qubits, each encoded in the mesoscopic field of a microwave cavity. We reveal the quantum correlations among these distinct elements by joint Wigner tomography of the two cavity fields conditional on the detection of the qubits and by test of a five-partite Bell inequality. The measured Bell signal is 8.381±0.038, surpassing the bound of 8 for a four-partite entanglement imposed by quantum correlations by 10 standard deviations, demonstrating the genuine five-partite entanglement in a hybrid quantum system.

Demonstration of Controlled-Phase Gates between Two Error-Correctable Photonic Qubits.

To realize fault-tolerant quantum computing, it is necessary to store quantum information in logical qubits with error correction functions, realized by distributing a logical state among multiple physical qubits or by encoding it in the Hilbert space of a high-dimensional system. Quantum gate operations between these error-correctable logical qubits, which are essential for implementation of any practical quantum computational task, have not been experimentally demonstrated yet. Here we demonstrate a geometric method for realizing controlled-phase gates between two logical qubits encoded in photonic fields stored in cavities. The gates are realized by dispersively coupling an ancillary superconducting qubit to these cavities and driving it to make a cyclic evolution depending on the joint photonic state of the cavities, which produces a conditional geometric phase. We first realize phase gates for photonic qubits with the logical basis states encoded in two quasiorthogonal coherent states, which have important implications for continuous-variable-based quantum computation. Then we use this geometric method to implement a controlled-phase gate between two binomially encoded logical qubits, which have an error-correctable function.

Deterministic Entanglement Swapping in a Superconducting Circuit.

Entanglement swapping, the process to entangle two particles without coupling them in any way, is one of the most striking manifestations of the quantum-mechanical nonlocal characteristic. Besides fundamental interest, this process has applications in complex entanglement manipulation and quantum communication. Here we report a high-fidelity, unconditional entanglement swapping experiment in a superconducting circuit. The measured concurrence characterizing the qubit-qubit entanglement produced by swapping is above 0.75, confirming most of the entanglement of one qubit with its partner is deterministically transferred to another qubit that has never interacted with it. We further realize delayed-choice entanglement swapping, showing whether two qubits previously behaved as in an entangled state or as in a separable state is determined by a later choice of the type of measurement on their partners. This is the first demonstration of entanglement-separability duality in a deterministic way.

The RopGEF2-ROP7/ROP2 Pathway Activated by phyB Suppresses Red Light-Induced Stomatal Opening.

Circadian rhythm of stomatal aperture is mainly regulated by light/darkness. Blue and red light induce stomatal opening through different mechanisms that are mediated by special receptors. ROP2, a member of Rho GTPase family in Arabidopsis (Arabidopsisthaliana), has been found to negatively regulate light-induced stomatal opening. However, the upstream guanine nucleotide exchange factor (GEF) RopGEFs have not been revealed, and it is unclear which photoreceptor is required for the action of RopGEFs-ROPs. Here, we showed that RopGEF2 acted as a negative regulator in phytochrome B (phyB)-mediated red light-induced stomatal opening. Meanwhile, ROP7, another member of ROP family, acting redundantly with ROP2, was regulated by RopGEF2 in this process. RopGEF2 interacted with ROP7 and ROP2 and enhanced their intrinsic nucleotide exchange rates. Furthermore, the direct interactions between phyB and RopGEF2 were detected in vitro and in plants, and phyB enhanced the GEF activity of RopGEF2 toward both ROP7 and ROP2 under light. In addition, RopGEF4 functioned redundantly with RopGEF2 in red light-induced stomatal opening by activating both ROP7 and ROP2, and RopGEF2/RopGEF4 acted genetically downstream of phyB; however, the GEF activity of RopGEF4 was not directly enhanced by phyB. These results revealed that red light-activated phyB enhances the GEF activities of RopGEF2 and RopGEF4 directly or indirectly, and then activate both ROP7 and ROP2 in guard cells. The negative mechanism triggered by phyB prevents the excessive stomatal opening under red light.

Holonomic Quantum Control with Continuous Variable Systems.

Universal computation of a quantum system consisting of superpositions of well-separated coherent states of multiple harmonic oscillators can be achieved by three families of adiabatic holonomic gates. The first gate consists of moving a coherent state around a closed path in phase space, resulting in a relative Berry phase between that state and the other states. The second gate consists of "colliding" two coherent states of the same oscillator, resulting in coherent population transfer between them. The third gate is an effective controlled-phase gate on coherent states of two different oscillators. Such gates should be realizable via reservoir engineering of systems that support tunable nonlinearities, such as trapped ions and circuit QED.

Preparation of two-qubit steady entanglement through driving a single qubit.

Inspired by a recent paper [J. Phys. B 47, 055502 (2014)], we propose a simplified scheme to generate and stabilize a Bell state of two qubits coupled to a resonator. In the scheme only one qubit is needed to be driven by external classical fields, and the entanglement dynamics is independent of the phases of these fields and insensitive to their amplitude fluctuations. This is a distinct advantage as compared with the previous ones that require each qubit to be addressed by well-controlled classical fields. Numerical simulation shows that the steady singlet state with high fidelity can be obtained with currently available techniques in circuit quantum electrodynamics.

Calcium participates in feedback regulation of the oscillating ROP1 Rho GTPase in pollen tubes.

Biological oscillation occurs at various levels, from cellular signaling to organismal behaviors. Mathematical modeling has allowed a quantitative understanding of slow oscillators requiring changes in gene expression (e.g., circadian rhythms), but few theoretical studies have focused on the rapid oscillation of cellular signaling. The tobacco pollen tube, which exhibits growth bursts every 80 s or so, is an excellent system for investigating signaling oscillation. Pollen tube growth is controlled by a tip-localized ROP1 GTPase, whose activity oscillates in a phase about 90 degrees ahead of growth. We constructed a mathematical model of ROP1 activity oscillation consisting of interlinking positive and negative feedback loops involving F-actin and calcium, ROP1-signaling targets that oscillate in a phase about 20 degrees and 110 degrees behind ROP1 activity, respectively. The model simulates the observed changes in ROP1 activity caused by F-actin disruption and predicts a role for calcium in the negative feedback regulation of the ROP1 activity. Our experimental data strongly support this role of calcium in tip growth. Thus, our findings provide insight into the mechanism of pollen tube growth and the oscillation of cellular signaling.

Entanglement transfer from two-mode continuous variable SU(2) cat states to discrete qubits systems in Jaynes-Cummings Dimers.

We study the entanglement transfer from a two-mode continuous variable system (initially in the two-mode SU(2) cat states) to a couple of discrete two-state systems (initially in an arbitrary mixed state), by use of the resonant Jaynes-Cummings (JC) interaction. We first quantitatively connect the entanglement transfer to non-Gaussianity of the two-mode SU(2) cat states and find a positive correlation between them. We then investigate the behaviors of the entanglement transfer and find that it is dependent on the initial state of the discrete systems. We also find that the largest possible value of the transferred entanglement exhibits a variety of behaviors for different photon number as well as for the phase angle of the two-mode SU(2) cat states. We finally consider the influences of the noise on the transferred entanglement.

Is ABP1 an auxin receptor yet?

AUXIN BINDING PROTEIN 1 (ABP1) has long been proposed as an auxin receptor to regulate cell expansion. The embryo lethality of ABP1-null mutants demonstrates its fundamental role in plant development, but also hinders investigation of its involvement in post-embryonic processes and its mode of action. By taking advantage of weak alleles and inducible systems, several recent studies have revealed a role for ABP1 in organ development, cell polarization, and shape formation. In addition to its role in the regulation of auxin-induced gene expression, ABP1 has now been shown to modulate non-transcriptional auxin responses. ABP1 is required for activating two antagonizing ROP GTPase signaling pathways involved in cytoskeletal reorganization and cell shape formation, and participates in the regulation of clathrin-mediated endocytosis to subsequently affect PIN protein distribution. These exciting discoveries provide indisputable evidence for the auxin-induced signaling pathways that are downstream of ABP1 function, and suggest intriguing mechanisms for ABP1-mediated polar cell expansion and spatial coordination in response to auxin.

RIP1 (ROP Interactive Partner 1)/ICR1 marks pollen germination sites and may act in the ROP1 pathway in the control of polarized pollen growth.

Rho family small GTPases are universal signaling switches in the control of cell polarity in eukaryotic cells. Their polar distribution to the cell cortex is critical for the execution of their functions, yet the mechanism for this distribution is poorly understood. Using a yeast two-hybrid method, we identified RIP1 (ROP interactive partner 1), which belongs to a family of five members of novel proteins that share a C-terminal region that interacts with ROP. When expressed in Arabidopsis pollen, green fluorescence protein GFP-tagged RIP1 was localized to the nucleus of mature pollen. When pollen grains were hydrated in germination medium, GFP-RIP1 switched from the nucleus to the cell cortex at the future pollen germination site and was maintained in the apical cortex of germinating pollen and growing pollen tubes. RIP1 was found to interact with ROP1 in pollen tubes, and the cortical RIP1 localization was influenced by the activity of ROP1. Overexpression of RIP1 induced growth depolarization in pollen tubes, a phenotype similar to that induced by ROP1 overexpression. Interestingly, RIP1 overexpression enhanced GFP-ROP1 recruitment to the plasma membrane (PM) of pollen tubes. Based on these observations, we hypothesize that RIP1 is involved in the positive feedback regulation of ROP1 localization to the PM, leading to the establishment of a polar site for pollen germination and pollen tube growth.