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.

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.

Nonreciprocal light transmission via optomechanical parametric interactions

Nonreciprocal transmission of optical or microwave signals is indispensable in various applications involving sensitive measurements. In this paper, we study optomechanically induced directional amplification and isolation in a generic setup including two cavities and two mechanical oscillators by exclusively using blue-sideband drive tones. The input and output ports defined by the two cavity modes are coupled through coherent and dissipative paths mediated by the two mechanical resonators, respectively. By choosing appropriate transfer phases and strengths of the driving fields, either a directional amplifier or an isolator can be implemented at low thermal temperature, and both of them show bi-directional nonreciprocity working at two mirrored frequencies. The nonreciprocal device can potentially be demonstrated by opto- and electromechanical setups in both optical and microwave domains.

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.

Improving macroscopic entanglement with nonlocal mechanical squeezing

We report an efficient mechanism to generate mechanical entanglement in a two-cascaded cavity optomechanical system with optical parametric amplifiers (OPAs) inside the two coupled cavities. We use the especially tuned OPAs to squeeze the hybrid mode composed of two mechanical modes, leading to strong macroscopic entanglement between the two movable mirrors. The squeezing parameter as well as the effective mechanical damping are both modulated by the OPA gains. The optimal degree of mechanical entanglement therefore depends on the balanced process between coherent hybrid mode squeezing and dissipation engineering. The mechanical entanglement is robust to strong cavity decay, going beyond simply resolved sideband regime, and is resistant to reasonable high thermal noise. The scheme provides an alternative way for generating strong macroscopic entanglement in cascaded optomechanical systems.

Nearly maximal violation of the Mermin-Klyshko inequality with multimode entangled coherent states

Entangled coherent states for multiple bosonic modes, also referred to as multimode cat states, not only are of fundamental interest but also have practical applications. The nonclassical correlation among these modes is well characterized by the violation of the Mermin-Klyshko inequality. We here study Mermin-Klyshko inequality violations for such multi-mode entangled states with rotated quantum-number parity operators. It is shown that the Mermin-Klyshko signal obtained with these operators can approach the maximal value even when the average quantum number in each mode is only 1, and the inequality violation exponentially increases with the number of entangled modes. This is in distinct contrast with the framework based on displaced parity operators, with which a nearly maximal Mermin-Klyshko inequality violation requires the size of the cat state to be increased by about 15 times.

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.

Quantum nonlocality for entanglement of quasiclassical states

Entanglement of quasiclassical (coherent) states of two harmonic oscillators leads to striking quantum effects and is useful for quantum technologies. These effects and applications are closely related to nonlocal correlations inherent in these states, manifested by the violation of Bell inequalities. With previous frameworks, this violation is limited by the size of the system, which does not approach the maximum, even when the amount of entanglement approaches its maximum. Here, we propose a new version of Bell correlation operators, with which a nearly maximal violation can be obtained, as long as the associated entanglement approximates to the maximum. Consequently, the revealed nonlocality is significantly stronger than those with previous frameworks for a wide range of the system size. We present a new scheme for realizing the gate necessary for measurement of the nonlocal correlations. In addition to the use in test of quantum nonlocality, this gate is useful for quantum information processing with coherent states.

Dephasing-Insensitive Quantum Information Storage and Processing with Superconducting Qubits

A central task towards building a practical quantum computer is to protect individual qubits from decoherence while retaining the ability to perform high-fidelity entangling gates involving arbitrary two qubits. Here we propose and demonstrate a dephasing-insensitive procedure for storing and processing quantum information in an all-to-all connected superconducting circuit involving multiple frequency-tunable qubits, each of which can be controllably coupled to any other through a central bus resonator. Although it is generally believed that the extra frequency tunability enhances the control freedom but induces more dephasing impact for superconducting qubits, our results show that any individual qubit can be dynamically decoupled from dephasing noise by applying a weak continuous and resonant driving field whose phase is reversed in the middle of the pulse. More importantly, we demonstrate a new method for realizing a two-qubit phase gate with inherent dynamical decoupling via the combination of continuous driving and qubit-qubit swapping coupling. We find that the weak continuous driving fields not only enable the conditional dynamics essential for quantum information processing, but also protect both qubits from dephasing during the gate operation.

Demonstration of Topological Robustness of Anyonic Braiding Statistics with a Superconducting Quantum Circuit

Anyons are quasiparticles occurring in two dimensions, whose topological properties are believed to be robust against local perturbations and may hold promise for fault tolerant quantum computing. Here we present an experiment of demonstrating the path independent nature of anyonic braiding statistics with a superconducting quantum circuit, which represents a 7-qubit version of the toric code model. We dynamically create the ground state of the model, achieving a state fidelity of 0.688±0.015 as verified by quantum state tomography. Anyonic excitations and braiding operations are subsequently implemented with single-qubit rotations. The braiding robustness is witnessed by looping an anyonic excitation around another one along two distinct, but topologically equivalent paths: Both reveal the nontrivial π-phase shift, the hallmark of Abelian 1/2 anyons, with a phase accuracy of ∼99% in the Ramsey-type interference measurement.

10-Qubit Entanglement and Parallel Logic Operations with a Superconducting Circuit

Here we report on the production and tomography of genuinely entangled Greenberger-Horne-Zeilinger states with up to ten qubits connecting to a bus resonator in a superconducting circuit, where the resonator-mediated qubit-qubit interactions are used to controllably entangle multiple qubits and to operate on different pairs of qubits in parallel. The resulting 10-qubit density matrix is probed by quantum state tomography, with a fidelity of 0.668±0.025. Our results demonstrate the largest entanglement created so far in solid-state architectures and pave the way to large-scale quantum computation.

Continuous-variable geometric phase and its manipulation for quantum computation in a superconducting circuit

Geometric phase, associated with holonomy transformation in quantum state space, is an important quantum-mechanical effect. Besides fundamental interest, this effect has practical applications, among which geometric quantum computation is a paradigm, where quantum logic operations are realized through geometric phase manipulation that has some intrinsic noise-resilient advantages and may enable simplified implementation of multi-qubit gates compared to the dynamical approach. Here we report observation of a continuous-variable geometric phase and demonstrate a quantum gate protocol based on this phase in a superconducting circuit, where five qubits are controllably coupled to a resonator. Our geometric approach allows for one-step implementation of n-qubit controlled-phase gates, which represents a remarkable advantage compared to gate decomposition methods, where the number of required steps dramatically increases with n. Following this approach, we realize these gates with n up to 4, verifying the high efficiency of this geometric manipulation for quantum computation.

Geometric phase is of fundamental interest and has practical application in quantum computation. Here the authors observe continuous-variable geometric phase in a superconducting circuit and demonstrate a multi-qubit controlled phase gate protocol based on this geometric effect.

A twofold quantum delayed-choice experiment in a superconducting circuit

Wave-particle complementarity lies at the heart of quantum mechanics. To illustrate this mysterious feature, Wheeler proposed the delayed-choice experiment, where a quantum system manifests the wave- or particle-like attribute, depending on the experimental arrangement, which is made after the system has entered the interferometer. In recent quantum delayed-choice experiments, these two complementary behaviors were simultaneously observed with a quantum interferometer in a superposition of being closed and open. We suggest and implement a conceptually different quantum delayed-choice experiment by introducing a which-path detector (WPD) that can simultaneously record and neglect the system's path information, but where the interferometer itself is classical. Our experiment is realized with a superconducting circuit, where a cavity acts as the WPD for an interfering qubit. Using this setup, we implement the first twofold delayed-choice experiment, which demonstrates that the system's behavior depends not only on the measuring device's configuration that can be chosen even after the system has been detected but also on whether we a posteriori erase or mark the which-path information, the latter of which cannot be revealed by previous quantum delayed-choice experiments. Our results represent the first demonstration of both counterintuitive features with the same experimental setup, significantly extending the concept of quantum delayed-choice experiment.

Improving the stimulated Raman adiabatic passage via dissipative quantum dynamics

We propose a method to improve the stimulated Raman adiabatic passage (STIRAP) via dissipative quantum dynamics, taking into account the dephasing effects. Fast and robust population transfer can be obtained with the scheme by the designed pulses and detuning, even though the initial state of the system is imperfect. With a concrete three-level system as an example, the influences of the imperfect initial state, variations in the control parameters, and various dissipation effects are discussed in detail. The numerical simulation shows that the scheme is insensitive to moderate fluctuations of experimental parameters and the relatively large dissipation effects of the excited state. Furthermore, the dominant dissipative factors, namely, the dephasing effects of the ground states and the imperfect initial state are no longer undesirable, in fact, they are the important resources to the scheme. Therefore, the scheme could provide more choices for the realization of the complete population transfer in the strong dissipative fields where the standard stimulated Raman adiabatic passage or shortcut schemes are invalid.

Correlation between polymorphisms in the visfatin gene and its expression in the serum and coronary artery calcification

We investigated the association between serum visfatin levels and single nucleotide polymorphisms (SNPs; rs61330082, rs2058539) in the visfatin gene and coronary artery calcification (CAC) in patients from Wenzhou, China. CAC patients (N = 206) were divided into two groups: mild CAC (MCAC) and moderate and severe CAC (MSCAC). Volunteers without CAC (N = 70) were included in the control group. The serum visfatin level was analyzed by enzyme-linked immunosorbent assay. SNPs (rs61330082, rs2058539) in the visfatin gene were analyzed by polymerase chain reaction-restriction fragment length polymorphism. Clinical data, serum visfatin levels, and genotype and allele frequencies of rs61330082 and rs2058539 were compared among the three groups. MSCAC patients expressed significantly higher serum visfatin levels (30.58 ± 6.12 ng/mL) than individuals in the MCAC (29.03 ± 1.87 ng/mL) and control (24.45 ± 5.44 ng/mL) groups (P < 0.05). The genotype distributions and frequencies of rs61330082 differed significantly among the groups (P < 0.05), while those of rs2058539 did not. The serum visfatin level was positively correlated with the body mass index (BMI), high-density lipoprotein cholesterol (HDL-C), and insulin resistance index (IRI), and negatively correlated with the triglyceride (TG) levels (P < 0.05) of patients. Serum visfatin is associated with the development of CAC. The T allele of the rs61330082 SNP in the visfatin gene had a cardioprotective effect on patients with CAC; the SNP at rs2058539 was not significantly associated with CAC. The BMI, HDL-C, IRI, and TG levels influenced the development of CAC.

Quantum Delayed-Choice Experiment with a Beam Splitter in a Quantum Superposition

A quantum system can behave as a wave or as a particle, depending on the experimental arrangement. When, for example, measuring a photon using a Mach-Zehnder interferometer, the photon acts as a wave if the second beam splitter is inserted, but as a particle if this beam splitter is omitted. The decision of whether or not to insert this beam splitter can be made after the photon has entered the interferometer, as in Wheeler's famous delayed-choice thought experiment. In recent quantum versions of this experiment, this decision is controlled by a quantum ancilla, while the beam splitter is itself still a classical object. Here, we propose and realize a variant of the quantum delayed-choice experiment. We configure a superconducting quantum circuit as a Ramsey interferometer, where the element that acts as the first beam splitter can be put in a quantum superposition of its active and inactive states, as verified by the negative values of its Wigner function. We show that this enables the wave and particle aspects of the system to be observed with a single setup, without involving an ancilla that is not itself a part of the interferometer. We also study the transition of this quantum beam splitter from a quantum to a classical object due to decoherence, as observed by monitoring the interferometer output.

Association between MTHFR gene polymorphisms (C677T, A1298C) and genetic susceptibility to prostate cancer: a meta-analysis

Genetic polymorphisms (C677T and A1298C) in methylenetetrahydrofolate reductase (MTHFR) were shown to be related to prostate cancer risk in previous studies; however, the results are controversial. We performed a meta-analysis of previous studies and quantitatively estimated these associations. Pubmed, Embase, and Cochrane Library Database were searched for published case-control studies evaluating the association between C677T (or A1298C) and prostate cancer risk. Pooled associations were presented as odds ratios (ORs) along with their 95% confidence intervals. Twenty-one case control studies were identified for meta-analysis that included 21,581 participants. No significant associations were found between the MTHFR polymorphisms C677T or A1298C and prostate cancer risk in our meta-analysis. However, in subgroup analyses, the C677T CT polymorphism was associated with increased prostate cancer risk in East Asians (CT vs CC+TT: OR = 1.324, P = 0.03). The A1298C CC polymorphism in MTHFR was also linked to slightly reduced prostate cancer risk in European residents (CC vs AC+AA: OR = 0.751, P = 0.004; CC vs AA: OR = 0.768, P = 0.011), whereas it was associated with a significantly increased prostate cancer risk in Asian residents (CC vs AA: OR = 1.862, P = 0.006). The C677T CT polymorphism of MTHFR may be a risk factor for prostate cancer in East Asians. The association between the MTHFR A1298C CC genotype and prostate cancer risk may vary within different populations. Large-scale well-designed studies are required to confirm these associations.

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.

Single-step implementation of a multiple-target-qubit controlled phase gate without need of classical pulses

We propose a simple method for achieving a multiqubit phase gate of one qubit simultaneously controlling n target qubits, by using three-level quantum systems (i.e., qutrits) coupled to a cavity or resonator. The gate can be realized via one operational step, without need of classical pulses, and by a virtual photon process. Thus, the gate operation is greatly simplified and decoherence from the cavity decay is much reduced, when compared with previous proposals. In addition, the operation time is independent of the number of qubits and no adjustment of the qutrit level spacings or the cavity frequency is needed during the operation.

Fast and simple scheme for generating NOON states of photons in circuit QED

The generation, manipulation and fundamental understanding of entanglement lies at very heart of quantum mechanics. Among various types of entangled states, the NOON states are a kind of special quantum entangled states with two orthogonal component states in maximal superposition, which have a wide range of potential applications in quantum communication and quantum information processing. Here, we propose a fast and simple scheme for generating NOON states of photons in two superconducting resonators by using a single superconducting transmon qutrit. Because only one superconducting qutrit and two resonators are used, the experimental setup for this scheme is much simplified when compared with the previous proposals requiring a setup of two superconducting qutrits and three cavities. In addition, this scheme is easier and faster to implement than the previous proposals, which require using a complex microwave pulse, or a small pulse Rabi frequency in order to avoid nonresonant transitions.

Nongeometric conditional phase shift via adiabatic evolution of dark eigenstates: a new approach to quantum computation

We propose a new approach to quantum phase gates via the adiabatic evolution. The conditional phase shift is neither of dynamical nor geometric origin. It arises from the adiabatic evolution of the dark state itself. Taking advantage of the adiabatic passage, this kind of quantum logic gates is robust against moderate fluctuations of experimental parameters. In comparison with the geometric phase gates, it is unnecessary to drive the system to undergo a desired cyclic evolution to obtain a desired solid angle. Thus, the procedure is simplified, and the fidelity may be further improved since the errors in obtaining the required solid angle are avoided. We illustrate such a kind of quantum logic gates in the ion trap system. The idea can also be realized in other systems, opening a new perspective for quantum information processing.

Quantum logic gates for hot ions without a speed limitation

We propose a scheme for realizing two-qubit quantum phase gates with trapped ions in thermal motion. In the scheme, the ions are simultaneously illuminated by a standing-wave laser tuned to the carrier, which virtually excites several vibrational modes. The scheme puts no limitations on the intensity of the laser field, allowing the production of a quantum logic gate for hot ions with an arbitrarily high speed as long as a laser field of sufficiently high intensity is available.

One-step synthesis of multiatom Greenberger-Horne-Zeilinger states

A scheme is proposed for generating maximally entangled Greenberger-Horne-Zeilinger (GHZ) atomic states for testing quantum nonlocality. In the scheme, three atoms are simultaneously sent through a nonresonant cavity in a vacuum state. They are initially in the same state, and thus there is no energy exchange in the process. The cavity-assisted collision results in a phase-shift which depends upon the collective atomic excitations. In principle, the scheme can be generalized to generate N-atom GHZ states. The scheme is insensitive to cavity decay and requires only one cavity, providing new prospects for testing fundamental aspects of quantum mechanics and for quantum information processing.

Efficient scheme for two-atom entanglement and quantum information processing in cavity QED

A scheme is proposed for the generation of two-atom maximally entangled states and realization of quantum logic gates and teleportation with cavity QED. The scheme does not require the transfer of quantum information between the atoms and cavity. In the scheme the cavity is only virtually excited and thus the requirement on the quality factor of the cavities is greatly loosened.