A cryogenic on-chip microwave pulse generator for large-scale superconducting quantum computing.

For superconducting quantum processors, microwave signals are delivered to each qubit from room-temperature electronics to the cryogenic environment through coaxial cables. Limited by the heat load of cabling and the massive cost of electronics, such an architecture is not viable for millions of qubits required for fault-tolerant quantum computing. Monolithic integration of the control electronics and the qubits provides a promising solution, which, however, requires a coherent cryogenic microwave pulse generator that is compatible with superconducting quantum circuits. Here, we report such a signal source driven by digital-like signals, generating pulsed microwave emission with well-controlled phase, intensity, and frequency directly at millikelvin temperatures. We showcase high-fidelity readout of superconducting qubits with the microwave pulse generator. The device demonstrated here has a small footprint, negligible heat load, great flexibility to operate, and is fully compatible with today's superconducting quantum circuits, thus providing an enabling technology for large-scale superconducting quantum computers.

An ultra-high gain single-photon transistor in the microwave regime.

A photonic transistor that can switch or amplify an optical signal with a single gate photon requires strong non-linear interaction at the single-photon level. Circuit quantum electrodynamics provides great flexibility to generate such an interaction, and thus could serve as an effective platform to realize a high-performance single-photon transistor. Here we demonstrate such a photonic transistor in the microwave regime. Our device consists of two microwave cavities dispersively coupled to a superconducting qubit. A single gate photon imprints a phase shift on the qubit state through one cavity, and further shifts the resonance frequency of the other cavity. In this way, we realize a gain of the transistor up to 53.4 dB, with an extinction ratio better than 20 dB. Our device outperforms previous devices in the optical regime by several orders in terms of optical gain, which indicates a great potential for application in the field of microwave quantum photonics and quantum information processing.

Quantum-Memory-Enhanced Preparation of Nonlocal Graph States.

Graph states are an important class of multipartite entangled states. Previous experimental generation of graph states and in particular the Greenberger-Horne-Zeilinger (GHZ) states in linear optics quantum information schemes is subjected to an exponential decay in efficiency versus the system size, which limits its large-scale applications in quantum networks. Here, we demonstrate an efficient scheme to prepare graph states with only a polynomial overhead using long-lived atomic quantum memories. We generate atom-photon entangled states in two atomic ensembles asynchronously, retrieve the stored atomic excitations only when both sides succeed, and further project them into a four-photon GHZ state. We measure the fidelity of this GHZ state and further demonstrate its applications in the violation of Bell-type inequalities and in quantum cryptography. Our work demonstrates the prospect of efficient generation of multipartite entangled states in large-scale distributed systems with applications in quantum information processing and metrology.

A flying Schrödinger's cat in multipartite entangled states.

Schrödinger's cat originates from the famous thought experiment querying the counterintuitive quantum superposition of macroscopic objects. As a natural extension, several "cats" (quasi-classical objects) can be prepared into coherent quantum superposition states, which is known as multipartite cat states demonstrating quantum entanglement among macroscopically distinct objects. Here, we present a highly scalable approach to deterministically create flying multipartite Schrödinger's cat states by reflecting coherent-state photons from a microwave cavity containing a superconducting qubit. We perform full quantum state tomography on the cat states with up to four photonic modes and confirm the existence of quantum entanglement among them. We also witness the hybrid entanglement between discrete-variable states (the qubit) and continuous-variable states (the flying multipartite cat) through a joint quantum state tomography. Our work provides an enabling step for implementing a series of quantum metrology and quantum information processing protocols based on cat states.

On-Demand Storage and Retrieval of Microwave Photons Using a Superconducting Multiresonator Quantum Memory.

We realize on-demand storage and retrieval of weak coherent microwave photon pulses at the single-photon level. A superconducting multiresonator system which is composed of a set of frequency-tunable coplanar waveguide resonators is implemented as the quantum memory. By dynamically tuning the resonant frequencies of the resonators, we achieve tunable memory bandwidth from 10 to 55 MHz, with well preserved phase coherence. We further demonstrate on-demand storage and retrieval of a time-bin flying qubit. This result opens up a prospect to integrate our chip-based quantum memory with the state-of-the-art superconducting quantum circuit technology for quantum information processing.

Machine Learning Topological Phases with a Solid-State Quantum Simulator.

We report an experimental demonstration of a machine learning approach to identify exotic topological phases, with a focus on the three-dimensional chiral topological insulators. We show that the convolutional neural networks-a class of deep feed-forward artificial neural networks with widespread applications in machine learning-can be trained to successfully identify different topological phases protected by chiral symmetry from experimental raw data generated with a solid-state quantum simulator. Our results explicitly showcase the exceptional power of machine learning in the experimental detection of topological phases, which paves a way to study rich topological phenomena with the machine learning toolbox.

NOON States of Nine Quantized Vibrations in Two Radial Modes of a Trapped Ion.

We develop a deterministic method to generate and verify arbitrarily high NOON states of quantized vibrations (phonons), through the coupling to the internal state. We experimentally create the entangled states up to N=9 phonons in two vibrational modes of a single trapped ^{171}Yb^{+} ion. We observe an increasing phase sensitivity of the generated NOON state as the number of phonons N increases and obtain the fidelity from the contrast of the phase interference and the population of the phonon states through the two-mode projective measurement, which are significantly above the classical bound. We also measure the quantum Fisher information of the generated state and observe Heisenberg scaling in the lower bounds of phase sensitivity as N increases. Our scheme is generic and applicable to other photonic or phononic systems such as circuit QED systems or nanomechanical oscillators, which have Jaynes-Cummings-type of interactions.

Experimental entanglement of 25 individually accessible atomic quantum interfaces.

A quantum interface links the stationary qubits in a quantum memory with flying photonic qubits in optical transmission channels and constitutes a critical element for the future quantum internet. Entanglement of quantum interfaces is an important step for the realization of quantum networks. Through heralded detection of photon interference, we generate multipartite entanglement between 25 (or 9) individually addressable quantum interfaces in a multiplexed atomic quantum memory array and confirm genuine 22-partite (or 9-partite) entanglement. This experimental entanglement of a record-high number of individually addressable quantum interfaces makes an important step toward the realization of quantum networks, long-distance quantum communication, and multipartite quantum information processing.

Corrigendum: Experimental Certification of Random Numbers via Quantum Contextuality.

This corrects the article DOI: 10.1038/srep01627.

Efficient representation of quantum many-body states with deep neural networks.

Part of the challenge for quantum many-body problems comes from the difficulty of representing large-scale quantum states, which in general requires an exponentially large number of parameters. Neural networks provide a powerful tool to represent quantum many-body states. An important open question is what characterizes the representational power of deep and shallow neural networks, which is of fundamental interest due to the popularity of deep learning methods. Here, we give a proof that, assuming a widely believed computational complexity conjecture, a deep neural network can efficiently represent most physical states, including the ground states of many-body Hamiltonians and states generated by quantum dynamics, while a shallow network representation with a restricted Boltzmann machine cannot efficiently represent some of those states.One of the challenges in studies of quantum many-body physics is finding an efficient way to record the large system wavefunctions. Here the authors present an analysis of the capabilities of recently-proposed neural network representations for storing physically accessible quantum states.

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.

Bound state properties of ABC-stacked trilayer graphene quantum dots.

The few-layer graphene quantum dot provides a promising platform for quantum computing with both spin and valley degrees of freedom. Gate-defined quantum dots in particular can avoid noise from edge disorders. In connection with the recent experimental efforts (Song et al 2016 Nano Lett. 16 6245), we investigate the bound state properties of trilayer graphene (TLG) quantum dots (QDs) through numerical simulations. We show that the valley degeneracy can be lifted by breaking the time reversal symmetry through the application of a perpendicular magnetic field. The spectrum under such a potential exhibits a transition from one group of Landau levels to another group, which can be understood analytically through perturbation theory. Our results provide insight into the transport property of TLG QDs, with possible applications to study of spin qubits and valleytronics in TLG QDs.

Coulomb Oscillations in a Gate-Controlled Few-Layer Graphene Quantum Dot.

Graphene quantum dots could be an ideal host for spin qubits and thus have been extensively investigated based on graphene nanoribbons and etched nanostructures; however, edge and substrate-induced disorders severely limit device functionality. Here, we report the confinement of quantum dots in few-layer graphene with tunable barriers, defined by local strain and electrostatic gating. Transport measurements unambiguously reveal that confinement barriers are formed by inducing a band gap via the electrostatic gating together with local strain induced constriction. Numerical simulations according to the local top-gate geometry confirm the band gap opening by a perpendicular electric field. We investigate the magnetic field dependence of the energy-level spectra in these graphene quantum dots. Experimental results reveal a complex evolution of Coulomb oscillations with the magnetic field, featuring kinks at level crossings. The simulation of energy spectrum shows that the kink features and the magnetic field dependence are consistent with experimental observations, implying the hybridized nature of energy-level spectrum of these graphene quantum dots.

Towards photonic quantum simulation of ground states of frustrated Heisenberg spin systems.

Photonic quantum simulators are promising candidates for providing insight into other small- to medium-sized quantum systems. Recent experiments have shown that photonic quantum systems have the advantage to exploit quantum interference for the quantum simulation of the ground state of Heisenberg spin systems. Here we experimentally characterize this quantum interference at a tuneable beam splitter and further investigate the measurement-induced interactions of a simulated four-spin system by comparing the entanglement dynamics using pairwise concurrence. We also study theoretically a four-site square lattice with next-nearest neighbor interactions and a six-site checkerboard lattice, which might be in reach of current technology.

Experimental certification of random numbers via quantum contextuality.

The intrinsic unpredictability of measurements in quantum mechanics can be used to produce genuine randomness. Here, we demonstrate a random number generator where the randomness is certified by quantum contextuality in connection with the Kochen-Specker theorem. In particular, we generate random numbers from measurements on a single trapped ion with three internal levels, and certify the generated randomness by showing a bound on the minimum entropy through observation of violation of the Klyachko-Can-Binicioglu-Shumovsky (KCBS) inequality. Concerning the test of the KCBS inequality, we close the detection efficiency loophole for the first time and make it relatively immune to the compatibility loophole. In our experiment, we generate 1 × 10(5) random numbers that are guaranteed to have 5.2 × 10(4) bits of minimum entropy with a 99% confidence level.

State-independent experimental test of quantum contextuality with a single trapped ion.

Using a single trapped ion, we have experimentally demonstrated state-independent violation of a recent version of the Kochen-Specker inequality in a three-level system (qutrit) that is intrinsically indivisible. Three ground states of the (171)Yb(+) ion representing a qutrit are manipulated with high fidelity through microwaves and detected with high efficiency through a two-step quantum jump technique. Qutrits constitute the most fundamental system to show quantum contextuality and our experiment represents the first one that closes the detection efficiency loophole for experimental tests of quantum contextuality in such a system.

Experimental teleportation of a quantum controlled-NOT gate.

Teleportation of quantum gates is a critical step for the implementation of quantum networking and teleportation-based models of quantum computation. We report an experimental demonstration of teleportation of the prototypical quantum controlled-NOT (CNOT) gate. Assisted with linear optical manipulations, photon entanglement produced from parametric down-conversion, and postselection from the coincidence measurements, we teleport the quantum CNOT gate from acting on local qubits to acting on remote qubits. The quality of the quantum gate teleportation is characterized through the method of quantum process tomography, with an average fidelity of 0.84 demonstrated for the teleported gate.