Deterministic quantum state transfer and remote entanglement using microwave photons

Evolution of Propagating Coherent Pulses Driving a Single Superconducting Artificial Atom

An electromagnetic wave propagating through a waveguide with a strongly coupled two-level superconducting artificial atom exhibits an evolving superposition with the atom. The Rabi oscillations in the atom result from a single excitation-relaxation, corresponding to photon absorption and stimulated emission from and to the field. In this study, we experimentally investigated the time-dependent behavior of the field transmitted through a waveguide with a strongly coupled transmon. The scattered fields agree well with the predictions of the input-output theory. We demonstrate that the time evolution of the propagating fields, because of the interaction, encapsulates all information about the atom. Furthermore, we deduced the dynamics of the incoherent radiation component from the first-order correlation function of the measured field.

Virtual Photon-Mediated Quantum State Transfer and Remote Entanglement between Spin Qubits in Quantum Dots Using Superadiabatic Pulses

Spin qubits in semiconductor quantum dots are an attractive candidate for scalable quantum information processing. Reliable quantum state transfer and entanglement between spatially separated spin qubits is a highly desirable but challenging goal. Here, we propose a fast and high-fidelity quantum state transfer scheme for two spin qubits mediated by virtual microwave photons. Our general strategy involves using a superadiabatic pulse to eliminate non-adiabatic transitions, without the need for increased control complexity. We show that arbitrary quantum state transfer can be achieved with a fidelity of 95.1% within a 60 ns short time under realistic parameter conditions. We also demonstrate the robustness of this scheme to experimental imperfections and environmental noises. Furthermore, this scheme can be directly applied to the generation of a remote Bell entangled state with a fidelity as high as 97.6%. These results pave the way for fault-tolerant quantum computation on spin quantum network architecture platforms.

Dispersive nonreciprocity between a qubit and a cavity

The dispersive interaction between a qubit and a cavity is ubiquitous in circuit and cavity quantum electrodynamics. It describes the frequency shift of one quantum mode in response to excitations in the other and, in closed systems, is necessarily bidirectional, i.e., reciprocal. Here, we present an experimental study of a nonreciprocal dispersive-type interaction between a transmon qubit and a superconducting cavity, arising from a common coupling to dissipative intermediary modes with broken time reversal symmetry. We characterize the qubit-cavity dynamics, including asymmetric frequency pulls and photon shot noise dephasing, under varying degrees of nonreciprocity by tuning the magnetic field bias of a ferrite component in situ. We introduce a general master equation model for nonreciprocal interactions in the dispersive regime, providing a compact description of the observed qubit-cavity dynamics agnostic to the intermediary system. Our result provides an example of quantum nonreciprocal phenomena beyond the typical paradigms of non-Hermitian Hamiltonians and cascaded systems.

Photonic Which-Path Entangler Based on Longitudinal Cavity-Qubit Coupling

We show that a modulated longitudinal cavity-qubit coupling can be used to control the path taken by a multiphoton coherent-state wave packet conditioned on the state of a qubit, resulting in a qubit-which-path (QWP) entangled state. QWP states can generate long-range multipartite entanglement using strategies for interfacing discrete- and continuous-variable degrees of freedom. Using the approach presented here, entanglement can be distributed in a quantum network without the need for single-photon sources or detectors.

Bidirectional Multiphoton Communication between Remote Superconducting Nodes

Quantum communication test beds provide a useful resource for experimentally investigating a variety of communication protocols. Here we demonstrate a superconducting circuit test bed with bidirectional multiphoton state transfer capability using time-domain shaped wave packets. The system we use to achieve this comprises two remote nodes, each including a tunable superconducting transmon qubit and a tunable microwave-frequency resonator, linked by a 2 m-long superconducting coplanar waveguide, which serves as a transmission line. We transfer both individual and superposition Fock states between the two remote nodes, and additionally show that this bidirectional state transfer can be done simultaneously, as well as being used to entangle elements in the two nodes.

Demonstrating Path-Independent Anyonic Braiding on a Modular Superconducting Quantum Processor

Anyons, exotic quasiparticles in two-dimensional space exhibiting nontrivial exchange statistics, play a crucial role in universal topological quantum computing. One notable proposal to manifest the fractional statistics of anyons is the toric code model; however, scaling up its size through quantum simulation poses a serious challenge because of its highly entangled ground state. In this Letter, we demonstrate that a modular superconducting quantum processor enables hardware-pragmatic implementation of the toric code model. Through in-parallel control across separate modules, we generate a 10-qubit toric code ground state in four steps and realize six distinct braiding paths to benchmark the performance of anyonic statistics. The path independence of the anyonic braiding statistics is verified by correlation measurements in an efficient and scalable fashion. Our modular approach, serving as a hardware embodiment of the toric code model, offers a promising avenue toward scalable simulation of topological phases, paving the way for quantum simulation in a distributed fashion.

Autonomous Distribution of Programmable Multiqubit Entanglement in a Dual-Rail Quantum Network

We propose and analyze a scalable and fully autonomous scheme for preparing spatially distributed multiqubit entangled states in a dual-rail waveguide QED setup. In this approach, arrays of qubits located along two separated waveguides are illuminated by correlated photons from the output of a nondegenerate parametric amplifier. These photons drive the qubits into different classes of pure entangled steady states, for which the degree of multipartite entanglement can be conveniently adjusted by the chosen pattern of local qubit-photon detunings. Numerical simulations for moderate-sized networks show that the preparation time for these complex multiqubit states increases at most linearly with the system size and that one may benefit from an additional speedup in the limit of a large amplifier bandwidth. Therefore, this scheme offers an intriguing new route for distributing ready-to-use multipartite entangled states across large quantum networks, without requiring any precise pulse control and relying on a single Gaussian entanglement source only.

Iterative Adaptive Spectroscopy of Short Signals

We develop an iterative, adaptive frequency sensing protocol based on Ramsey interferometry of a two-level system. Our scheme allows one to estimate unknown frequencies with a high precision from short, finite signals consisting of only a small number of Ramsey fringes. It avoids several issues related to processing of decaying signals and reduces the experimental overhead related to sampling. High precision is achieved by enhancing the Ramsey sequence to prepare with high fidelity both the sensing and readout state and by using an iterative procedure built to mitigate systematic errors when estimating frequencies from Fourier transforms. A comparison with state-of-the-art dynamical decoupling techniques reveals a significant speedup of the frequency estimation without loss of precision.

Loophole-free Bell inequality violation with superconducting circuits

Superposition, entanglement and non-locality constitute fundamental features of quantum physics. The fact that quantum physics does not follow the principle of local causality1-3 can be experimentally demonstrated in Bell tests4 performed on pairs of spatially separated, entangled quantum systems. Although Bell tests, which are widely regarded as a litmus test of quantum physics, have been explored using a broad range of quantum systems over the past 50 years, only relatively recently have experiments free of so-called loopholes5 succeeded. Such experiments have been performed with spins in nitrogen-vacancy centres6, optical photons7-9 and neutral atoms10. Here we demonstrate a loophole-free violation of Bell's inequality with superconducting circuits, which are a prime contender for realizing quantum computing technology11. To evaluate a Clauser-Horne-Shimony-Holt-type Bell inequality4, we deterministically entangle a pair of qubits12 and perform fast and high-fidelity measurements13 along randomly chosen bases on the qubits connected through a cryogenic link14 spanning a distance of 30 metres. Evaluating more than 1 million experimental trials, we find an average S value of 2.0747 ± 0.0033, violating Bell's inequality with a P value smaller than 10-108. Our work demonstrates that non-locality is a viable new resource in quantum information technology realized with superconducting circuits with potential applications in quantum communication, quantum computing and fundamental physics15.

Distributed Quantum Error Correction for Chip-Level Catastrophic Errors

Quantum error correction holds the key to scaling up quantum computers. Cosmic ray events severely impact the operation of a quantum computer by causing chip-level catastrophic errors, essentially erasing the information encoded in a chip. Here, we present a distributed error correction scheme to combat the devastating effect of such events by introducing an additional layer of quantum erasure error correcting code across separate chips. We show that our scheme is fault tolerant against chip-level catastrophic errors and discuss its experimental implementation using superconducting qubits with microwave links. Our analysis shows that in state-of-the-art experiments, it is possible to suppress the rate of these errors from 1 per 10 s to less than 1 per month.

The nonequilibrium cost of accurate information processing

Accurate information processing is crucial both in technology and in nature. To achieve it, any information processing system needs an initial supply of resources away from thermal equilibrium. Here we establish a fundamental limit on the accuracy achievable with a given amount of nonequilibrium resources. The limit applies to arbitrary information processing tasks and arbitrary information processing systems subject to the laws of quantum mechanics. It is easily computable and is expressed in terms of an entropic quantity, which we name the reverse entropy, associated to a time reversal of the information processing task under consideration. The limit is achievable for all deterministic classical computations and for all their quantum extensions. As an application, we establish the optimal tradeoff between nonequilibrium and accuracy for the fundamental tasks of storing, transmitting, cloning, and erasing information. Our results set a target for the design of new devices approaching the ultimate efficiency limit, and provide a framework for demonstrating thermodynamical advantages of quantum devices over their classical counterparts.

Deterministic Loading of Microwaves onto an Artificial Atom Using a Time-Reversed Waveform

Loading quantum information deterministically onto a quantum node is an important step toward a quantum network. Here, we demonstrate that coherent-state microwave photons with an optimal temporal waveform can be efficiently loaded onto a single superconducting artificial atom in a semi-infinite one-dimensional (1D) transmission-line waveguide. Using a weak coherent state (the number of photons (N) contained in the pulse ≪1) with an exponentially rising waveform, whose time constant matches the decoherence time of the artificial atom, we demonstrate a loading efficiency of 94.2% ± 0.7% from 1D semifree space to the artificial atom. The high loading efficiency is due to time-reversal symmetry: the overlap between the incoming wave and the time-reversed emitted wave is up to 97.1% ± 0.4%. Our results open up promising applications in realizing quantum networks based on waveguide quantum electrodynamics.

High-fidelity quantum information transmission using a room-temperature nonrefrigerated lossy microwave waveguide

Quantum microwave transmission is key to realizing modular superconducting quantum computers and distributed quantum networks. A large number of incoherent photons are thermally generated within the microwave frequency spectrum. The closeness of the transmitted quantum state to the source-generated quantum state at the input of the transmission link (measured by the transmission fidelity) degrades due to the presence of the incoherent photons. Hence, high-fidelity quantum microwave transmission has long been considered to be infeasible without refrigeration. In this study, we propose a novel method for high-fidelity quantum microwave transmission using a room-temperature lossy waveguide. The proposed scheme consists of connecting two cryogenic nodes (i.e., a transmitter and a receiver) by the room-temperature lossy microwave waveguide. First, cryogenic preamplification is implemented prior to transmission. Second, at the receiver side, a cryogenic loop antenna is placed inside the output port of the waveguide and coupled to an LC harmonic oscillator located outside the waveguide. The loop antenna converts quantum microwave fields to a quantum voltage across the coupled LC harmonic oscillator. Noise photons are induced across the LC oscillator including the source generated noise, the preamplification noise, the thermal occupation of the waveguide, and the fluctuation-dissipation noise. The loop antenna detector at the receiver is designed to extensively suppress the induced photons across the LC oscillator. The signal transmittance is maintained intact by providing significant preamplification gain. Our calculations show that high-fidelity quantum transmission (i.e., more than [Formula: see text]) is realized based on the proposed scheme for transmission distances reaching 100 m.

Engineering Symmetry-Selective Couplings of a Superconducting Artificial Molecule to Microwave Waveguides

Tailoring the decay rate of structured quantum emitters into their environment opens new avenues for nonlinear quantum optics, collective phenomena, and quantum communications. Here, we demonstrate a novel coupling scheme between an artificial molecule comprising two identical, strongly coupled transmon qubits and two microwave waveguides. In our scheme, the coupling is engineered so that transitions between states of the same (opposite) symmetry, with respect to the permutation operator, are predominantly coupled to one (the other) waveguide. The symmetry-based coupling selectivity, as quantified by the ratio of the coupling strengths, exceeds a factor of 30 for both waveguides in our device. In addition, we implement a Raman process activated by simultaneously driving both waveguides, and show that it can be used to coherently couple states of different symmetry in the single-excitation manifold of the molecule. Using that process, we implement frequency conversion across the waveguides, mediated by the molecule, with efficiency of about 95%. Finally, we show that this coupling arrangement makes it possible to straightforwardly generate spatially separated Bell states propagating across the waveguides. We envisage further applications to quantum thermodynamics, microwave photodetection, and photon-photon gates.

Entanglement Purification and Protection in a Superconducting Quantum Network

High-fidelity quantum entanglement is a key resource for quantum communication and distributed quantum computing, enabling quantum state teleportation, dense coding, and quantum encryption. Any sources of decoherence in the communication channel, however, degrade entanglement fidelity, thereby increasing the error rates of entangled state protocols. Entanglement purification provides a method to alleviate these nonidealities by distilling impure states into higher-fidelity entangled states. Here we demonstrate the entanglement purification of Bell pairs shared between two remote superconducting quantum nodes connected by a moderately lossy, 1-meter long superconducting communication cable. We use a purification process to correct the dominant amplitude damping errors caused by transmission through the cable, with fractional increases in fidelity as large as 25%, achieved for higher damping errors. The best final fidelity the purification achieves is 94.09±0.98%. In addition, we use both dynamical decoupling and Rabi driving to protect the entangled states from local noise, increasing the effective qubit dephasing time by a factor of 4, from 3 to 12  μs. These methods demonstrate the potential for the generation and preservation of very high-fidelity entanglement in a superconducting quantum communication network.

Experimental quantum teleportation of propagating microwaves

The field of quantum communication promises to provide efficient and unconditionally secure ways to exchange information, particularly, in the form of quantum states. Meanwhile, recent breakthroughs in quantum computation with superconducting circuits trigger a demand for quantum communication channels between spatially separated superconducting processors operating at microwave frequencies. In pursuit of this goal, we demonstrate the unconditional quantum teleportation of propagating coherent microwave states by exploiting two-mode squeezing and analog feedforward over a macroscopic distance of d = 0.42 m. We achieve a teleportation fidelity of F = 0.689 ± 0.004, exceeding the asymptotic no-cloning threshold. Thus, the quantum nature of the teleported states is preserved, opening the avenue toward unconditional security in microwave quantum communication.

Rapid and unconditional parametric reset protocol for tunable superconducting qubits

Qubit initialization is a critical task in quantum computation and communication. Extensive efforts have been made to achieve this with high speed, efficiency and scalability. However, previous approaches have either been measurement-based and required fast feedback, suffered from crosstalk or required sophisticated calibration. Here, we report a fast and high-fidelity reset scheme, avoiding the issues above without any additional chip architecture. By modulating the flux through a transmon qubit, we realize a swap between the qubit and its readout resonator that suppresses the excited state population to 0.08% ± 0.08% within 34 ns (284 ns if photon depletion of the resonator is required). Furthermore, our approach (i) can achieve effective second excited state depletion, (ii) has negligible effects on neighboring qubits, and (iii) offers a way to entangle the qubit with an itinerant single photon, useful in quantum communication applications.

Photons and qubits get a better connection

[Figure: see text].

Quantum control of bosonic modes with superconducting circuits

Bosonic modes have wide applications in various quantum technologies, such as optical photons for quantum communication, magnons in spin ensembles for quantum information storage and mechanical modes for reversible microwave-to-optical quantum transduction. There is emerging interest in utilizing bosonic modes for quantum information processing, with circuit quantum electrodynamics (circuit QED) as one of the leading architectures. Quantum information can be encoded into subspaces of a bosonic superconducting cavity mode with long coherence time. However, standard Gaussian operations (e.g., beam splitting and two-mode squeezing) are insufficient for universal quantum computing. The major challenge is to introduce additional nonlinear control beyond Gaussian operations without adding significant bosonic loss or decoherence. Here we review recent advances in universal control of a single bosonic code with superconducting circuits, including unitary control, quantum feedback control, driven-dissipative control and holonomic dissipative control. Various approaches to entangling different bosonic modes are also discussed.

Optically Heralded Entanglement of Superconducting Systems in Quantum Networks

Networking superconducting quantum computers is a longstanding challenge in quantum science. The typical approach has been to cascade transducers: converting to optical frequencies at the transmitter and to microwave frequencies at the receiver. However, the small microwave-optical coupling and added noise have proven formidable obstacles. Instead, we propose optical networking via heralding end-to-end entanglement with one detected photon and teleportation. This new protocol can be implemented on standard transduction hardware while providing significant performance improvements over transduction. In contrast to cascaded direct transduction, our scheme absorbs the low optical-microwave coupling efficiency into the heralding step, thus breaking the rate-fidelity trade-off. Moreover, this technique unifies and simplifies entanglement generation between superconducting devices and other physical modalities in quantum networks.

Bidirectional interconversion of microwave and light with thin-film lithium niobate

Superconducting cavity electro-optics presents a promising route to coherently convert microwave and optical photons and distribute quantum entanglement between superconducting circuits over long-distance. Strong Pockels nonlinearity and high-performance optical cavity are the prerequisites for high conversion efficiency. Thin-film lithium niobate (TFLN) offers these desired characteristics. Despite significant recent progresses, only unidirectional conversion with efficiencies on the order of 10-5 has been realized. In this article, we demonstrate the bidirectional electro-optic conversion in TFLN-superconductor hybrid system, with conversion efficiency improved by more than three orders of magnitude. Our air-clad device architecture boosts the sustainable intracavity pump power at cryogenic temperatures by suppressing the prominent photorefractive effect that limits cryogenic performance of TFLN, and reaches an efficiency of 1.02% (internal efficiency of 15.2%). This work firmly establishes the TFLN-superconductor hybrid EO system as a highly competitive transduction platform for future quantum network applications.

Quantum Non-Gaussian Photon Coincidences

Photon coincidences represent an important resource for quantum technologies. They expose nonlinear quantum processes in matter and are essential for sources of entanglement. We derive broadly applicable criteria for quantum non-Gaussian two-photon coincidences that certify a new quality of photon sources. The criteria reject states emerging from Gaussian parametric processes, which often limit applications in quantum technologies. We also analyze the robustness of the quantum non-Gaussian coincidences and compare it to the heralded quantum non-Gaussianity of single photons based on them.

Microwave response in a topological superconducting quantum interference device

Photon detection at microwave frequency is of great interest due to its application in quantum computation information science and technology. Herein are results from studying microwave response in a topological superconducting quantum interference device (SQUID) realized in Dirac semimetal Cd₃As₂. The temperature dependence and microwave power dependence of the SQUID junction resistance are studied, from which we obtain an effective temperature at each microwave power level. It is observed the effective temperature increases with the microwave power. This observation of large microwave response may pave the way for single photon detection at the microwave frequency in topological quantum materials.

Searching for Dark Matter with a Superconducting Qubit

Detection mechanisms for low mass bosonic dark matter candidates, such as the axion or hidden photon, leverage potential interactions with electromagnetic fields, whereby the dark matter (of unknown mass) on rare occasion converts into a single photon. Current dark matter searches operating at microwave frequencies use a resonant cavity to coherently accumulate the field sourced by the dark matter and a near standard quantum limited (SQL) linear amplifier to read out the cavity signal. To further increase sensitivity to the dark matter signal, sub-SQL detection techniques are required. Here we report the development of a novel microwave photon counting technique and a new exclusion limit on hidden photon dark matter. We operate a superconducting qubit to make repeated quantum nondemolition measurements of cavity photons and apply a hidden Markov model analysis to reduce the noise to 15.7 dB below the quantum limit, with overall detector performance limited by a residual background of real photons. With the present device, we perform a hidden photon search and constrain the kinetic mixing angle to ε≤1.68×10^{-15} in a band around 6.011 GHz (24.86  μeV) with an integration time of 8.33 s. This demonstrated noise reduction technique enables future dark matter searches to be sped up by a factor of 1,300. By coupling a qubit to an arbitrary quantum sensor, more general sub-SQL metrology is possible with the techniques presented in this Letter.

Deterministic multi-qubit entanglement in a quantum network

The generation of high-fidelity distributed multi-qubit entanglement is a challenging task for large-scale quantum communication and computational networks^1-4. The deterministic entanglement of two remote qubits has recently been demonstrated with both photons^5-10 and phonons¹¹. However, the deterministic generation and transmission of multi-qubit entanglement has not been demonstrated, primarily owing to limited state-transfer fidelities. Here we report a quantum network comprising two superconducting quantum nodes connected by a one-metre-long superconducting coaxial cable, where each node includes three interconnected qubits. By directly connecting the cable to one qubit in each node, we transfer quantum states between the nodes with a process fidelity of 0.911 ± 0.008. We also prepare a three-qubit Greenberger-Horne-Zeilinger (GHZ) state^12-14 in one node and deterministically transfer this state to the other node, with a transferred-state fidelity of 0.656 ± 0.014. We further use this system to deterministically generate a globally distributed two-node, six-qubit GHZ state with a state fidelity of 0.722 ± 0.021. The GHZ state fidelities are clearly above the threshold of 1/2 for genuine multipartite entanglement¹⁵, showing that this architecture can be used to coherently link together multiple superconducting quantum processors, providing a modular approach for building large-scale quantum computers^16,17.

Microwave Quantum Link between Superconducting Circuits Housed in Spatially Separated Cryogenic Systems

Superconducting circuits are a strong contender for realizing quantum computing systems and are also successfully used to study quantum optics and hybrid quantum systems. However, their cryogenic operation temperatures and the current lack of coherence-preserving microwave-to-optical conversion solutions have hindered the realization of superconducting quantum networks spanning different cryogenic systems or larger distances. Here, we report the successful operation of a cryogenic waveguide coherently linking transmon qubits located in two dilution refrigerators separated by a physical distance of five meters. We transfer qubit states and generate entanglement on demand with average transfer and target state fidelities of 85.8% and 79.5%, respectively, between the two nodes of this elementary network. Cryogenic microwave links provide an opportunity to scale up systems for quantum computing and create local area superconducting quantum communication networks over length scales of at least tens of meters.

Nonreciprocal Optomechanical Entanglement against Backscattering Losses

We propose how to achieve nonreciprocal quantum entanglement of light and motion and reveal its counterintuitive robustness against random losses. We find that by splitting the counterpropagating lights of a spinning resonator via the Sagnac effect, photons and phonons can be entangled strongly in a chosen direction but fully uncorrelated in the other. This makes it possible both to realize quantum nonreciprocity even in the absence of any classical nonreciprocity and also to achieve significant entanglement revival against backscattering losses in practical devices. Our work provides a way to protect and engineer quantum resources by utilizing diverse nonreciprocal devices, for building noise-tolerant quantum processors, realizing chiral networks, and backaction-immune quantum sensors.

Generating spatially entangled itinerant photons with waveguide quantum electrodynamics

Realizing a fully connected network of quantum processors requires the ability to distribute quantum entanglement. For distant processing nodes, this can be achieved by generating, routing, and capturing spatially entangled itinerant photons. In this work, we demonstrate the deterministic generation of such photons using superconducting transmon qubits that are directly coupled to a waveguide. In particular, we generate two-photon N00N states and show that the state and spatial entanglement of the emitted photons are tunable via the qubit frequencies. Using quadrature amplitude detection, we reconstruct the moments and correlations of the photonic modes and demonstrate state preparation fidelities of 84%. Our results provide a path toward realizing quantum communication and teleportation protocols using itinerant photons generated by quantum interference within a waveguide quantum electrodynamics architecture.

Universal Logical Gates on Topologically Encoded Qubits via Constant-Depth Unitary Circuits

A fundamental question in the theory of quantum computation is to understand the ultimate space-time resource costs for performing a universal set of logical quantum gates to arbitrary precision. Here we demonstrate that non-Abelian anyons in Turaev-Viro quantum error correcting codes can be moved over a distance of order of the code distance, and thus braided, by a constant depth local unitary quantum circuit followed by a permutation of qubits. Our gates are protected in the sense that the lengths of error strings do not grow by more than a constant factor. When applied to the Fibonacci code, our results demonstrate that a universal logical gate set can be implemented on encoded qubits through a constant depth unitary quantum circuit, and without increasing the asymptotic scaling of the space overhead. These results also apply directly to braiding of topological defects in surface codes. Our results reformulate the notion of braiding in general as an effectively instantaneous process, rather than as an adiabatic, slow process.

Cavity piezo-mechanics for superconducting-nanophotonic quantum interface

Hybrid quantum systems are essential for the realization of distributed quantum networks. In particular, piezo-mechanics operating at typical superconducting qubit frequencies features low thermal excitations, and offers an appealing platform to bridge superconducting quantum processors and optical telecommunication channels. However, integrating superconducting and optomechanical elements at cryogenic temperatures with sufficiently strong interactions remains a tremendous challenge. Here, we report an integrated superconducting cavity piezo-optomechanical platform where 10 GHz phonons are resonantly coupled with photons in a superconducting cavity and a nanophotonic cavity at the same time. Taking advantage of the large piezo-mechanical cooperativity (Cem ~7) and the enhanced optomechanical coupling boosted by a pulsed optical pump, we demonstrate coherent interactions at cryogenic temperatures via the observation of efficient microwave-optical photon conversion. This hybrid interface makes a substantial step towards quantum communication at large scale, as well as novel explorations in microwave-optical photon entanglement and quantum sensing mediated by gigahertz phonons.

Remote Entanglement via Adiabatic Passage Using a Tunably Dissipative Quantum Communication System

Effective quantum communication between remote quantum nodes requires high fidelity quantum state transfer and remote entanglement generation. Recent experiments have demonstrated that microwave photons, as well as phonons, can be used to couple superconducting qubits, with a fidelity limited primarily by loss in the communication channel [P. Kurpiers et al., Nature (London) 558, 264 (2018)NATUAS0028-083610.1038/s41586-018-0195-y; C. J. Axline et al., Nat. Phys. 14, 705 (2018)NPAHAX1745-247310.1038/s41567-018-0115-y; P. Campagne-Ibarcq et al., Phys. Rev. Lett. 120, 200501 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.200501; N. Leung et al., npj Quantum Inf. 5, 18 (2019)2056-638710.1038/s41534-019-0128-0; Y. P. Zhong et al., Nat. Phys. 15, 741 (2019)NPAHAX1745-247310.1038/s41567-019-0507-7; A. Bienfait et al., Science 364, 368 (2019)SCIEAS0036-807510.1126/science.aaw8415]. Adiabatic protocols can overcome channel loss by transferring quantum states without populating the lossy communication channel. Here, we present a unique superconducting quantum communication system, comprising two superconducting qubits connected by a 0.73 m-long communication channel. Significantly, we can introduce large tunable loss to the channel, allowing exploration of different entanglement protocols in the presence of dissipation. When set for minimum loss in the channel, we demonstrate an adiabatic quantum state transfer protocol that achieves 99% transfer efficiency as well as the deterministic generation of entangled Bell states with a fidelity of 96%, all without populating the intervening communication channel, and competitive with a qubit-resonant mode-qubit relay method. We also explore the performance of the adiabatic protocol in the presence of significant channel loss, and show that the adiabatic protocol protects against loss in the channel, achieving higher state transfer and entanglement fidelities than the relay method.

Light-mediated strong coupling between a mechanical oscillator and atomic spins 1 meter apart

Engineering strong interactions between quantum systems is essential for many phenomena of quantum physics and technology. Typically, strong coupling relies on short-range forces or on placing the systems in high-quality electromagnetic resonators, which restricts the range of the coupling to small distances. We used a free-space laser beam to strongly couple a collective atomic spin and a micromechanical membrane over a distance of 1 meter in a room-temperature environment. The coupling is highly tunable and allows the observation of normal-mode splitting, coherent energy exchange oscillations, two-mode thermal noise squeezing, and dissipative coupling. Our approach to engineering coherent long-distance interactions with light makes it possible to couple very different systems in a modular way, opening up a range of opportunities for quantum control and coherent feedback networks.

Spin-photon module for scalable network architecture in quantum dots

Reliable information transmission between spatially separated nodes is fundamental to a network architecture for scalable quantum technology. Spin qubit in semiconductor quantum dots is a promising candidate for quantum information processing. However, there remains a challenge to design a practical path from the existing experiments to scalable quantum processor. Here we propose a module consisting of spin singlet-triplet qubits and single microwave photons. We show a high degree of control over interactions between the spin qubit and the quantum light field can be achieved. Furthermore, we propose preparation of a shaped single photons with an efficiency of 98%, and deterministic quantum state transfer and entanglement generation between remote nodes with a high fidelity of 90%. This spin-photon module has met the threshold of particular designed error-correction protocols, thus provides a feasible approach towards scalable quantum network architecture.

Proposal for Heralded Generation and Detection of Entangled Microwave-Optical-Photon Pairs

Quantum state transfer between microwave and optical frequencies is essential for connecting superconducting quantum circuits to optical systems and extending microwave quantum networks over long distances. However, establishing such a quantum interface is extremely challenging because the standard direct quantum transduction requires both high coupling efficiency and small added noise. We propose an entanglement-based scheme-generating microwave-optical entanglement and using it to transfer quantum states via quantum teleportation-which can bypass the stringent requirements in direct quantum transduction and is robust against loss errors. In addition, we propose and analyze a counterintuitive design-suppress the added noise by placing the device at a higher temperature environment-which can improve both the device quality factor and power handling capability. We systematically analyze the generation and verification of entangled microwave-optical-photon pairs. The parameter for entanglement verification favors the regime of cooperativity mismatch and can tolerate certain thermal noises. Our scheme is feasible given the latest advances on electro-optomechanics, and can be generalized to various physical systems.

Microwave-to-optics conversion using a mechanical oscillator in its quantum groundstate

Conversion between signals in the microwave and optical domains is of great interest both for classical telecommunication, as well as for connecting future superconducting quantum computers into a global quantum network. For quantum applications, the conversion has to be both efficient, as well as operate in a regime of minimal added classical noise. While efficient conversion has been demonstrated using mechanical transducers, they have so far all operated with a substantial thermal noise background. Here, we overcome this limitation and demonstrate coherent conversion between GHz microwave signals and the optical telecom band with a thermal background of less than one phonon. We use an integrated, on-chip electro-opto-mechanical device that couples surface acoustic waves driven by a resonant microwave signal to an optomechanical crystal featuring a 2.7 GHz mechanical mode. We initialize the mechanical mode in its quantum groundstate, which allows us to perform the transduction process with minimal added thermal noise, while maintaining an optomechanical cooperativity >1, so that microwave photons mapped into the mechanical resonator are effectively upconverted to the optical domain. We further verify the preservation of the coherence of the microwave signal throughout the transduction process.

Hardware-Efficient Quantum Random Access Memory with Hybrid Quantum Acoustic Systems

Hybrid quantum systems in which acoustic resonators couple to superconducting qubits are promising quantum information platforms. High quality factors and small mode volumes make acoustic modes ideal quantum memories, while the qubit-phonon coupling enables the initialization and manipulation of quantum states. We present a scheme for quantum computing with multimode quantum acoustic systems, and based on this scheme, propose a hardware-efficient implementation of a quantum random access memory (QRAM). Quantum information is stored in high-Q phonon modes, and couplings between modes are engineered by applying off-resonant drives to a transmon qubit. In comparison to existing proposals that involve directly exciting the qubit, this scheme can offer a substantial improvement in gate fidelity for long-lived acoustic modes. We show how these engineered phonon-phonon couplings can be used to access data in superposition according to the state of designated address modes-implementing a QRAM on a single chip.

Tripartite Entanglement: Foundations and Applications

We review some current ideas of tripartite entanglement. In particular, we consider the case representing the next level of complexity beyond the simplest (though far from trivial) one, namely the bipartite case. This kind of entanglement plays an essential role in understanding the foundations of quantum mechanics. It also allows for implementing several applications in the fields of quantum information processing and quantum computing. In this paper, we review the fundamental aspects of tripartite entanglement focusing on Greenberger–Horne–Zeilinger and W states for discrete variables. We discuss the possibility of using it as a resource to execute quantum protocols and present some examples in detail.

Phonon-mediated quantum state transfer and remote qubit entanglement

Phonons, and in particular surface acoustic wave phonons, have been proposed as a means to coherently couple distant solid-state quantum systems. Individual phonons in a resonant structure can be controlled and detected by superconducting qubits, enabling the coherent generation and measurement of complex stationary phonon states. We report the deterministic emission and capture of itinerant surface acoustic wave phonons, enabling the quantum entanglement of two superconducting qubits. Using a 2-millimeter-long acoustic quantum communication channel, equivalent to a 500-nanosecond delay line, we demonstrate the emission and recapture of a phonon by one superconducting qubit, quantum state transfer between two superconducting qubits with a 67% efficiency, and, by partial transfer of a phonon, generation of an entangled Bell pair with a fidelity of 84%.

Deterministic Shaping and Reshaping of Single-Photon Temporal Wave Functions

Thorough control of the optical mode of a single photon is essential for quantum information applications. We present a comprehensive experimental and theoretical study of a light-matter interface based on cavity quantum electrodynamics. We identify key parameters like the phases of the involved light fields and demonstrate absolute, flexible, and accurate control of the time-dependent complex-valued wave function of a single photon over several orders of magnitude. This capability will be an important tool for the development of distributed quantum systems with multiple components that interact via photons.

Entanglement classifier in chemical reactions

The Einstein, Podolsky, and Rosen (EPR) entanglement, which features the essential difference between classical and quantum physics, has received wide theoretical and experimental attentions. Recently, the desire to understand and create quantum entanglement between particles such as spins, photons, atoms, and molecules is fueled by the development of quantum teleportation, quantum communication, quantum cryptography, and quantum computation. Although most of the work has focused on showing that entanglement violates the famous Bell's inequality and its generalization for discrete measurements, few recent attempts focus on continuous measurement results. Here, we have developed a general practical inequality to test entanglement for continuous measurement results, particularly scattering of chemical reactions. After we explain how to implement this inequality to classify entanglement in scattering experiments, we propose a specific chemical reaction to test the violation of this inequality. The method is general and could be used to classify entanglement for continuous measurement results.

Secure quantum remote state preparation of squeezed microwave states

Quantum communication protocols based on nonclassical correlations can be more efficient than known classical methods and offer intrinsic security over direct state transfer. In particular, remote state preparation aims at the creation of a desired and known quantum state at a remote location using classical communication and quantum entanglement. We present an experimental realization of deterministic continuous-variable remote state preparation in the microwave regime over a distance of 35 cm. By employing propagating two-mode squeezed microwave states and feedforward, we achieve the remote preparation of squeezed states with up to 1.6 dB of squeezing below the vacuum level. Finally, security of remote state preparation is investigated by using the concept of the one-time pad and measuring the von Neumann entropies. We find nearly identical values for the entropy of the remotely prepared state and the respective conditional entropy given the classically communicated information and, thus, demonstrate close-to-perfect security.

Photon-mediated electronic correlation effects in irradiated two-dimensional Dirac systems

Periodically driven systems can host many interesting phenomena. Two-dimensional Dirac systems irradiated by circularly polarized light are especially attractive thanks to the special absorption and emission of photons near Dirac cones. Here, letting the light travel in the two-dimensional plane, we treat the light-driven Dirac systems by using a unitary transformation, instead of usual Floquet theory, to capture the photon-mediated electronic correlation effects. In this approach, the direct electron-photon interaction terms can be removed and the resulting effective electron-electron interactions can produce important effects. The effective interactions can produce topological band structure in the case of irradiated 2D Dirac fermion system, and can lift the energy degeneracy of the Dirac cones for irradiated graphene. This method can be applied to other light-driven Dirac systems to investigate their photon-mediated electronic effects. These phenomena would be observed with ultraviolet light in some effective two-dimensional Dirac systems of honeycomb long-period superstructures.

Parity-Assisted Generation of Nonclassical States of Light in Circuit Quantum Electrodynamics

We propose a method to generate nonclassical states of light in multimode microwave cavities. Our approach considers two-photon processes that take place in a system composed of N extended cavities and an ultrastrongly coupled light–matter system. Under specific resonance conditions, our method generates, in a deterministic manner, product states of uncorrelated photon pairs, Bell states, and W states in different modes on the extended cavities. Furthermore, the numerical simulations show that the generation scheme exhibits a collective effect which decreases the generation time in the same proportion as the number of extended cavity increases. Moreover, the entanglement encoded in the photonic states can be transferred towards ancillary two-level systems to generate genuine multipartite entanglement. Finally, we discuss the feasibility of our proposal in circuit quantum electrodynamics. This proposal could be of interest in the context of quantum random number generator, due to the quadratic scaling of the output state.

Single-Loop Realization of Arbitrary Nonadiabatic Holonomic Single-Qubit Quantum Gates in a Superconducting Circuit

Geometric phases are noise resilient, and thus provide a robust way towards high-fidelity quantum manipulation. Here we experimentally demonstrate arbitrary nonadiabatic holonomic single-qubit quantum gates for both a superconducting transmon qubit and a microwave cavity in a single-loop way. In both cases, an auxiliary state is utilized, and two resonant microwave drives are simultaneously applied with well-controlled but varying amplitudes and phases for the arbitrariness of the gate. The resulting gates on the transmon qubit achieve a fidelity of 0.996 characterized by randomized benchmarking and the ones on the cavity show an averaged fidelity of 0.978 based on a full quantum process tomography. In principle, a nontrivial two-qubit holonomic gate between the qubit and the cavity can also be realized based on our presented experimental scheme. Our experiment thus paves the way towards practical nonadiabatic holonomic quantum manipulation with both qubits and cavities in a superconducting circuit.

Fast and Unconditional All-Microwave Reset of a Superconducting Qubit

Active qubit reset is a key operation in many quantum algorithms, and particularly in quantum error correction. Here, we experimentally demonstrate a reset scheme for a three-level transmon artificial atom coupled to a large bandwidth resonator. The reset protocol uses a microwave-induced interaction between the |f,0⟩ and |g,1⟩ states of the coupled transmon-resonator system, with |g⟩ and |f⟩ denoting the ground and second excited states of the transmon, and |0⟩ and |1⟩ the photon Fock states of the resonator. We characterize the reset process and demonstrate reinitialization of the transmon-resonator system to its ground state in less than 500 ns and with 0.2% residual excitation. Our protocol is of practical interest as it has no additional architectural requirements beyond those needed for fast and efficient single-shot readout of transmons, and does not require feedback.

Unitary entanglement construction in hierarchical networks

The construction of large-scale quantum computers will require modular architectures that allow physical resources to be localized in easy-to-manage packages. In this work we examine the impact of different graph structures on the preparation of entangled states. We begin by explaining a formal framework, the hierarchical product, in which modular graphs can be easily constructed. This framework naturally leads us to suggest a class of graphs, which we dub hierarchies. We argue that such graphs have favorable properties for quantum information processing, such as a small diameter and small total edge weight, and use the concept of Pareto efficiency to identify promising quantum graph architectures. We present numerical and analytical results on the speed at which large entangled states can be created on nearest-neighbor grids and hierarchy graphs. We also present a scheme for performing circuit placement-the translation from circuit diagrams to machine qubits-on quantum systems whose connectivity is described by hierarchies.