Generation Of Graph States Research Articles

Optical spin initialization and readout with a cavity-coupled quantum dot in an in-plane magnetic field

The spin of a charged semiconductor quantum dot (QD) coupled to an optical cavity is a promising candidate for high-fidelity spin-photon interfaces; the cavity selectively modifies the decay rates of optical transitions such that spin initialization, manipulation, and readout are all possible in a single magnetic field geometry. By performing cavity QED calculations, we show that a cavity with a single, linearly polarized mode can simultaneously support both high-fidelity optical spin initialization and readout in a single, in-plane (Voigt geometry) magnetic field. Furthermore, we demonstrate that single-mode cavities always outperform bimodal cavities in experimentally favorable driving regimes. Our analysis, when combined with established methods of control in a Voigt geometry field, provides optimal parameter regimes for high-fidelity initialization and readout, and coherent control in both cavity configurations, providing insights for the design and development of QD spin-photon interfaces as the basis of quantum network nodes and for the generation of photonic graph states. Published by the American Physical Society 2024

GraphiQ: Quantum circuit design for photonic graph states

GraphiQ is a versatile open-source framework for designing photonic graph state generation schemes, with a particular emphasis on photon-emitter hybrid circuits. Built in Python, GraphiQ consists of a suite of design tools, including multiple simulation backends and optimization methods. The library supports scheme optimization in the presence of circuit imperfections, as well as user-defined optimization goals. Our framework thus represents a valuable tool for the development of practical schemes adhering to experimentally-relevant constraints. As graph states are a key resource for measurement-based quantum computing, all-photonic quantum repeaters, and robust quantum metrology, among others, we envision GraphiQ's broad impact for advancing quantum technologies.

Graph states of atomic ensembles engineered by photon-mediated entanglement

Graph states are a broad family of entangled quantum states, each defined by a graph composed of edges representing the correlations between subsystems. Such states constitute versatile resources for quantum computation and quantum-enhanced measurement. Their generation and engineering require a high level of control over entanglement. Here we report on the generation of continuous-variable graph states of atomic spin ensembles, which form the nodes of the graph. We program the entanglement structure encoded in the graph edges by combining global photon-mediated interactions in an optical cavity with local spin rotations. By tuning the entanglement between two subsystems, we either localize correlations within each subsystem or enable Einstein–Podolsky–Rosen steering—a strong form of entanglement that enables the extraction of precise information from one subsystem through measurements on the other. We further engineer a four-mode square graph state, highlighting the flexibility of our approach. Our method is scalable to larger and more complex graphs, laying groundwork for measurement-based quantum computation and advanced protocols in quantum metrology.

Graph-theoretical optimization of fusion-based graph state generation

Graph states are versatile resources for various quantum information processing tasks, including measurement-based quantum computing and quantum repeaters. Although the type-II fusion gate enables all-optical generation of graph states by combining small graph states, its non-deterministic nature hinders the efficient generation of large graph states. In this work, we present a graph-theoretical strategy to effectively optimize fusion-based generation of any given graph state, along with a Python package OptGraphState. Our strategy comprises three stages: simplifying the target graph state, building a fusion network, and determining the order of fusions. Utilizing this proposed method, we evaluate the resource overheads of random graphs and various well-known graphs. Additionally, we investigate the success probability of graph state generation given a restricted number of available resource states. We expect that our strategy and software will assist researchers in developing and assessing experimentally viable schemes that use photonic graph states.

Near-deterministic hybrid generation of arbitrary photonic graph states using a single quantum emitter and linear optics

Since linear-optical two-photon gates are inherently probabilistic, measurement-based implementations are particularly well suited for photonic platforms: a large highly-entangled photonic resource state, called a graph state, is consumed through measurements to perform a computation. The challenge is thus to produce these graph states. Several generation procedures, which use either interacting quantum emitters or efficient spin-photon interface, have been proposed to create these photonic graph states deterministically. Yet, these solutions are still out of reach experimentally since the state-of-the-art is the generation of a linear graph state. Here, we introduce near-deterministic solutions for the generation of graph states using the current quantum emitter capabilities. We propose hybridizing quantum-emitter-based graph state generation with all-photonic fusion gates to produce graph states of complex topology near-deterministically. Our results should pave the way towards the practical implementation of resource-efficient quantum information processing, including measurement-based quantum communication and quantum computing.

Coherent driving of direct and indirect excitons in a quantum dot molecule

Quantum dot molecules (QDMs) are one of the few quantum light sources that promise deterministic generation of one- and two-dimensional photonic graph states. The proposed protocols rely on coherent excitation of the tunnel-coupled and spatially indirect exciton states. Here, we demonstrate power-dependent Rabi oscillations of direct excitons, spatially indirect excitons, and excitons with a hybridized electron wave function. An off-resonant detection technique based on phonon-mediated state transfer allows for spectrally filtered detection under resonant excitation. Applying a gate voltage to the QDM-device enables a continuous transition between direct and indirect excitons and, thereby, control of the overlap of the electron and hole wave function. This does not only vary the Rabi frequency of the investigated transition by a factor of $\approx3$, but also allows to optimize graph state generation in terms of optical pulse power and reduction of radiative lifetimes.

Parity-encoding-based quantum computing with Bayesian error tracking

Measurement-based quantum computing (MBQC) in linear optical systems is promising for near-future quantum computing architecture. However, the nondeterministic nature of entangling operations and photon losses hinder the large-scale generation of graph states and introduce logical errors. In this work, we propose a linear optical topological MBQC protocol employing multiphoton qubits based on the parity encoding, which turns out to be highly photon-loss tolerant and resource-efficient even under the effects of nonideal entangling operations that unavoidably corrupt nearby qubits. For the realistic error analysis, we introduce a Bayesian methodology, in conjunction with the stabilizer formalism, to track errors caused by such detrimental effects. We additionally suggest a graph-theoretical optimization scheme for the process of constructing an arbitrary graph state, which greatly reduces its resource overhead. Notably, we show that our protocol is advantageous over several other existing approaches in terms of the fault-tolerance and resource overhead.

A quantum processor based on coherent transport of entangled atom arrays

The ability to engineer parallel, programmable operations between desired qubits within a quantum processor is key for building scalable quantum information systems1,2. In most state-of-the-art approaches, qubits interact locally, constrained by the connectivity associated with their fixed spatial layout. Here we demonstrate a quantum processor with dynamic, non-local connectivity, in which entangled qubits are coherently transported in a highly parallel manner across two spatial dimensions, between layers of single- and two-qubit operations. Our approach makes use of neutral atom arrays trapped and transported by optical tweezers; hyperfine states are used for robust quantum information storage, and excitation into Rydberg states is used for entanglement generation3–5. We use this architecture to realize programmable generation of entangled graph states, such as cluster states and a seven-qubit Steane code state6,7. Furthermore, we shuttle entangled ancilla arrays to realize a surface code state with thirteen data and six ancillary qubits8 and a toric code state on a torus with sixteen data and eight ancillary qubits9. Finally, we use this architecture to realize a hybrid analogue–digital evolution2 and use it for measuring entanglement entropy in quantum simulations10–12, experimentally observing non-monotonic entanglement dynamics associated with quantum many-body scars13,14. Realizing a long-standing goal, these results provide a route towards scalable quantum processing and enable applications ranging from simulation to metrology.

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. Wemeasure 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.

Generation of arbitrary all-photonic graph states from quantum emitters

We present protocols to generate arbitrary photonic graph states from quantum emitters that are in principle deterministic. We focus primarily on two-dimensional cluster states of arbitrary size due to their importance for measurement-based quantum computing. Our protocols for these and many other types of two-dimensional graph states require a linear array of emitters in which each emitter can be controllably pumped, rotated about certain axes, and entangled with its nearest neighbors. We show that an error on one emitter produces a localized region of errors in the resulting graph state, where the size of the region is determined by the coordination number of the graph. We describe how these protocols can be implemented for different types of emitters, including trapped ions, quantum dots, and nitrogen-vacancy centers in diamond.

A quantum network stack and protocols for reliable entanglement-based networks

We present a stack model for breaking down the complexity of entanglement-based quantum networks. More specifically, we focus on the structures and architectures of quantum networks and not on concrete physical implementations of network elements. We construct the quantum network stack in a hierarchical manner comprising several layers, similar to the classical network stack, and identify quantum networking devices operating on each of these layers. The layers responsibilities range from establishing point-to-point connectivity, over intra-network graph state generation, to inter-network routing of entanglement. In addition we propose several protocols operating on these layers. In particular, we extend the existing intra-network protocols for generating arbitrary graph states to ensure reliability inside a quantum network, where here reliability refers to the capability to compensate for devices failures. Furthermore, we propose a routing protocol for quantum routers which enables the generation of arbitrary graph states across network boundaries. This protocol, in correspondence with classical routing protocols, can compensate dynamically for failures of routers, or even complete networks, by simply re-routing the given entanglement over alternative paths. We also consider how to connect quantum routers in a hierarchical manner to reduce complexity, as well as reliability issues arising in connecting these quantum networking devices.

Photonic graph state generation from quantum dots and color centers for quantum communications

Highly entangled graph states of photons have applications in universal quantum computing and in quantum communications. In the latter context, they have been proposed as the key ingredient in the establishment of long-distance entanglement across quantum repeater networks. Recently, a general deterministic approach to generate repeater graph states from quantum emitters was given. However, a detailed protocol for the generation of such states from realistic systems is still needed in order to guide experiments. Here, we provide such explicit protocols for the generation of repeater graph states from two types of quantum emitters: NV centers in diamond and self-assembled quantum dots. A crucial element of our designs is an efficient controlled-Z gate between the emitter and a nuclear spin, used as an ancilla qubit. Additionally, a fast protocol for using pairs of exchange-coupled quantum dots to produce repeater graph states is described. Our focus is on near-term experiments feasible with existing experimental capabilities.

Modular architectures for quantum networks

We consider the problem of generating multipartite entangled states in a quantum network upon request. We follow a top-down approach, where the required entanglement is initially present in the network in form of network states shared between network devices, and then manipulated in such a way that the desired target state is generated. This minimizes generation times, and allows for network structures that are in principle independent of physical links. We present a modular and flexible architecture, where a multi-layer network consists of devices of varying complexity, including quantum network routers, switches and clients, that share certain resource states. We concentrate on the generation of graph states among clients, which are resources for numerous distributed quantum tasks. We assume minimal functionality for clients, i.e. they do not participate in the complex and distributed generation process of the target state. We present architectures based on shared multipartite entangled Greenberger–Horne–Zeilinger states of different size, and fully connected decorated graph states, respectively. We compare the features of these architectures to an approach that is based on bipartite entanglement, and identify advantages of the multipartite approach in terms of memory requirements and complexity of state manipulation. The architectures can handle parallel requests, and are designed in such a way that the network state can be dynamically extended if new clients or devices join the network. For generation or dynamical extension of the network states, we propose a quantum network configuration protocol, where entanglement purification is used to establish high fidelity states. The latter also allows one to show that the entanglement generated among clients is private, i.e. the network is secure.

Universal weighted graph state generation with the cross phase modulation

We introduce an architecture of cascade C Z θ operation for conveniently generating universal weighted graph state. The entanglement bonds between dependent or independent single photons can be created efficiently with only one ancilla single photon. The generation is scalable for universal weighted graph states, including arbitrary two-dimensional or three-dimensional weighted graph states. Moreover, the generation is flexible, including that the controlled phase shift θ between each pair of single photons can be different, the traces of the ancilla single photon walking is not fixed, and the prior entangled states are not required.

Optical parity gate and a wide range of entangled states generation

Generating entangled states efficiently is a hot topic in the area of quantum information science. With the approach presented in this paper, a general parity gate could be realized and a wide range of entangled states, including GHZ state, W state, Dicke state, arbitrary graph state and locally maximally entanglable states, can be generated flexibly. The generation of GHZ state, W state, and Dicke state is probabilistic but heralded and the total success probability is unit. In addition, the arbitrary graph state and locally maximally entanglable states generation is deterministic, flexible, and highly efficient. Especially, with the “simultaneous” generation pattern, the complexity of the graph state generation and locally maximally entanglable states generation could be reduced greatly, providing a more efficient and feasible way to generate the entangled states.

Efficient graph state generation and operation error detection with a controlled-path gate

How to generate photonic graph states efficiently is the main problem in optical measurement-based quantum computation. We propose a deterministic approach based on an element two-qubit gate called the controlled-path (CP) gate (Lin and He 2009 Phys. Rev. A 80 042310 and Lin et al 2009 Phys. Rev. A 80 042311) for this purpose. For the generation of wheel-shaped graph states, the procedure is especially simplified compared with the other methods. Moreover, we consider the possibility of finding the operation errors occurring in generating the graph states of large numbers of qubits; the use of the CP gate allows us to detect with a certain probability if an entangling operation is missing for the input qubits.

Generation of atomic momentum cluster and graph states via cavity QED

We present an experimentally feasible method, based on currently available cavity QED technology, to generate n-partite linear cluster and graph states in external degree of freedom of atoms. The scheme is based on first tagging n two-level atoms with the respective cavity fields in momentum space. Later on an effective Ising interaction between such tagged atoms, realized through consecutive resonant and dispersive interactions of auxiliary atoms with the remanent cavity fields, can generate the desired atomic momenta states. The procedure is completed when the auxiliary atoms after passing through Ramsey zones are detected in either of their internal states. We also briefly explain the generation of weighted graph states in the atomic external degree of freedom.

Generation of Multi-qubit Graph States via Spin Networks

We propose an efficient scheme for preparing multi-qubit graph states via spin networks. The classical types of graph states including cluster state, Greenberger-Horne-Zeilinger state and circle-shaped states can be generated by using imaginary SWAP gate. Our method makes the generation of multipartite entangled graph states more efficient than the ones based on conventional controlled-NOT and controlled phase flip gate for solid-state devices.

Generation of graph-state streams

We propose a protocol to generate a stream of mobile qubits in a graph state through a single stationary parent qubit and discuss two types of its physical implementation, namely, the generation of photonic graph states through an atom-like qubit and those of flying atoms through a cavity-mode photonic qubit. The generated graph states fall into an important class that can hugely reduce the resource requirement of fault-tolerant linear optics quantum computation, which was previously known to be far from realistic. In regard to the flying atoms, we also propose a heralded generation scheme, which allows for high-fidelity graph states even under the photon loss.

Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state

Coherent manipulation of an increasing number of qubits for the generation of entangled states has been an important goal and benchmark in the emerging field of quantum information science. The multiparticle entangled states serve as physical resources for measurement-based quantum computing and high-precision quantum metrology. However, their experimental preparation has proved extremely challenging. To date, entangled states up to six, eight atoms, or six photonic qubits have been demonstrated. Here, by exploiting both the photons' polarization and momentum degrees of freedom, we report the creation of hyper-entangled six-, eight-, and ten-qubit Schr\"odinger cat states. We characterize the cat states by evaluating their fidelities and detecting the presence of genuine multi-partite entanglement. Small modifications of the experimental setup will allow the generation of various graph states up to ten qubits. Our method provides a shortcut to expand the effective Hilbert space, opening up interesting applications such as quantum-enhanced super-resolving phase measurement, graph-state generation for anyonic simulation and topological error correction, and novel tests of nonlocality with hyper-entanglement.