Distributed Quantum Computation Research Articles

Experimental quantum teleportation of a Toffoli gate across three spatially distributed parties in a photonic quantum network

Quantum computers may offer significant computational advantages over classical counterparts, revolutionizing the technology landscape in the near future. When networked together, the advantage of quantum computing may be further amplified, and there may emerge innovative applications. Among various active explorations on distributed quantum computing, multiqubit quantum gates between distant networked quantum computers are of particular interest because they offer operational advantages of efficiency and fidelity. Here we report the first experimental demonstration of quantum teleportation for a Toffoli gate, which is a commonly used multiqubit quantum gate, across three spatially distributed parties within a photonic quantum network. Employing the Hofmann method, we estimate the fidelity of the teleported Toffoli gate to be at least 0.706 ± 0.131. This successful demonstration of the quantum teleportation of a Toffoli gate constitutes a critical step toward the ultimate realization of distributed quantum computation.

Multi-objective simulated annealing-based quantum circuit cutting for distributed quantum computation

In the current noisy intermediate-scale quantum (NISQ) era, the number of qubits and the depth of quantum circuits in a quantum computer are limited because of complex operation among increasing number of qubits, low-fidelity quantum gates under noise, and short coherence time of physical qubits. However, with distributed quantum computation (DQC) in which multiple small-scale quantum computers cooperate, large-scale quantum circuits can be implemented. In DQC, it is a key step to decompose large-scale quantum circuits into several small-scale subcircuits equivalently. In this paper, we propose a quantum circuit cutting scheme for the circuits consisting of only single-qubit gates and two-qubit gates. In the scheme, the number of non-local gates and the rounds of subcircuits operation are minimized by using the multi-objective simulated annealing (MOSA) algorithm to cluster the gates and to choose the cutting positions whilst using non-local gates. A reconstruction process is also proposed to calculate the probability distribution of output states of the original circuit. As an example, the 7-qubit circuit of Shor algorithm factoring 15 is used to verify the algorithm. Five cutting schemes are recommended, which can be selected according to practical requirements. Compared with the results of the mixing integer programming (MIP) algorithm, the number of execution rounds is efficiently reduced by slightly increasing the number of nonlocal gates.

Efficient multi-party quantum secret-sharing protocol

ContextQuantum secret sharing allows one secret dealer to divide his/her secret among different participants. Only when all the participants pool their secret pieces together can the secret be reconstructed. Quantum secret-sharing protocol can provide high security for users who need to share some secret information among some partners. It is also a useful tool in many applications such as secure operations of joint sharing of quantum money, sharing ancilla states, and distributed quantum computation. ObjectiveWe propose a novel multi-party quantum secret-sharing protocol (MPQSSP). MethodsIn our protocol, the dealer mixes the particle sequence of the Bell states and sends the sequence to the participants. The participants encode their secret pieces into Pauli operators, which are applied to the received particle sequence. After annularly transmitting and operating the particle sequence, the participants return the particle sequence to the dealer, who can share a secret with the partners by measuring the returned sequence with the Bell basis. ResultsThe proposed MPQSSP has the merits as follows. First, its qubit efficiency can be 100% when the sample bits of the secret and the corresponding sample qubits are ignored (In our protocol when the qubit efficiency is computed, the sample bits and the corresponding Bell states used to check eavesdropping are ignored). Second, it can protect participants' privacy and interests, since the dealer cannot derive the secret piece of any participant although he/she masters the secret. Third, the participants need not perform many quantum operations and measurements to check the eavesdropping, which helps improve the efficiency of the protocol. Fourth, compared with most of the similar MPQSSPs, the quantum resources of the proposed one are relatively easier to prepare. At last, the proposed protocol has the security against various eavesdropping attacks. ConclusionThe merits above show that Our MPQSSP is relatively more practical and efficient than similar ones.

N-qubit universal quantum logic with a photonic qudit and O(N) linear optics elements

High-dimensional quantum units of information, or qudits, can carry more than one quantum bit of information in a single degree of freedom and can, therefore, be used to boost the performance of quantum communication and quantum computation protocols. A photon in a superposition of 2N time bins—a time-bin qudit—contains as much information as N qubits. Here, we show that N-qubit states encoded in a single time-bin qudit can be arbitrarily and deterministically generated, manipulated, and measured using a number of linear optics elements that scale linearly with N, as opposed to prior proposals of single-qudit implementation of N-qubit logic, which typically requires O(2N) elements. The simple and cost-effective implementation we propose can be used as a small-scale quantum processor. We then demonstrate a path toward scalability by interfacing distinct qudit processors to a matter qubit (atom or quantum dot spin) in an optical resonator. Such a cavity quantum electrodynamics system allows for more advanced functionalities, such as single-qubit nondemolition measurement and two-qubit gates between distinct qudits. It could also enable quantum interfaces with other matter quantum nodes in the context of quantum networks and distributed quantum computing.

Nonlocal photonic quantum gates over 7.0 km

Quantum networks provide a prospective paradigm to connect separated quantum nodes, which relies on the distribution of long-distance entanglement and active feedforward control of qubits between remote nodes. Such approaches can be utilized to construct nonlocal quantum gates, forming building blocks for distributed quantum computing and other novel quantum applications. However, these gates have only been realized within single nodes or between nodes separated by a few tens of meters, limiting the ability to harness computing resources in large-scale quantum networks. Here, we demonstrate nonlocal photonic quantum gates between two nodes spatially separated by 7.0 km using stationary qubits based on multiplexed quantum memories, flying qubits at telecom wavelengths, and active feedforward control based on field-deployed fibers. Furthermore, we illustrate quantum parallelism by implementing the Deutsch-Jozsa algorithm and the quantum phase estimation algorithm between the two remote nodes. These results represent a proof-of-principle demonstration of quantum gates over metropolitan-scale distances and lay the foundation for the construction of large-scale distributed quantum networks relying on existing fiber channels.

Blind Quantum Machine Learning with Quantum Bipartite Correlator.

Distributed quantum computing is a promising computational paradigm for performing computations that are beyond the reach of individual quantum devices. Privacy in distributed quantum computing is critical for maintaining confidentiality and protecting the data in the presence of untrusted computing nodes. In this Letter, we introduce novel blind quantum machine learning protocols based on the quantum bipartite correlator algorithm. Our protocols have reduced communication overhead while preserving the privacy of data from untrusted parties. We introduce robust algorithm-specific privacy-preserving mechanisms with low computational overhead that do not require complex cryptographic techniques. We then validate the effectiveness of the proposed protocols through complexity and privacy analysis. Our findings pave the way for advancements in distributed quantum computing, opening up new possibilities for privacy-aware machine learning applications in the era of quantum technologies.

Automatic Architecture Design for Distributed Quantum Computing

Abstract In distributed quantum computing (DQC), quantum hardware design mainly focuses on providing as many as possible high-quality inter-chip connections. Meanwhile, quantum software tries best to reduce the required number of remote quantum gates between chips. However, this "hardware first, software follows" methodology may not fully exploit the potential of DQC. Inspired by classical software-hardware co-design, this paper explores the design space of application-specific DQC architectures. More specifically, we propose AutoArch, an automated quantum chip network (QCN) structure design tool. With qubits grouping followed by a customized QCN design, AutoArch can generate a near-optimal DQC architecture suitable for target quantum algorithms. Experimental results show that the DQC architecture generated by AutoArch can outperform other general QCN architectures when executing target quantum algorithms.

A two-step linear programming approach for repeater placement in large-scale quantum networks

Thanks to the applications such as Quantum Key Distribution and Distributed Quantum Computing, the deployment of quantum networks is gaining great momentum. A major component in quantum networks is repeaters, which are essential for reducing the error rate of qubit transmission for long-distance links. However, repeaters are expensive devices, so minimizing the number of repeaters placed in a quantum network while satisfying performance requirements becomes an important problem. Existing solutions typically solve this problem optimally by formulating an Integer Linear Program (ILP). However, the number of variables in their ILPs is O(n2), where n is the number of nodes in a network. This incurs infeasible running time when the network scale is large. To overcome this drawback, this paper proposes to solve the repeater placement problem by two steps, with each step using a linear program of a much smaller scale with O(n) variables. Although this solution is not optimal, it dramatically reduces the time complexity, making it practical for large-scale networks. Moreover, it constructs networks that have higher node connectivity than those by existing solutions, since it deploys slightly more number of repeaters into networks. Our extensive experiments on both synthetic and real-world network topologies verified our claims.

Stabilizing Remote Entanglement via Waveguide Dissipation

Distributing entanglement between remote sites is integral to quantum networks. Here, we demonstrate the autonomous stabilization of remote entanglement between a pair of noninteracting superconducting qubits connected by an open waveguide on a chip. In this setting, the interplay between a classical continuous drive—supplied through the waveguide—and dissipation into the waveguide stabilizes the qubit pair in a dark state, which, asymptotically, takes the form of a Bell state. We use field-quadrature measurements of the photons emitted to the waveguide to perform quantum state tomography on the stabilized states, where we find a concurrence of 0.504−0.029+0.007 in the optimal setting with a stabilization time constant of 56±4 ns. We examine the imperfections within our system and discuss avenues for enhancing fidelities and achieving scalability in future work. The decoherence-protected steady-state remote entanglement offered via dissipative stabilization may find applications in distributed quantum computing, sensing, and communication. Published by the American Physical Society 2024

Automated Distribution of Polarization-Entangled Photons Using Deployed New York City Fibers

The distribution of high-fidelity high-rate entanglement over telecommunication infrastructure is one of the main paths toward large-scale quantum networks, enabling applications such as quantum encryption and network protection, blind quantum computing, distributed quantum computing, and distributed quantum sensing. However, the fragile nature of entangled photons operating in real-world fiber infrastructure has historically limited continuous operation of such networks. Here, we present a fully automated system capable of distributing polarization-entangled photons over a 34-km deployed fiber in New York City, achieving high rates of nearly 5×105 pairs/s. Separately, we demonstrate a high fidelity of approximately 99% for rates up to 2×104 pairs/s. Lastly, we achieve 15 days of continuous distribution, with a network up-time of 99.84%. Our work paves the way for practical deployment of always-on entanglement-based networks with rates and fidelity adequate for many current and future use cases. Published by the American Physical Society 2024

Thresholds for the distributed surface code in the presence of memory decoherence

In the search for scalable, fault-tolerant quantum computing, distributed quantum computers are promising candidates. These systems can be realized in large-scale quantum networks or condensed onto a single chip with closely situated nodes. We present a framework for numerical simulations of a memory channel using the distributed toric surface code, where each data qubit of the code is part of a separate node, and the error-detection performance depends on the quality of four-qubit Greenberger–Horne–Zeilinger (GHZ) states generated between the nodes. We quantitatively investigate the effect of memory decoherence and evaluate the advantage of GHZ creation protocols tailored to the level of decoherence. We do this by applying our framework for the particular case of color centers in diamond, employing models developed from experimental characterization of nitrogen-vacancy centers. For diamond color centers, coherence times during entanglement generation are orders of magnitude lower than coherence times of idling qubits. These coherence times represent a limiting factor for applications, but previous surface code simulations did not treat them as such. Introducing limiting coherence times as a prominent noise factor makes it imperative to integrate realistic operation times into simulations and incorporate strategies for operation scheduling. Our model predicts error probability thresholds for gate and measurement reduced by at least a factor of three compared to prior work with more idealized noise models. We also find a threshold of 4×102 in the ratio between the entanglement generation and the decoherence rates, setting a benchmark for experimental progress.

Single entanglement connection architecture between multi-layer bipartite hardware efficient ansatz

Variational quantum algorithms are among the most promising algorithms to achieve quantum advantages in the noisy intermediate-scale quantum (NISQ) era. One important challenge in implementing such algorithms is to construct an effective parameterized quantum circuit (also called an ansatz). In this work, we propose a single entanglement connection architecture (SECA) for a bipartite hardware efficient ansatz (HEA) by balancing its expressibility, entangling capability, and trainability. Numerical simulations with a one-dimensional Heisenberg model and quadratic unconstrained binary optimization (QUBO) issues were conducted. Our results indicate the superiority of SECA over the common full entanglement connection architecture in terms of computational performance. Furthermore, combining SECA with gate-cutting technology to construct distributed quantum computation (DQC) can efficiently expand the size of NISQ devices under low overhead. We also demonstrated the effectiveness and scalability of the DQC scheme. Our study is a useful indication for understanding the characteristics associated with an effective training circuit.

Preface

From 22nd to 24th December 2023, the 2023 3rd International Conference on Computational Modeling, Simulation and Data Analysis (CMSDA 2023) was held in Sanya, China via virtual form. The Conference attracted about 150 researchers, engineers, teachers and students worldwide working in or interested in the fields related to computational modeling, simulation and data analysis. The general objectives of the CMSDA 2023 were: To generate an adequate academic and scientific forum to present the work and experiences of researchers/teachers/students, contributing, in this way, to the production of new knowledge in the fields of computational modeling and data analysis. To create a path of establishing certain relationships for the speakers, authors and listeners, and providing opportunities for collaboration among the universities and institutions, in order to promote scientific research activities and develop relevant technologies. The subject areas in which the accepted papers were presented cover but are but not limited to: Perceptual Issues in Visualization and Modeling; Mathematical and Numerical Methods in Simulation and Modeling; Parallel and Distributed Computing Simulation; Big Data Visual Analysis; Data Analysis Algorithms and Systems, etc. We have invited renowned professors at home and abroad in these academic fields who shared with the attendees the latest innovations and research results in the domains of computational modeling, data mining and analysis. The Conference mainly featured keynote speeches by renowned experts and presentations of peer-reviewed papers by the authors. Among them, Prof. Daowen Qiu (Sun Yat-Sen University, China) shared his research on Distributed Quantum Algorithm for Simon’s Problem. Limited by today’s physical devices, quantum circuits are usually noisy and difficult to be designed deeply. The novel computing architecture of distributed quantum computing is expected to reduce the noise and depth of quantum circuits. And in his study, he presented the Simon’s problem in distributed scenarios and designed a distributed quantum algorithm to solve the problem. The algorithm proposed by him has the advantage of not only exponential acceleration compared with the classical distributed computing, but also square acceleration compared with the best distributed quantum algorithm proposed before. The Conference Proceedings was made so fruitful with all the excellent contributions collected from both domestic and international channels including the wonderful presentations in the Conference. It is a pleasure to thank the organizers, sponsors and all the participants and contributors for making the Conference possible and interesting. And our appreciation also to the members of Journal of Physics: Conference Series for providing us help in publishing this paper volume. The Committee of CMSDA 2023 List of Committee Member is available in this pdf.

Schrödinger as a Quantum Programmer: Estimating Entanglement via Steering

Quantifying entanglement is an important task by which the resourcefulness of a quantum state can be measured. Here, we develop a quantum algorithm that tests for and quantifies the separability of a general bipartite state by using the quantum steering effect, the latter initially discovered by Schrödinger. Our separability test consists of a distributed quantum computation involving two parties: a computationally limited client, who prepares a purification of the state of interest, and a computationally unbounded server, who tries to steer the reduced systems to a probabilistic ensemble of pure product states. To design a practical algorithm, we replace the role of the server with a combination of parameterized unitary circuits and classical optimization techniques to perform the necessary computation. The result is a variational quantum steering algorithm (VQSA), a modified separability test that is implementable on quantum computers that are available today. We then simulate our VQSA on noisy quantum simulators and find favorable convergence properties on the examples tested. We also develop semidefinite programs, executable on classical computers, that benchmark the results obtained from our VQSA. Thus, our findings provide a meaningful connection between steering, entanglement, quantum algorithms, and quantum computational complexity theory. They also demonstrate the value of a parameterized mid-circuit measurement in a VQSA.

Bidirectional state transfer between superconducting and microwave-photon qubits by single reflection

The number of superconducting qubits contained in a single quantum processor is increasing steadily. However, to realize a truly useful quantum computer, it is inevitable to increase the number of qubits much further by distributing quantum information among distant processors using flying qubits. A key element towards this goal is a deterministic quantum interaction between superconducting-atom and propagating microwave-photon qubits. Here, we confirm the bidirectional state transfer between them, which completes by simply reflecting the photon at the atom. The averaged fidelity of the photon-to-atom (atom-to-photon) state transfer reaches 0.826 (0.801), limited mainly by the lifetime of the atom qubit. The present technology would be useful for future distributed quantum computation with superconducting qubits. Published by the American Physical Society 2024

All-optical spin access via a cavity-broadened optical transition in on-chip hybrid quantum photonics

Hybrid quantum photonic systems connect classical photonics to the quantum world and promise to deliver efficient light-matter quantum interfaces while leveraging the advantages of both, the classical and the quantum, subsystems. However, combining efficient, scalable photonics and solid-state quantum systems with desirable optical and spin properties remains a formidable challenge. In particular, the access to individual spin states and coherent mapping to photons remains unsolved for hybrid systems. In this paper, we demonstrate all-optical initialization and readout of the electron spin of a negatively charged silicon-vacancy center in a nanodiamond coupled to a silicon nitride photonic crystal cavity. We characterize relevant parameters of the coupled emitter-cavity system and determine the silicon-vacancy center’s spin-relaxation and spin-decoherence rate. Our results mark a key step towards the realization of a hybrid spin-photon interface based on silicon nitride photonics and the silicon-vacancy center’s electron spin in nanodiamonds with potential use for quantum networks, quantum communication, and distributed quantum computation. Published by the American Physical Society 2024

Low-cost nonlocal Toffoli gate in a linear quantum network topology

Although a Toffoli gate can be equivalently implemented using several single-qubit and two-qubit gates, it will consume much resource, two of which are nonlocal controlled-NOT (CNOT) gates acting on two non-adjacent nodes, especially in distributed quantum computation (DQC). We, for the first time, employ an ancillary qubit to construct a nonlocal Toffoli gate for DQC in linear network topology. The ancillary-qubit-based scheme needs fewer qubits, quantum gates, and entanglement states than that based on quantum teleportation scheme and the entanglement swapping scheme. We also analyze the performance of the three proposed schemes under different application scenarios, and present their pros and cons. Our work will help to implement DQC in noisy intermediate-scale quantum (NISQ) era.

Privacy-preserving quantum federated learning via gradient hiding

Distributed quantum computing, particularly distributed quantum machine learning, has gained substantial prominence for its capacity to harness the collective power of distributed quantum resources, transcending the limitations of individual quantum nodes. Meanwhile, the critical concern of privacy within distributed computing protocols remains a significant challenge, particularly in standard classical federated learning (FL) scenarios where data of participating clients is susceptible to leakage via gradient inversion attacks by the server. This paper presents innovative quantum protocols with quantum communication designed to address the FL problem, strengthen privacy measures, and optimize communication efficiency. In contrast to previous works that leverage expressive variational quantum circuits or differential privacy techniques, we consider gradient information concealment using quantum states and propose two distinct FL protocols, one based on private inner-product estimation and the other on incremental learning. These protocols offer substantial advancements in privacy preservation with low communication resources, forging a path toward efficient quantum communication-assisted FL protocols and contributing to the development of secure distributed quantum machine learning, thus addressing critical privacy concerns in the quantum computing era.

Superadiabatic-based shortcuts for the fast generation of multi-partite W states of distant transmon qubits

We propose an efficient scheme for the fast generating three-partite W states of distant transmon qubits. With the help of superadiabatic shortcuts technology, we construct shortcuts to adiabaticity (STA) passage. The Rabi frequencies of the designed driving pulses in the scheme can be expressed by the superpositions of Gaussian functions. These make our scheme more feasible in the experiment. Compare with the adiabatic case, we show that the preparation of the target state can be greatly accelerated. We analyze the influences of decoherent factors on the fidelity of W states, and numerical results show our proposal is suitable to generate high fidelity three-partite W states. In addition, the present scheme can also be generalized to prepare n-partite W states of distant transmon qubits. This work may useful applications for the realization of distributed quantum computation.

DECENTRALIZED QUANTUM COMPILATION FRAMEWORK: EMPOWERING DISTRIBUTED QUANTUM COMPUTING THROUGH MODULARITY

Quantum algorithms require large resources in terms of qubit number, much larger than those available with current NISQ processors. With the network and communication functionalities provided by the Quantum Internet, Distributed Quantum Computing (DQC) is considered as a scalable approach for increasing the number of available qubits for computational tasks. For DQC to be effective and efficient, a quantum compiler must find the best partitioning for the quantum algorithm and then perform smart remote operation scheduling to optimize EPR pair consumption. At the same time, the quantum compiler should also find the best local transformation for each partition. In this paper we present a modular quantum compilation framework for DQC that takes into account both network and device constraints and characteristics. We implemented and tested a quantum compiler based on the proposed framework with some circuits of interest, such as the VQE and QFT ones, considering different network topologies, with quantum processors characterized by heavy hexagon coupling maps. We also devised a strategy for remote scheduling that can exploit both TeleGate and TeleData operations and tested the impact of using either only TeleGates or both. The evaluation results show that TeleData operations may have a positive impact on the number of consumed EPR pairs, while choosing a more connected network topology helps reduce the number of layers dedicated to remote operations. Keywords— Distributed quantum computing (DQC), quantum compilation, quantum Internet