Building a large-scale quantum computer with continuous-variable optical technologies

To see the feasibility of a large-scale quantum computing, it is required to accurately analyze the performance and the quantum resource. However, most of the analysis reported so far have focused on the statistical examination, i.e., simply calculating the performance and resource based on individual data, and even worse usually only a few components have been considered. In this work, to achieve more exact analysis, we propose an integrated analysis method for a practical quantum computing model with three components (\textit{algorithm}, \textit{error correction} and \textit{device}) under a realistic quantum computer system architecture. To implement the above method, we develop a quantum computing framework composed of three functional layers: compile, system and building block. This framework can support, for the first time, the mapping of quantum algorithm from physical qubit level to system architecture level with a given fault-tolerant scheme. Therefore, the proposed method can measure the effect of dynamic situation when the quantum computer practically runs. By using our method, we found that Shor algorithm to factorize 512-bit integer requires $8.78\times 10^ 5$ hours. We also show how the proposed method can be used for analyzing optimal concatenation level and code distance of fault-tolerant quantum computing.

The Google Quantum AI team's long-term goal is to realize a large-scale fault-tolerant quantum computer. Of the technologies available to implement the quantum processor at the core of such a system, solid-state superconducting circuits based on Josephson junctions (JJs) are among the strongest contenders. Recent demonstrations with this technology include computation beyond the capabilities of today's most powerful supercomputers [1] and execution of quantum error correction (QEC) codes that can detect and correct either bit or phase flip errors [2]. These exciting results were enabled by low-error-rate quantum processors with tens of qubits and the supporting infrastructure to run these devices. However, today's quantum computers still have orders of magnitude fewer qubits than is required for a useful fault-tolerant quantum computer; for this, an estimated million or more qubits will be needed and scaling-up today's technology to this extent is non-trivial. Here, we review the Google Quantum AI team's recent progress and future plans. Specifically, we describe our post-classical Sycamore quantum computer and discuss the Google Quantum AI roadmap to fault-tolerant quantum computing.

Quantum computing becomes viable when a quantum state can be protected from environment-induced error. If quantum bits (qubits) are sufficiently reliable, errors are sparse and quantum error correction (QEC) is capable of identifying and correcting them. Adding more qubits improves the preservation of states by guaranteeing that increasingly larger clusters of errors will not cause logical failure-a key requirement for large-scale systems. Using QEC to extend the qubit lifetime remains one of the outstanding experimental challenges in quantum computing. Here we report the protection of classical states from environmental bit-flip errors and demonstrate the suppression of these errors with increasing system size. We use a linear array of nine qubits, which is a natural step towards the two-dimensional surface code QEC scheme, and track errors as they occur by repeatedly performing projective quantum non-demolition parity measurements. Relative to a single physical qubit, we reduce the failure rate in retrieving an input state by a factor of 2.7 when using five of our nine qubits and by a factor of 8.5 when using all nine qubits after eight cycles. Additionally, we tomographically verify preservation of the non-classical Greenberger-Horne-Zeilinger state. The successful suppression of environment-induced errors will motivate further research into the many challenges associated with building a large-scale superconducting quantum computer.

One reason why building large-scale quantum computers will be particularly challenging is that quantum computers are far more susceptible to making errors than conventional digital computers. I will explain the principles of quantum error correction and fault-tolerant quantum computation, which can enable a properly designed quantum computer with imperfect components to achieve good reliability. Some recent developments in the theory of quantum fault tolerance will be reviewed, including quantum error-correcting codes for systems described by continuous quantum variables, robust storage of quantum information based on topological principles, and applications of quantum error-correcting codes to quantum cryptography.

Active quantum error correction has been identified as a crucial ingredient of future quantum computers, motivating the recent experimental efforts to encode logical quantum bits using small topological codes. In addition to the demonstration of the beneficial role of the encoding, a break-even point in the progress towards large-scale quantum computers will be the implementation of a universal set of gates. This midterm challenge will soon be faced by various quantum technologies, which urges the need of realistic assessments of their prospects. In this work, we pursue this goal by assessing the capability of current trapped-ion architectures in facing one of the most demanding parts of this quest: the implementation of an entangling controlled-NOT (CNOT) gate between encoded logical qubits. We present a detailed comparative study of two alternative strategies for trapped-ion topological color codes, either a transversal or a lattice-surgery approach, characterized by a detailed microscopic modeling of both current technological capabilities and experimental sources of noise afflicting the different operations. Our careful fault-tolerant design, together with a low-resource optimization, allows us to determine via exhaustive numerical simulations the experimental regimes where each of the approaches becomes favorable. We hope that our study thereby contributes to guiding the future development of trapped-ion quantum computers.

Large-scale quantum computers can solve certain problems that are not tractable by currently available classical computational resources. The building blocks of quantum computers are qubits. Among many different physical realizations for qubits, superconducting qubits are one of the promising candidates to realize gate model quantum computers. In this dissertation, we present new multi-qubit gates for nearest-neighbor superconducting quantum systems. In the absence of a physical hardware, we simulate the dynamics of the quantum system and use the simulated environment as a framework for test, design, and optimization of quantum gates and architectures. We explore three different simulation-based gate design methodologies: analytical approach, heuristic method, and machine learning techniques. Furthermore, we propose novel quantum error correction architectures utilizing our new gates, which have reduced computational overhead with better performance and reliability.

To implement fault-tolerant quantum computation with continuous variables, the Gottesman--Kitaev--Preskill (GKP) qubit has been recognized as an important technological element. We have proposed a method to reduce the required squeezing level to realize large scale quantum computation with the GKP qubit [Phys. Rev. X. {\bf 8}, 021054 (2018)], harnessing the virtue of analog information in the GKP qubits. In the present work, to reduce the number of qubits required for large scale quantum computation, we propose the tracking quantum error correction, where the logical-qubit level quantum error correction is partially substituted by the single-qubit level quantum error correction. In the proposed method, the analog quantum error correction is utilized to make the performances of the single-qubit level quantum error correction almost identical to those of the logical-qubit level quantum error correction in a practical noise level. The numerical results show that the proposed tracking quantum error correction reduces the number of qubits during a quantum error correction process by the reduction rate $\left\{{2(n-1)\times4^{l-1}-n+1}\right\}/({2n \times 4^{l-1}})$ for $n$-cycles of the quantum error correction process using the Knill's $C_{4}/C_{6}$ code with the concatenation level $l$. Hence, the proposed tracking quantum error correction has great advantage in reducing the required number of physical qubits, and will open a new way to bring up advantage of the GKP qubits in practical quantum computation.

Quantum computing has the capability of parallel computing and is superior to classical computing in solving some specific problems. Once a large-scale quantum computer is developed, the security of classical cryptographic algorithms and protocols, which is based on the assumption of computational complexity, will be severely challenged. Quantum cryptography is a new cryptosystem; its security is based on the principles of quantum mechanics, and can resist the attack of quantum computing. This paper focuses on the nearly 40 years development of quantum cryptographic protocols, including quantum key distribution (QKD), quantum secure direct communication, quantum secret sharing, quantum identity authentication, two-party secure computation, and quantum private query, and summarizes the problems in the process of development. The analysis shows that the quantum cryptographic protocols are in an unbalanced state: QKD is far ahead of other protocols and other protocols are difficult to achieve breakthroughs. In the future, practical quantum protocols for digital signature and two-party secure computation are core issues that needs to be addressed urgently. Therefore, research on quantum and post-quantum cryptography should be conducted synchronously, cross-over study and talent cultivation for the quantum science and cryptography disciplines should be strengthened, and the examination and evaluation mechanism of relevant basic research needs to be optimized.

There are a number of systems that are currently being considered as candidates for the construction of qubits, quantum logic gates and quantum computers. Some of the systems, notably atoms in magnetic traps and nuclear magnetic resonance (NMR) systems, have had some success in performing the elementary operations that would be required in large-scale quantum computer. However, these systems are not necessarily seen as viable technologies for quantum computing in the longer term. The recent demonstration of macroscopic coherence in a superconducting ring (consisting of a thick superconducting ring containing one or more Josephson weak link devices) has added significant weight to the idea of using superconducting persistent current devices (SQUIDs) in quantum logic systems. In this paper, we consider one aspect of the quantum mechanical SQUID, the nonlinear effect of SQUID on the classical control parameters, and we discuss how it may influence the construction and design of quantum logic gates based on SQUID devices. In particular, we look at problems associated with fixing the classical magnetic flux bias for a quantum mechanical SQUID at, or near, a quantum mechanical transition or resonance.

A lower bound on the amount of energy needed to carry out an elementary logical operation on a quantum computer, with a given accuracy and in a given time, is derived. The bound arises from the requirement that the controls used to manipulate the qubits, which ultimately are themselves quan-tum mechanical systems, must nonetheless be classical to a sufficiently good approximation; it is expected to hold under a wide variety of conditions, and independently of the nature of the physical systems used to encode the qubits. This could have important consequences for very large-scale quantum computations.

Quantum security is an evolving field that leverages principles of quantum physics to strengthen computing systems. Core concepts such as superposition and entanglement are foundation to this domain. However, current systems face significant challenges due to the extraordinary processing capabilities of quantum computers. As large-scale quantum computers with high qubit counts become operational, existing cybersecurity mechanisms are increasingly inadequate. This rapid advancement in quantum computing poses substantial risks to software, networks, web-based systems, and other security measures. To address these challenges, enhancing cybersecurity mechanisms is imperative. This paper explores various quantum security strategies categorized into six mechanisms (E1 to E6) and examines their effects on cybersecurity factors labeled H1 through H8. The analysis employs the Fuzzy Analytic Hierarchy Process (F-AHP) method, which assesses the relative importance of these factors based on an extensive literature review. By calculating the weight of different security aspects, the F-AHP method provides insights to prioritize critical components throughout the development cycle. The findings reveal that quantum-resistant cryptography is the most effective security measure. In contrast, digital signatures resistant to quantum errors were assigned the lowest priority, while the software system (H2) received the highest priority. These results underscore the importance of developing robust cybersecurity frameworks that align with the capabilities of quantum technology. As the field advances, it is crucial to design software, networks, and security systems that support the optimal functionality of quantum computers. Implementing quantum security mechanisms can significantly reduce vulnerabilities and mitigate the risk of cyberattacks. Over the next decade, new approaches to cybersecurity risk analysis leveraging quantum technology are expected to emerge, paving the way for enhanced cyber resilience in a quantum-powered future.

Quantum error correction technology is an important method to eliminate errors during the operation of quantum computers. In order to solve the problem of influence of errors on physical qubits, we propose an approximate error correction scheme that performs dimension mapping operations on surface codes. This error correction scheme utilizes the topological properties of error correction codes to map the surface code dimension to three dimensions. Compared to previous error correction schemes, the present three-dimensional surface code exhibits good scalability due to its higher redundancy and more efficient error correction capabilities. By reducing the number of ancilla qubits required for error correction, this approach achieves savings in measurement space and reduces resource consumption costs. In order to improve the decoding efficiency and solve the problem of the correlation between the surface code stabilizer and the 3D space after dimension mapping, we employ a reinforcement learning (RL) decoder based on deep Q-learning, which enables faster identification of the optimal syndrome and achieves better thresholds through conditional optimization. Compared to the minimum weight perfect matching decoding, the threshold of the RL trained model reaches 0.78%, which is 56% higher and enables large-scale fault-tolerant quantum computation.

Quantum computing has been pursued with various hardware platforms and an optical system is one of the most reasonable choices for large-scale computation. In the optical continuous-variable computation scheme, the incorporation of Gaussian gates and a highly nonclassical non-Gaussian state enables universal quantum computation. Although basic technologies for Gaussian gates and non-Gaussian state generation have long been developed, these building blocks have not yet been integrated in a scalable fashion. Here, we integrate them to develop a scalable and programmable optical quantum computing platform that can sequentially perform an essential Gaussian gate, the squeezing gate, on a non-Gaussian input state. The key enablers are a loop-based optical circuit with dynamical and programmable controllability and its time synchronization with the probabilistic non-Gaussian state generation. We verify the deterministic, programmable, and repeatable quantum gates on a typical non-Gaussian state by implementing up to three-step gates. The gates implemented are of such high quality that strong evidence of the nonclassicalities of the states, the negativities of the Wigner functions, are preserved even after multistep gates. This platform is compatible with other non-Gaussian states and can in principle realize large-scale universal quantum computing by incorporating other existing processing technologies. Published by the American Physical Society 2025

Developing hardware for high-dimensional unitary operators plays a vital role in implementing quantum computations and deep learning accelerations. Programmable photonic circuits are singularly promising candidates for universal unitaries owing to intrinsic unitarity, ultrafast tunability and energy efficiency of photonic platforms. Nonetheless, when the scale of a photonic circuit increases, the effects of noise on the fidelity of quantum operators and deep learning weight matrices become more severe. Here we demonstrate a nontrivial stochastic nature of large-scale programmable photonic circuits—heavy-tailed distributions of rotation operators—that enables the development of high-fidelity universal unitaries through designed pruning of superfluous rotations. The power law and the Pareto principle for the conventional architecture of programmable photonic circuits are revealed with the presence of hub phase shifters, allowing for the application of network pruning to the design of photonic hardware. For the Clements design of programmable photonic circuits, we extract a universal architecture for pruning random unitary matrices and prove that “the bad is sometimes better to be removed” to achieve high fidelity and energy efficiency. This result lowers the hurdle for high fidelity in large-scale quantum computing and photonic deep learning accelerators.

Large scale quantum computers will consist of many interacting qubits. In\nthis paper we expand the two flux qubit coupling scheme first devised in [Phys.\nRev. B {\\bf 70}, 140501 (2004)] and realized in [Science {\\bf 314}, 1427\n(2006)] to a three-qubit, two-coupler scenario. We study L-shaped and\nline-shaped coupler geometries, and show how the interaction strength between\nqubits changes in terms of the couplers' dimensions. We explore two cases: the\n"on-state" where the interaction energy between two nearest-neighbor qubits is\nhigh, and the "off-state" where it is turned off. In both situations we study\nthe undesirable crosstalk with the third qubit. Finally, we use the GRAPE\nalgorithm to find efficient pulse sequences for two-qubit gates subject to our\ncalculated physical constraints on the coupling strength.\n