Uncovering local integrability in quantum many-body dynamics

Recently, the dynamics of quantum systems that involve both unitary evolution and quantum measurements have attracted attention due to the exotic phenomenon of measurement-induced phase transitions. The latter refers to a sudden change in a property of a state of n qubits, such as its entanglement entropy, depending on the rate at which individual qubits are measured. At the same time, quantum complexity emerged as a key quantity for the identification of complex behaviour in quantum many-body dynamics. In this work, we investigate the dynamics of the quantum state complexity in monitored random circuits, where n qubits evolve according to a random unitary circuit and are individually measured with a fixed probability at each time step. We find that the evolution of the exact quantum state complexity undergoes a phase transition when changing the measurement rate. Below a critical measurement rate, the complexity grows at least linearly in time until {saturating to a value eΩ(n).} Above, the complexity does not exceed poly⁡(n). In our proof, we make use of percolation theory to find paths along which an exponentially long quantum computation can be run below the critical rate, and to identify events where the state complexity is reset to zero above the critical rate. We lower bound the exact state complexity in the former regime using recently developed techniques from algebraic geometry. Our results combine quantum complexity growth, phase transitions, and computation with measurements to help understand the behavior of monitored random circuits and to make progress towards determining the computational power of measurements in many-body systems.

Quantum mechanics is the most ground-breaking and fascinating theoretical concept developed in physics during the past century. Much of our present understanding of the microscopic world and its extension into the macroscopic world, including modern technical applications, is based upon quantum mechanics. We have experienced a remarkable development of information and communication technology during the past two decades, to a large extent depending upon successful fabrication of smaller and smaller components and circuits. However, we are finally approaching the physical limits of component miniaturization as we enter a microscopic world ruled by quantum mechanics.

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.

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.

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.

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.

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.

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.

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.

Faster manipulation of large quantum circuits using wire label reference diagrams

Quantum information theory has provided the formal framework for describing how information is stored, transmitted, and transformed in physical quantum systems [Renes, 2022; Tomamichel, 2015; Wilde, 2013]. Its entropic formulations underpin our understanding of quantum computation, communication, and cryptography. Yet this theory traditionally treats all quantum operations as freely available, ignoring computational restrictions. In practice, however, any manipulation of quantum information must be performed by devices of bounded complexity and runtime. Capturing such realistic constraints requires extending quantum information theory to include computational efficiency as a fundamental component. This work takes a first step toward building a computational version of quantum information theory, one that treats efficiency as part of the theory itself. The goal is to understand how the behavior of quantum information changes when the parties involved can only perform computationally efficient operations. This approach bridges the abstract, ideal setting of quantum information theory with the practical limitations of real quantum devices, offering a means to study information processing under realistic resource constraints. At the center of this work are two new quantities: the quantum computational min-entropy and the quantum computational max-entropy. These entropies extend standard quantum entropies by explicitly limiting the computational power of the observer or adversary. The quantum computational min-entropy captures how unpredictable a quantum system A remains to an observer holding system B, when that observer is restricted to quantum circuits of bounded size. Formally, for a bipartite state ρ_{AB}, we define {H^c}^s_{min}(A|B)_{ρ} ≔ -log d_A max_{ℰ^s_{B→A'}} F((𝕀_A ⊗ ℰ^s)(ρ_{AB}),|Φ_{AA'}⟩⟨Φ_{AA'}|) , where the maximization is over quantum channels that can be implemented by circuits of size at most s, and F denotes fidelity with a maximally entangled state. In the classical setting, the min-entropy can be expressed through the maximal probability of correctly guessing a random variable given some side-information. In the fully quantum setting, this idea extends to uncertainty about quantum information [König et al., 2009], quantifying how well one system can be inferred from another using local quantum operations. Our definition generalizes this operational viewpoint by restricting the computational power of the observer to efficient quantum circuits. This definition extends the operational meaning of the information-theoretic quantum min-entropy [König et al., 2009] by incorporating computational constraints, and it provides the fully quantum counterpart of the classical unpredictability entropy [Hsiao et al., 2007]. We establish fundamental properties for the computational min-entropy, including monotonicity in the circuit size and smoothing parameters, efficient data-processing inequalities, and fully quantum leakage and purification chain rules, which were left as open questions in earlier definitions of quantum computational entropies [Yi-Hsiu Chen et al., 2017; Munson et al., 2025]. For classical–quantum states, it coincides with the previously defined quantum computational unpredictability entropy [Noam Avidan and Rotem Arnon, 2025], showing that the new definition correctly generalizes known results. We also introduce the quantum computational max-entropy through a duality relation [Tomamichel et al., 2010] with the min-entropy using a fixed purification. Finally, we prove unconditional separations between the computational and information-theoretic entropies, demonstrating that computational restrictions can fundamentally alter entropic behavior even for simple states. These results establish the fundamental mathematical framework for studying quantum information within realistic computational constraints. By integrating efficiency directly into entropic quantities, they open the door to a fully developed computational quantum information theory that parallels its information-theoretic counterpart. Such a framework provides the foundation for analyzing cryptographic security against computationally bounded quantum adversaries [Noam Avidan and Rotem Arnon, 2025] and the limits of efficient quantum state manipulation. More broadly, it suggests that many core notions in quantum information theory may have refined computational analogues yet to be explored.

An architecture for a quantum computer is presented in which spins associated\nwith donors in silicon function as qubits. Quantum operations on the spins are\nperformed using a combination of voltages applied to gates adjacent to the\nspins and radio frequency applied magnetic fields resonant with spin\ntransitions. Initialization and measurement of electron spins is made by\nelectrostatic probing of a two electron system, whose orbital configuration\nmust depend on the spin states of the electrons because of the Pauli Principle.\nSpecific devices will be discussed which perform all the necessary operations\nfor quantum computing, with an emphasis placed on the qualitative principles\nunderlying their operation.\n The likely impediments to achieving large-scale quantum computation using\nthis architecture will be addressed: the computer must operate at extremely low\ntemperature, must be fabricated from devices built with near atomic precision,\nand will require extremely accurate gating operations in order to perform\nquantum logic. Refinements to the computer architecture will be presented which\ncould remedy each of these deficiencies. I will conclude by discussing a\nspecific realization of the computer using Si/SiGe heterostructures into which\ndonors are deposited using a low energy focused ion beam.\n

Quantum computing has been gradually developed from a theory to practice in recent years. The desire for more powerful computational capability keeps promoting the scaling up of quantum computers. For quantum machines with large scales, limited coherence time and bloated instruction bandwidth may obstruct the continuous scaling up. In this paper, we propose a new quantum computing architecture named QuPAA, which leverages multiple layers of arbitrary waveform generator (AWG) units to exploit the parallelism among quantum operations. QuPAA provides a series of mechanisms, including parallelism exploitation, microcode streaming, and a quantum flexible instruction set (QuFIS). These mechanisms assist QuPAA to generate instructions adaptively and reduce the requirement for coherence time and instruction bandwidth. The evaluation results show that, compared to the baseline quantum computer with a single AWG unit, QuPAA reduces 25.9% to 97.4% coherence time requirement, and saves 26.9% to 79.1 % instruction bandwidth. The improvement effectively breaks the limitations and provides strong support for the extension of the scale for quantum computers.