We investigate the integrability-to-chaos transition and information scrambling in Ising spin networks via a graph-theoretic formulation. Modeling spins as vertices and interactions via adjacency matrices across path, Erdős--Rényi, and Watts--Strogatz topologies, we demonstrate that long-range couplings and heterogeneous degree distributions drastically accelerate quantum information propagation. The Hamiltonian comprises local and normalized non-local interactions; tuning the non-local coupling and field heterogeneity drives integrability breaking. To quantify scrambling, we employ bipartite mutual and tripartite information. Increasing non-local interactions drives tripartite information to large negative values, signaling deep information scrambling. Out-of-time-order correlators (OTOCs) exhibit exponential early-time growth, yielding quantum Lyapunov exponents that scale systematically with parameters governing the chaotic regime. Complementing this, Krylov complexity reveals rapid operator growth in the chaotic phase, synchronizing with OTOC and mutual information dynamics. Spectrally, the transition manifests as a shift from Poissonian to Wigner--Dyson level spacing statistics. The spectral form factor (SFF) exhibits the characteristic slope-dip-ramp-plateau structure, enabling the extraction of Thouless and Heisenberg times. Crucially, a reduced Thouless time strongly correlates with accelerated informational and operator scrambling. Ultimately, this work establishes a unified framework bridging network topology with information-theoretic, operator, and spectral diagnostics, offering profound insights into thermalization and non-equilibrium dynamics in quantum many-body systems. less

Quantum networks require qubits that combine efficient optical access, coherent control, and long-lived quantum memory, but realizing all three in one scalable platform remains a central bottleneck. Diamond color centers are leading candidates, yet widely studied defects retain tradeoffs among these capabilities. Here, we show that transition-metal defects in diamond provide a distinct route beyond these platforms by combining spin-orbit protected ground-state coherence, all-optical control, and near-infrared emission. Using a single nickel-vacancy (NiV$^-$), we demonstrate an all-optically controlled diamond spin qubit with coherence exceeding one millisecond at 1.65 K, compatible with compact closed-cycle cryogenics. We implement Raman Rabi oscillations and Ramsey interferometry and use all-optical dynamical decoupling to extend coherence from $T_2^*$ = 371 ns to $T_2^{CPMG-4}$ = 1.27 ms, establishing NiV$^-$ as a deployable diamond spin-photon interface. less

Characterizing noise in quantum circuits is fundamentally limited by gauge degrees of freedom; certain parameters, such as the individual contributions of state preparation and measurement (SPAM) errors, are in principle unlearnable from any experiment within the gate set. Here, we show that the physical structure of realistic noise processes imposes approximate symmetry constraints on the Pauli fidelities of gate noise channels. These symmetries relate the fidelity of a Pauli $P$ and its gate-conjugate $U_g P U_g ^{\dagger}$, and can be used to fix the gauge using only knowledge of the error type and not its magnitude. Using Lindbladian perturbation theory, we analyze a broad class of Clifford gates, including $ZZ_{π/2}$, CZ, CNOT, iSWAP, and SWAP, and demonstrate that coherent errors do not induce first-order asymmetry, while only a restricted set of predominantly off-diagonal dissipative errors can break the symmetry at first order, for which we derive simple selection rules. Notably, common single-qubit noise sources such as $T_1$-relaxation and $T_{2φ}$-pure-dephasing can only cause asymmetry at second order. Leveraging these symmetries to fix the gauge enables systematic identification of SPAM errors, simplifying error characterization and mitigation. We validate our results numerically and experimentally on IBM Kingston. less

Transversal CNOTs are ubiquitous for entangling logical qubits of identical CSS codes pairwise. For distinct codes, the options are much more limited, and are typically known only for structurally related code families. We introduce an automated framework for synthesising inter-code logical CNOT circuits between arbitrary CSS codes using chain maps. Given a prescribed bipartite logical CNOT network between these codes, our method constructs the affine space of chain maps realising the desired logical action, and then searches this space for shallow and sparse physical circuit candidates. We benchmark this method on a range of heterogeneous CSS code pairs, recovering known transversal constructions, and finding new low-depth solutions, including distance-preserving and partially distance-preserving examples, which we demonstrate can be promoted to the full code distance using additional flag measurements. We discuss applications to code switching, magic-state injection, Pauli product measurements, and operations on concatenated codes, where bespoke chain maps offer favourable spacetime tradeoffs for logical interfaces tailored to heterogeneous architectures. Finally, we show how our framework straightforwardly extends to targeted logical CZ gates. less

Scalable fault-tolerant quantum computation requires quantum error-correcting codes that simultaneously support universal logical operations, suppress hardware-specific noise, and enable efficient handling of photon-loss errors. Bosonic encodings such as the dual-rail and cat codes each offer attractive features but also exhibit important limitations when used in isolation. The dual-rail code enables efficient single-photon-loss detection by converting leakage out of the computational subspace induced by photon-loss errors into an erasure error. In contrast, the cat code provides a resource-efficient, bias-tailored error-correction scheme with bias-preserving logical gate operations. Here, we introduce the dual-rail cat code (DRCC), a concatenated bosonic encoding that combines an inner cat code with an outer dual-rail structure, thereby inheriting and enhancing the advantages of both constituent codes. We analyse the error-correction properties of the DRCC and propose a deterministic single-photon-loss correction protocol by concatenating it with an outer repetition code. Exploiting the code's intrinsic noise bias, we construct a universal set of logical gates using only beam-splitter interactions and demonstrate that all logical operations preserve the erasure-biased noise structure. The DRCC offers several distinctive advantages, including the absence of relative geometric phases during gate operations, deterministic erasure detection and correction, and simultaneous syndrome extraction without interrupting stabilisation. These features make the DRCC a promising bosonic code for hardware-efficient, bias-preserving, and erasure-resilient fault-tolerant quantum computation. less

Efficient classical simulation of large-scale quantum networks frequently relies on noise approximations, which consider a restricted set of operators to describe noisy channels and operations. In this work, we demonstrate how such simplified error models, such as Pauli twirling or reset channels, can lead to severe quantitative and qualitative discrepancies in protocol performance predictions. We analyze, in particular, how small differences can accumulate in iterative and sequential protocols such as entanglement purification, entanglement swapping, and repeater chains. Our results reveal that neglected error contributions can lead to important performance under- and over-estimations, measurement-outcome dependency, and oscillations in the fidelity, which are entirely overlooked by the simplified error model approximations. These results show that rigorous validation of complete noise architectures is indispensable for accurately predicting operational thresholds in future quantum technologies. less

Extracting the full power of non-local correlations in prepare-and-measure (PM) scenarios requires precise control over the timing and structure of the receiver's measurements. Indeed, recent developments in entanglement-assisted classical communication scenarios have shown that adaptive strategies-where the receiver uses the transmitted message to guide their measurement choice-can outperform standard non-adaptive protocols. Moving beyond quantum theory, however, the ultimate limits of such advantages remain largely unexplored. In this work, we thoroughly study adaptive and non-adaptive non-signaling (NS) assistance in PM scenarios with classical communication. We provide simple characterizations of the sets of behaviors that can be realized using both non-adaptive and adaptive NS assistance in arbitrary PM scenarios. As a consequence, we show that non-adaptive NS assistance is already strong enough to reproduce quantum communication with the same message dimension: the transmission of a qudit can be simulated by a classical dit assisted non-adaptively by NS correlations. We then compare adaptive and non-adaptive NS assistance. We prove that any adaptive NS advantage can be traced back to scenarios in which the receiver has no measurement choice, ruling out the genuinely multi-setting advantages found in entanglement-assisted quantum protocols. Finally, we identify all PM scenarios where adaptive NS strategies provide a strict advantage over non-adaptive ones. less

Kinetic uncertainty relations bound current precision of stochastic processes by dynamical activity. The extension of these bounds to quantum systems has been impeded by coherence, strong system-reservoir coupling, and the subtlety of defining dynamical activity in the quantum regime. Here, we introduce a partial dynamical activity through the quantum Fisher information associated with the rescaling of the system-reservoir coupling and show that it bounds current precision via a universal susceptibility-kinetic uncertainty relation. The general validity of this relation for any open quantum system is guaranteed by the natural contribution of a susceptibility term, which is experimentally accessible by tuning the system-reservoir coupling strength. We show how the partial dynamical activity encompasses previous definitions of activity in the weak-coupling Markovian limit and that it provides an information-geometric interpretation of correlator-based activities. We illustrate the tight constraint on precision that our bound provides with the example of steady-state transport through a double quantum dot, where quantum effects invalidate previously developed kinetic uncertainty relations. We expect our bound to provide a powerful tool for optimizing precision in arbitrary quantum systems. less

The transverse-field Ising model has attracted a lot of attention in recent years, especially in the quantum simulation and quantum computation literature. This interest is driven by many platforms for analog quantum computation, which implement the transverse-field Ising model for solving optimization problems, such as quantum annealing. However, it has remained an open question whether the Ising model with a global transverse field is equivalent to the gate model of quantum computation. Here we answer this question affirmatively for the case of a non-monotonic time-dependent transverse field. Building on a recent result by Cesa and Pichler on global control of Rydberg atoms, we provide a construction that allows simulating arbitrary quantum circuits using the Ising model with global transverse field with polynomial overhead in time, qubit number, and energy scale. Although the polynomial overheads we establish here are large relative to what is feasible on real-world quantum hardware, our result motivates the development of more sophisticated methods for simulating quantum circuits using the Ising model with a global transverse field. Additionally, under the assumption that quantum computing is strictly more powerful than classical computing, our result serves as a no-go theorem for efficient classical simulation of the transverse-field Ising model with a time-dependent global transverse field. Therefore, our finding is relevant for multiple communities, from analog quantum simulation and quantum optimization on various platforms to complexity and control theory. less

Portfolio diversification - a cornerstone of modern investment management - can be formulated as a Maximum Independent Set (MIS) problem on asset correlation graphs. Solving this problem at scale is computationally challenging, motivating the exploration of quantum algorithms for practical financial optimization. We propose an end-to-end pipeline leveraging qReduMIS, a recursive hybrid quantum-classical algorithm. Rather than using quantum optimization to directly produce a final solution, qReduMIS leverages independent set measurements from the Quantum Approximate Optimization Algorithm (QAOA) to identify frozen nodes - vertices likely to belong to optimal solutions - thereby guiding and unblocking subsequent (provably optimal) classical reductions on the remaining graph. We benchmark qReduMIS on real financial data from four major market indices with up to 225 assets, executing experiments on Quantinuum's 98-qubit trapped-ion Helios system, with QAOA circuits acting on kernels of up to 78 qubits and 1016 two-qubit gates. While standalone QAOA fails to find the optimal solution for two of the largest indices (S&P 100 and Nikkei 225), qReduMIS achieves success probabilities of $0.40$ and $0.95$, respectively, with average approximation ratios $\geq 0.96$ across all four indices. We perform a systematic benchmark on the Quantinuum H2-1 noisy emulator over 73 asset correlation graphs of varying size showing that, for $p=2$ QAOA layers, the optimal time-to-solution scaling exponent of qReduMIS is $3.2$ times smaller than that of standalone QAOA. less