Papers

Hall viscosity characterizes the geometric response of a quantum Hall droplet to deformations of the underlying metric, yet it has remained difficult to measure directly. We propose a spectroscopic probe based on circular dichroism, using chiral metric-sensitive drives – implemented as rotating quadrupolar ("saddle") perturbations – that effectively modulate the metric and couple to the generators of area-preserving deformations. The resulting dichroic signal directly measures the Hall viscosity, while frequency-resolved spectroscopy disentangles it from other excitations. A local formulation further enables spatially resolved markers of Hall viscosity applicable to both continuum and lattice systems. Our results open a direct route to measuring Hall viscosity in quantum-engineered platforms such as cold atoms in optical lattices.

The ability to control quantum correlations in strongly driven systems is a central challenge across quantum science, with implications for ultrafast dynamics, quantum control, and information processing. In photoionization, the emitted electron and residual ion may form an entangled system whose correlations encode the underlying light-matter interaction, yet control of their generation and observable manifestation in continuum systems remains largely unexplored. Here we demonstrate phase-resolved control of electron-ion correlations using phase-locked pulse sequences in the strong-coupling regime. We show that entanglement can be halted and reshaped with attosecond precision, and that phase-dependent correlations can be redistributed into population-based correlations, leading to entanglement that is directly reflected in joint observables. These results establish a route to coherently shape entanglement in photoionization and open new possibilities for accessing and controlling quantum correlations in systems where measurements are intrinsically basis constrained.

The ability of bosonic energy quanta to bunch together in an energy-conserving interaction is a fundamental feature of quantum harmonic oscillators. Linear systems together with measurement allow for the conditional concentration of energy quanta and, subsequently, breeding of the quantum states, but only with an exponentially decreasing success rate. Deterministic, energy-conserving and unconditional bunching however, requires nonlinearity. We investigate which nonlinear energy-conserving interactions deterministically combine bosons into high number states at the same frequency. We show that in order to do so it is advantageous to use nonlinear interactions involving highly saturable systems, such as qubits, as they preserve the hierarchical quantum non-Gaussian features and are also sufficiently robust against pure loss. Nonlinear bunching therefore demonstrates the advantage of a qubit-inside nonlinearity and opens new directions in the deterministic preparation, processing, and detection of quantum non-Gaussian states.

Uncertainty relations play a fundamental role in quantum mechanics by quantifying the intrinsic limitations on the simultaneous sharpness of incompatible observables. Beyond the standard two-observable product form, additive uncertainty relations for triples of observables provide a natural framework for describing collective constraints among three noncommuting components. In this work, we study an additive uncertainty relation for three Hermitian observables from the viewpoint of rotational symmetry and covariance geometry. We give a short rotational derivation by rotating the observable triple and applying the Robertson uncertainty relation to the two transverse observables. This derivation makes the saturation mechanism transparent and leads to a necessary and sufficient condition for equality for general density operators. In the nontrivial equality case, the covariance ellipsoid of the observable triple degenerates into a disk perpendicular to the expectation value of the commutator vector. We also discuss an inverse construction based on finite-dimensional representations of the Lie algebra \(\mathfrak{su}(2)\), which provides a systematic way to construct observable triples with prescribed saturating states. These results clarify the geometric and representation-theoretic structure underlying the tightness of additive three-observable uncertainty relations.

Traditional light rendering techniques treat the optical properties of materials as static, yet this assumption breaks down in cases where these properties dynamically evolve in response to incident illumination. We present a novel shading framework that combines classical ray-tracing with a quantum collision model to explore the effect of coherent light-matter interactions in rendering. By treating incident light and material excitations as quantized modes, we model sub-surface scattering as a sequence of symmetry-constrained unitary collisions. This formulation allows for the incorporation of non-integrable dynamics and chaotic optical responses due to multi-layer interference effects. We demonstrate how these collision operators can be pre-computed using near-term quantum computers to generate standard BSDFs, enabling the rendering of new physics-inspired materials with distinct optical signatures.

Non-Gaussian quantum states of light are of paramount importance to quantum computing. Nevertheless, their deterministic generation is challenging problem due to the difficulty to control nonlinearities in physical systems. In this work, we characterize the light stemming from one of the most fundamental quantum optics configurations: the unidirectional scattering of multimode and multiphoton light by a two-level system. We provide an analytic and explicit description of the output light solely in terms of the corresponding input temporal modes which allows a straightforward physical interpretation and is computationally more effective compared to numerical methods. Then, we focus on the specific case of the scattering of two photons in a single mode. By numerically decomposing the output state in terms of its principal modes, we find that it is possible to map single-mode two-photon inputs to be into two-mode entangled output states, i.e., two-photon NOON states, to very good approximation. The latter states, in turn, are known to have more Wigner negativity compared to the associated input, which ultimately suggests a potential application of our considered setup in the deterministic generation of non-Gaussian states.

Quantum computing provides a powerful paradigm for representing and transforming high-dimensional information through superposition, entanglement, and measurement-induced nonlinear features. While current quantum hardware is not yet practical for direct large-scale vision-language model (VLM) inference, simulated quantum computation can be used during model construction to generate structured parameters for compact classical AI systems. We build RiverONE, a lightweight vision-language model for quantum calibration plot understanding, using simulated quantum computation. It employs a specialized visual encoder and an InternVL-based language backbone. To compensate for compression-induced information loss, we introduce quantum-generated parameters, which are materialized as classical tensors after training. This allows RiverONE to run entirely on classical GPUs at inference time, with no quantum hardware or runtime quantum simulation. With approximately 1.9 billion parameters, RiverONE achieves at least 95% of the performance of NVIDIA Ising Calibration 1 on quantum calibration plot understanding tasks while using less than 10% of its parameter count. These results suggest that simulated quantum computation can serve as a practical construction-stage mechanism for building lightweight, knowledge-intensive scientific VLMs. Our code is available at https://github.com/THeWakeSystems/RiverOne.

Universal blind quantum computation (UBQC) hides a client's computation by using a computation-independent BFK09 brickwork graph and encoding the computation in measurement angles, which limits the use of graph-changing optimizations. We study blindness-preserving brickwork optimization (BPBO): certified local resynthesis of BFK09-compatible brickwork patterns below the blinding layer. BPBO detects one-, two-, and three-wire regions; for each candidate region it either proves a semantic floor or supplies an executable witness, and it accepts a replacement only after its branch-frame, output-frame, and blinding behavior have been checked. The optimized outputs remain standard brickwork patterns and are evaluated with a logical qubit-recycled UBQC execution stack that runs arbitrary-length patterns using n x 2 active logical qubits. The layer evidence includes a one-wire H-count floor, a two-wire CNOT-cost floor, a three-wire parity-ledger floor, a clean three-cell CCZ witness whose optimality claim is scoped to the CNOT+T phase-gadget family, and an endpoint-target three-cell CCX/Toffoli application witness; the fixed middle-target CCX case is retained as a four-cell fallback. The security statement is a compatibility result: BPBO preserves UBQC blindness at the declared optimized dimensions and remains compatible with inherited verification guarantees under explicit test-round conditions, without introducing a new trap-soundness theorem. On Bell/CX, Grover-2, endpoint-Toffoli, and Grover-3 evaluation cases, BPBO demonstrates certified local reductions; in the largest case, Grover-3, the materialized pattern is reduced from 3 x 725 to 3 x 98 while preserving the expected marked-state statistics up to sampling noise.

Using the soft-gluon theorem, we identify a soft-recoil mechanism by which unresolved gluon radiation induces decoherence in the spin correlations of heavy quark-antiquark pairs produced by longitudinally polarized virtual photons in deep-inelastic scattering. Upon tracing over the unresolved gluon, the reduced spin density matrix is block diagonal in the mirror parity of the production plane and is governed by two coefficients: a parity-odd normal-spin flip, which reduces the normal-axis correlation, and a parity-even stochastic rotation of the spin-correlation plane about its normal, which suppresses the in-plane spin coherences while leaving the normal-axis correlation unchanged. From the complete tree-level next-to-soft amplitude with the exact color-octet structure we derive both coefficients, together with the trace and antisymmetric in-plane terms, in closed form. The parity-odd coefficient is the larger one, by a factor of at least $3.5$, and grows as the inverse square of the heavy-quark transverse momentum. We estimate the resulting reduction of concurrence and Bell-CHSH violation, and propose an infrared-safe, radiation-binned EIC observable, formed at fixed Born kinematics after longitudinal-transverse separation, which isolates the two channels. We estimate its size, including multiple wide-angle emissions in an independent-emission model, the conditions under which detector and kinematic effects cancel, and the statistics required. The latter, however, exceed the yield of exclusive heavy-baryon pairs at nominal EIC luminosity by several orders of magnitude, makes the observable elusive for the measurement accessible in that channel.

Decoy-state quantum key distribution (QKD) is the most widely adopted approach for overcoming the limitations of imperfect single-photon sources. However, existing security proofs typically either neglect important device imperfections or rely on assumptions that are difficult to justify in realistic high-speed implementations, such as the independent and identically distributed nature of the emitted signals. In this work, we combine and extend several recent theoretical advances to provide a comprehensive analytical finite-key security proof for decoy-state QKD that simultaneously incorporates multiple practically relevant transmitter and receiver imperfections, including state-preparation flaws, bit and basis side-channel leakage and correlations, setting-independent intensity fluctuations, and detection-efficiency mismatches.

A Kerr-cat qubit encodes a logical bit in the two wells of a parametrically driven nonlinear oscillator, and a logic gate is a transient change of the drive. In the phase plane the gate deforms the double well and can split its separatrix into a turnstile that carries trajectories across the dividing surface between the wells; the same pulse, acting on the quantum oscillator, can corrupt the encoded bit. We study this process over a disk of coherent-state preparations, comparing classical phase-space transport diagnostics with the open-system quantum outcome on a common domain so that the two can be compared point by point. The central finding is that the corruption depends on the full temporal protocol, not on pulse strength alone: a sudden quench erases the bit, whereas a smooth ramp of the same peak amplitude largely preserves it. A finite-time sensitivity field locates the classical transport boundary, and a Loschmidt echo evaluated near the end of the gate predicts the much later quantum outcome. Sweeps of pulse amplitude and width, of cat size, and of engineered two-photon dissipation map where the classical transport picture predicts the quantum loss of the bit and where it does not.

Effective quantum control is essential for quantum computing and information processing, yet level leakage remains a bottleneck limiting control fidelity. The leakage elimination operator (LEO) approach is highly effective at suppressing leakage from a target subspace to other subspaces. Analytical control conditions under the high-frequency driving limit have been derived via the Feshbach PQ partitioning technique. However, the driving intensity is subject to fundamental physical bounds, and low-frequency driving is experimentally more feasible. In this work, we reformulate LEO within the Magnus framework and extend it beyond the high-frequency limit. We show that the analytical control conditions obtained from the Feshbach PQ partitioning technique are equivalent to the zeroth-order Magnus expansion. We then analyze the higher-order Magnus corrections. By minimizing the leakage, we obtain a modified pulse condition suitable for the low-frequency regime. As an illustrative example, we study near-perfect state transfer through a one-dimensional spin chain under LEO control. We find that the second-order Magnus correction improves the transmission fidelity at low-frequency driving, while the improvement becomes negligible at high frequencies. Our results provide an effective route for designing control pulses in the low-frequency regime, with potential applications in superconducting qubits, trapped ions, and solid-state spin systems.

Linear combination of Hamiltonian simulation (LCHS) provides an efficient method for implementing matrix exponentials $e^{-tA}$ on quantum computers. In this paper, we develop LCHS formulas for computing general matrix functions $f(A)$ when $f$ is analytic on the numerical range of $A$, with $A$ possibly non-normal. The essential technical tool is Weyl calculus, which reduces the construction of LCHS formulas for noncommuting operators to scalar Fourier approximation problems. Our construction yields a quantum eigenvalue transformation algorithm with optimal $\mathcal{O}(\log\frac{1}{\epsilon})$ query complexity scaling. Furthermore, our Weyl-calculus-based theory gives rise to an ansatz-free convex optimization framework that directly produces discrete LCHS formulas. This circumvents the inefficiencies of traditional quadrature rules and yields formulas highly optimized for coherent implementation on quantum computers. In addition, both our theory and optimization framework apply to the simulation of time-dependent dissipative ODE $\frac{\mathrm{d}}{\mathrm{d} t} \psi(t) = -A(t)\psi(t)$, for which we achieve a $2.1\times$ cost reduction over prior art.

Graphene-based Sierpiński fractals host a zero-energy chiral mode and spin-1 Dirac dispersions within the nearest-neighbor tight-binding model. However, the presence of complex next-nearest neighbor hopping arising from the local flux and the staggered Semenoff mass terms, modeled within the Haldane Hamiltonian, breaks the time-reversal and spatial inversion symmetries, respectively, and makes these flat bands dispersive. Moreover, they introduce rich topological phases in this class of systems that can be characterized by Chern numbers up to $\pm 3$, i.e., beyond the conventional honeycomb lattice. These observations pave the way for the exploration of 2D periodic fractals beyond graphene, where topological phase transitions can be realized through externally applied fields.

The discard ZX-calculus, a diagrammatic language for mixed-state quantum mechanics, is used to give a nonperturbative, categorical proof of the Bloch-Nordsieck cancellation of infrared divergences in QED. Soft photons are treated as an open quantum system: the resolved charged particles and hard photons form the system, while photons below a detector resolution form the environment. The reduced hard channel is a completely positive trace-preserving (CPTP) map, and the soft-photon theorem replaces the full S-matrix by a controlled displacement operator whose Feynman-Vernon influence functional satisfies the equal-history normalization ${\cal F}[J,J]=1 $. In the ZX-calculus, this normalization is a single diagrammatic identity: the doubled displacement diagram collapses to the bare wire under the unitarity, cyclicity, and discard rules. The proof therefore serves as a categorical consistency check on the open-system treatment of soft QED given in a companion paper; it confirms that the physical derivation is logically complete and free of hidden assumptions about the infrared limit. For off-diagonal hard-state elements, the same diagram yields the coherent-state overlap, giving a first-principles account of soft-cloud decoherence. The soft-shell coarse graining is then constructed as a CPTP Schur channel whose infinitesimal limit produces the exact Lindblad generator with jump operators determined by the eikonal emission amplitudes. Finally, a local CPTP-certification pipeline is developed for non-Markovian process tensors, enabling constant-time verification of trace preservation in open quantum simulations. The framework bridges categorical quantum semantics, non-equilibrium field theory, and practical open-system compilation.

We introduce a quantum Fisher information based measurement-induced nonlocality (QFI-MIN), which quantifies the maximal statistical distinguishability induced by locally invariant unitary dynamics. The proposed measure inherits desirable properties including positivity, local unitary invariance, monotonicity under local operations, and immunity to the local ancilla problem. Analytical expressions are obtained for pure states, arbitrary two-qubit states, and two-qubit X states, revealing a direct connection with entanglement for pure systems. We further establish clear operational interpretations of QFI-MIN in quantum parameter estimation, local channel discrimination, and correlation-assisted communication. Its behavior under amplitude damping, depolarizing, and generalized amplitude damping channels demonstrates robustness against environmental noise. The proposed framework provides a physically consistent and operationally meaningful quantifier of quantum correlations, linking nonlocality, quantum metrology, and quantum information processing

Distributed quantum resources in practical multi-user quantum networks are inevitably degraded by environmental noise, channel loss, and device-induced imperfections. To address these issues, quantum resource distillation offers a fundamental approach to recovering stronger resources from imperfect states. However, conventional implementations often require additional copies, dedicated physical filtering elements, or restrict to bipartite systems, posing challenges for scalable multipartite networks. Here, we introduce the method of quantum resource distillation based on the local measurement program (LMP), which transfers completely positive maps into programmable measurement processes. We experimentally demonstrate the performance of resource distillation through LMP in both bipartite and tripartite photonic systems, including the activation and enhancement of multipartite steering configurations. To demonstrate the flexibility and extensibility of the LMP framework, we also show that virtual resource distillation can be naturally reformulated within it. Our results establish a programmable and experimentally economical approach for distilling quantum resources in multipartite and higher-dimensional systems, thereby providing a practical route toward scalable quantum networks.

This study formulates observer-dependent Krylov spreading for non-inertial quantum systems driven by linear Bogoliubov transformations. Starting with the closed single Rindler-pair $SU(1,1)$ sector, we show that its Lanczos basis is identical to the Rindler pair-number basis. As a result, the Krylov spread complexity reduces exactly to the mean number of correlated Rindler pairs, $C_k=\vert\beta_k\vert^2$. Within this framework, we demonstrate that Krylov spreading dynamics are governed by the competition between the detuning parameter and the coupling constant, naturally dividing the dynamics into three distinct regimes. Notably, Krylov complexity becomes localized in the detuning-dominated regime. By extending this to a multimode, strictly quadratic Bogoliubov Hamiltonian, we find that inequivalent Rindler wave-packet pairs violate the $C_k=\vert\beta_k\vert^2$ correspondence, thereby highlighting the single-pair $SU(1,1)$ model as an exactly solvable, observer-adapted benchmark. In such multimode scenarios, the mean pair-number eigenstates no longer dictate Krylov complexity. Overall, our work provides a new perspective for analyzing Krylov complexity in non-inertial quantum systems.

The efficient detection of quantum entanglement is a central problem in quantum information processing. This paper systematically proposes a quantum circuit implementation scheme based on the Positive Partial Transpose (PPT) and the Computable Cross-Norm Realignment (CCNR) criteria, providing a complete quantum algorithmic pathway for efficient and computable entanglement detection. By encoding quantum states into specific forms and utilizing SWAP operations, complex matrix operations such as partial transpose and realignment are transformed into executable quantum circuits. Furthermore, by integrating an improved variational quantum singular value decomposition subroutine, the scheme enables the efficient estimation of the trace norm, thereby determining the existence of entanglement. Designed to operate within a hybrid quantum-classical framework, this scheme exhibits excellent scalability and practicality, offering a theoretical tool and methodological support for analyzing the entanglement structure of complex quantum systems on future intermediate-scale quantum devices.

We theoretically investigate the coherent manipulation of biphoton generation via spontaneous four-wave mixing in a cavity-QED system with a single atom. The atom is driven by pumping, coupling, and driving fields, and the generation of the Stokes and anti-Stokes photons are enhanced by two cavities. By solving the master equation in the steady state, we analyze the spectral brightness, as well as the degree of the auto-correlation and cross-correlation. Our results show that when the pumping and driving fields are in two-photon resonance, the dark state established between the ground and Rydberg states. efficiently enhances the controllability of the driving field over the biphoton generation and the quantum statistics. In contrast, under large two-photon detuning, the control capability of the driving field is significantly reduced. The coupling field, which directly relates to the electromagnetically induced transparency, modifies the linewidth of the biphoton, while the atom-cavity coupling strength only changes the brightness without affecting the linewidth.

Owing to their simplicity and low overhead, Suzuki-Trotter formulas remain the de facto Hamiltonian simulation methods on current quantum computing platforms. Systematic Trotter errors, however, will quickly become limiting when scaling to larger problems and aiming for higher accuracy. We present a mechanism that removes the systematic error of any $k$-th order Suzuki-Trotter simulation, at the cost of a constant sampling overhead. The key insight is that the Trotter error is itself a coherent dynamics to be reversed, rather than a deviation to be bounded. By identifying the structure of this error in closed form, we carry out that reversal through quasi-probabilistic decompositions. The resulting algorithm, called Probabilistic Trotter Error Reversal (PTER), is unbiased and still improves the gate-count scaling of Suzuki-Trotter formulas while retaining their simplicity. Numerical simulations of a Heisenberg spin chain support the predicted resource advantage already at modest system sizes.

We present a rigorous analysis of the algebraic and geometric structure of the quantum complexity resource of a system of bosonic modes in Gaussian boson sampling. This resource underlies the quantum advantage of the system: its photon-counting statistics require the evaluation of a hafnian of the resource covariance matrix, and that computation is #P-hard. The resource covariance matrix is the solution of a semidefinite program that extracts the minimum-trace physical quantum part of the total covariance matrix; the complementary part is positive semidefinite and can therefore be simulated classically. Earlier work characterized this resource only through the trace of the quantum part, equal to its photon number. We characterize the optimizer itself, as a quantum state and as a geometric object, beyond the scalar given by its trace. We prove that it is a unique pure Gaussian state and construct an explicit oracle map, obeying an algebraic Riccati identity, that reconstructs the resource. We prove that the full problem compresses exactly onto the active symplectic sector that the dual program support generates. The passive-diagonalizable states are solved in closed form, the first explicit solvable class, and the whole program is shown to be equivalent to a minimization over the symplectic group, that is, over the Siegel upper half-space. Together these results establish that the program determines a canonical localized pure Gaussian component of the resource, and they provide the structural foundation for its detailed analysis.

The Variational Quantum Eigensolver (VQE) is a leading algorithm for noisy intermediate-scale quantum (NISQ) devices, but its adaptive variants (e.g., ADAPT-VQE) suffer from severe classical simulation bottlenecks during the ansatz growth phase. Representing and exponentiating pool operators for multi-qubit systems constructs massive sparse matrices that quickly scale to millions of elements, choking classical memory bandwidth and CPU/GPU cycle capacity. In this work, we present a resource-efficient software-layer framework that completely bypasses dense matrix exponentiation by evaluating state updates through a deterministic fifth-order (O(5)) Taylor series expansion. This approach reframes the costly unitary evolution into a chained sequence of five lightweight, successive sparse matrix-vector multiplications scaling strictly as O(Nz), where Nz is the number of non-zero elements. We validate our framework using equilibrium BeH2 (14 qubits), equilibrium H2O (12 qubits), and strongly correlated asymmetrically stretched H2O molecular profiles under both Jordan-Wigner (JW) and Bravyi-Kitaev (BK) transformations. The simulation results demonstrate that the O(5) truncation maintains exceptional numerical fidelity, retaining a state fidelity > 0.999999 and matching absolute ground state energies down to subchemical accuracy, while effortlessly navigating matrix spaces exceeding 268 million structural elements. This framework provides a scalable, high-performance pathway for executing deep variational simulations on hardware platforms with constrained computational budgets.

We report a machine-verified resolution of a problem open for over a decade in quantum optimization: the Farhi, Goldstone and Gutmann (FGG) conjecture that depth-$p$ Quantum Approximate Optimization Algorithm (QAOA) on the ring of disagrees attains approximation ratio $(2p+1)/(2p+2)$ exactly. We found the proof using a large language model, Claude Fable 5, and verified its correctness end-to-end by the Lean 4 proof assistant. Our methodology includes several ingredients: building on a substantial Lean library of quantum information, we formalized the QAOA components and the known parts of the problem, and reduced the conjecture to a single open mathematical statement. The model was then handed the library and our agentic toolkit, and tasked with closing that gap by constructing a proof in Lean. The resulting process is a feedback loop between the model's natural-language reasoning and Lean's mechanical verification, which converged to a machine-verified proof. Human verification is required only for the structural scaffolding - that the formal statement faithfully encodes the intended claim - while the proof itself is supplied by the model and certified mechanically by Lean. The proof is nevertheless striking - the model uncovered a hidden dynamical symmetry of the problem and exploited it, borrowing tools and machinery from an adjacent field to turn a hard existence problem into an explicit construction. This work paves the way for resolving open conjectures in quantum information science and beyond.

Symmetry provides a quantum neural network structure, but on its own it does not keep the network trainable once noise is present. We ask which physical quantity decides whether the gradients of an equivariant circuit survive decoherence, and we answer with a compact training law. Working with U(1)-equivariant brickwork circuits that conserve a charge, we find that two distinct effects govern a trainable gradient. Causality fixes where the gradient can live, confining it to the backward light cone of the readout inside the active charge sector. Coherence then determines how fast it decays through the contraction of the off-diagonal sector modes that the projected readout can actually observe. We prove a light-cone reduction that pins the noiseless gradient to the sector-restricted cone with a lower bound independent of the total qubit number, and we define a readout-visible aligned coherence rate as a Rayleigh quotient of the noise generator along the gradient-carrying mode. A perturbative open-system analysis turns this rate into a leading-order training law. Density-matrix simulations then confirm that the finite-noise degradation follows a single accumulated variable built from noise depth and coherence contraction, with a coefficient of determination of 0.979. The sharpest test comes from a correlated-dephasing channel that has a large worst-case rate but a near-zero aligned rate. The law predicts no gradient loss for this channel, and none is seen. Sector coherence outperforms every standard channel diagnostic we compare it against, and the analysis identifies readout-visible sector coherence as the quantity that links equivariant architecture, open-system dynamics and noisy trainability.

Large-scale combinatorial optimization is a challenge for near-term quantum computing because dense Quadratic Unconstrained Binary Optimization (QUBO) formulations yield interaction graphs that exceed the limits of NISQ processors. This work introduces Hybrid Quantum Neighborhood Selection (HQNS), a hybrid framework mitigating this via stochastic frontier decomposition. Instead of encoding all N variables into a monolithic circuit, HQNS selects a compact frontier of F << N active variables per stage, freezing the rest into reduced QUBO coefficients. A multi-stage crawling procedure rotates these frontiers, letting local quantum subproblems refine a global solution. We evaluate HQNS on the Maximum Diversity Subset Selection Problem (MDSSP) across six scales, N up to 1000. Circuit burden is reduced from the dense QAOA requirement of O(N^2) two-qubit terms per layer to O(F^2) per stage, with total complexity governed by the number of stages and classical overhead. Benchmarks show that HQNS achieves competitive solution quality relative to parallel simulated annealing (SA) while maintaining bounded circuit width and stable QPU time. In the N=1000 benchmark over ten executions, HQNS preserves 99.9908% of the mean diversity score of an 11-restart parallel SA baseline, while reducing wall-clock time by 65.03%, peak CPU usage by 55.97%, and peak memory by 35.21%. Ablation shows performance depends on frontier size, warm-starts, CVaR filtering, and stochastic rotation. These results demonstrate that structured frontier decomposition makes variational optimization executable for dense QUBO instances unsuitable for direct QAOA on present hardware.

Noise characterization of multi-qubit entangling Clifford operations is a key practical bottleneck for quantum error mitigation and for the calibration, validation, and optimization of quantum error-correction protocols, especially in the presence of state preparation and measurement (SPAM) errors. Although cycle benchmarking can isolate some Pauli error components, it cannot resolve the problem of coupled error parameters, which leads to unlearnable degrees of freedom even in simple noisy gates, not to mention general $n$-qubit Clifford gates. Here we introduce mid-circuit-measurement-based generalized cycle benchmarking, a framework that makes otherwise unidentifiable Pauli fidelities and non-Markovian noise learnable via repeated measurements and classical post-processing. Applying the deferred feed-forward principle to generalized cycle benchmarking, we show that an insertion of mid-circuit measurements can reverse Pauli cycles induced by a general Clifford gate. This fact enables us to reveal a Pauli-noise learnability condition for Clifford gates. Assuming sufficient state preparation quality, we numerically demonstrate the feasibility of characterizing the previously unlearnable noise components. We implement the protocol on superconducting quantum processing units and validate its effectiveness in disambiguating the coupled noise components, benchmarked against conventional tomography. Finally, we observe consistent measurement-induced bit-flip bias and non-Markovian correlations, which define a range of applicability for the Pauli noise model and the proposed noise-characterization protocol.

An important task in quantum computing is unitary circuit synthesis compatible with physical hardware constraints. This problem has a natural hybrid structure as local single-qubit gates are continuous variables on the Lie group $SU(2)$ while the entangling circuit structure is discrete and hardware-dependent. In this work, we use generative models to perform quantum circuit synthesis incorporating both the natural $SU(2)$ manifold geometry of quantum gates and hardware constraints that determine the overall circuit structure. Our model comprises two components: a circuit skeleton selector that chooses an entangling circuit and a diffusion model that generates quantum gates on the given circuit template by performing diffusion on the curved manifold $\mathrm{SU(2)} \simeq S^3$ itself. We demonstrate this approach with unitary compilation of physically motivated three-qubit Hamiltonian simulation targets such as the Transverse Field Ising Model and the Heisenberg-XXZ Model and show that Lie group diffusion outperforms comparable baselines. The synthesised circuits can also be customised subject to constraints, which we demonstrate by producing circuits with large and small gate rotation angles for the same target unitary evolution. We also investigate the fidelity-complexity frontier of the synthesised gates to demonstrate that the circuit selector learns to select circuits that balance fidelity with complexity rather than collapsing onto the most expansive entangling template. These results demonstrate that Lie group diffusion provides a natural generative framework for hardware-aware quantum circuit synthesis.

We address the precise characterization of coupling strength of nonlinear media in continuous-variable (CV) quantum systems using coherent and squeezed vacuum states as Gaussian probes, together with their photon-added and photon-subtracted counterparts as non-Gaussian probes. We consider three main classes of nonlinear Hamiltonians, namely quadrature nonlinearities, generalized squeezing and Kerr-type interactions. By analytically evaluating the quantum Fisher information (QFI), we compare the performance of Gaussian and non-Gaussian probes and assess the optimal probe based on the probe parameters, energy resource and non-Gaussianity. Our results are twofold as follows: first, for coherent-state family, the improvement provided by photon addition at fixed coherent amplitude originates mainly from the extra energy carried by the probe and does not provide a genuine metrological resource, since the same precision can be achieved by a Gaussian coherent-state signal of a larger energy, which can be more easily produced. Second, in contrast, photon addition and subtraction become effective resources when applied to already nonclassical states such as squeezed vacuum states. In this case, they lead to a significant enhancement of the QFI, particularly for higher-order interactions. Although Gaussian squeezed states remain optimal at equal energy constraint, photon-added and photon-subtracted squeezed states achieve comparable sensitives with significantly lower squeezing requirements. Since large squeezing level remains experimentally challenging, these non-Gaussian probes offer a practical route towards enhanced estimation of the nonlinear coupling strength within currently accessible squeezing regimes.

Bosonic modes provide hardware-efficient quantum memories and logical registers, including highly non-Gaussian encoded states, but transferring finite-dimensional bosonic states through a restricted ancilla interface requires identifying which collective mode is actually controlled. We study a restricted setting in which two oscillators couple with opposite signs to a single two-level ancilla. In the normal-mode basis, the symmetric mode is dark, while transfer between the physical modes is equivalent to synthesizing parity on the antisymmetric bright mode. This reduction gives exact finite-sum transfer formulas for Fock states, Fock-state qubits, and finite Fock superpositions, and explains why resonant single-ancilla transfer is recurrence-limited beyond the single-photon sector. We then show that detuned Jaynes–Cummings evolution provides a native two-parameter route to high-fidelity finite-cutoff parity synthesis, with residual ancilla excitation, calibration sensitivity, and a minimal Markovian noise estimate quantified separately. Bosonic-code examples illustrate how transfer sensitivity is governed by photon-number support and residual bright-mode phase errors. The result provides a practical benchmark and organizing principle for constrained ancilla-mediated bosonic transfer when direct exchange is unavailable or undesirable.