ALT In the companion paper (Part I), we developed an optimal-control framework to suppress intrinsic and decoherence-induced errors in controlled-Z (CZ) gates between directly coupled, frequency-tunable transmons. Here, we extend this framework to incorporate uncertainties in coupling strength, anharmonicities, and zero-flux qubit frequencies, enabling the design of high-fidelity gates robust against noise and parameter uncertainties. We classify these uncertainties by whether they perturb the off-diagonal coupling strengths or the diagonal detunings of the Hamiltonian, and we identify distinct suppression mechanisms for each class. Coupling errors are mitigated through dynamical decoupling induced by strong detuning modulation. For a 30-ns gate, this strategy reduces the coupling error to 6.21×10⁻⁷ and tolerates coupling-strength uncertainties up to 2π×4 MHz while keeping total gate infidelity below 10⁻³. Detuning errors are minimized near a symmetric-detuning operating point that balance

ALT Quantum key distribution (QKD), whose security is derived from quantum mechanics rather than computational assumptions, is moving into standardization and commercial deployment. Yet its security guarantees rest on technically delicate proofs checked by hand. Formal verification closes this gap, establishing a two-factor assurance: unconditional security from physical principles, and machine-checked proofs against reasoning errors. We present FVQKD, a Rocq library for machine-checking QKD security proofs. Its first result is a complete, end-to-end machine-checked proof of composable, finite-key security for BB84. The mechanization reconstructs the complete proof infrastructure from first principles, including the smooth entropy framework, the entropic uncertainty relation, and the Quantum Leftover Hash Lemma. It uncovers necessary side conditions that the published argument leaves unstated, one of which reveals a missing proof branch, and it grounds the information-theoretic bound in a

ALT Set coherence and set imaginarity are two important quantum resources defined by sets of states. We investigate tuples of qubit states under vanishing higher-order Bargmann invariants and show that their set coherence and set imaginarity are each related to whether they contain a pair of orthogonal states. Specifically, when the relevant higher-order Bargmann invariants vanish, the tuple contains a pair of orthogonal states if and only if removing some state makes the remaining tuple incoherent. Moreover, when maximally mixed states are excluded, the same vanishing conditions imply that the tuple is imaginarity-free if and only if it contains a pair of orthogonal states. As a consequence, under these conditions, a tuple of single-qubit states has imaginarity precisely when every tuple obtained by deleting one of its states is coherent.

ALT The purpose of this paper is to conduct a comprehensive structural analysis of quantum finite-level systems in the Heisenberg picture, where the evolution of system observables is modeled by bilinear quantum stochastic differential equations (QSDEs). Firstly, real coordinate transformations that preserve commutation and anticommutation relations are characterized, and relative admissibility between different orthonormal Hermitian bases is formulated. Secondly, strongly aligned subspaces are introduced, based on which decoherence-free subsystems (DFSs) are constructed in general orthonormal Hermitian basis as well as the generalized Gell-Mann basis. Thirdly, conditions for the existence of quantum nondemolition (QND) variables are given in terms of both linear systems theory and spectral separation by output-signal observables. Finally, a sufficient condition for quantum back-action-evading (BAE) measurements is established. A four-qubit nearest-neighbor Heisenberg chain with collective

ALT Excess micromotion induced by stray DC electric fields limits the control fidelity of trapped-ion experiments. Various techniques have been developed to detect and compensate ion displacements from the RF null by monitoring modulated fluorescence, ion positions, or micromotion sidebands. Although these approaches are effective, they do not probe the displacement through a ground-state-cooled motional mode and therefore offer limited compatibility with quantum-enhanced sensing protocols. Here, we demonstrate a micromotion compensation method based on the driven coherent amplitude of a ground-state-cooled motional mode. In this approach, the ion displacement is converted into a coherent motional excitation by an auxiliary RF drive and detected through the qubit. We determine the optimal compensation field with a 1σ statistical uncertainty of 8 mV/m. The method is naturally compatible with quantum-enhanced sensing protocols employing nonclassical motional states, including Fock, squeezed,

ALT Quasiperiodic systems combine sharply different spectral and localisation regimes with a dense hierarchy of dynamical time scales. We show that a finite-rate quantum Otto cycle can use this structure as a thermodynamic probe, revealing which parts of the spectrum become dynamically accessible and thermodynamically relevant during a driven transformation. For a generalised Aubry-André-Harper chain, the resulting response is not determined by the static quasiperiodic regime alone: extended, near-critical, and crossing protocols do not exhibit universal ordering of work fluctuations. Instead, the statistics reflect transition pathways that are simultaneously dynamically coupled, thermally occupied, and energetically significant. The same spectral accessibility separates thermodynamic recovery from microscopic adiabatic recovery. Positive mean work can reappear while the population transfer dynamics remain strongly nonadiabatic because finite-rate population transfer is redistributed towar

ALT Problem structure is regarded as a key factor influencing the performance of the Quantum Approximate Optimization Algorithm (QAOA), yet it remains an informal notion without a precise mathematical characterization. In this work, we address this issue by identifying a mathematical object that captures problem structure as seen from the perspective of the target state amplitude in single-layer QAOA. Specifically, we show that this structure is encoded in a joint probability distribution induced by the unique coarsest partition of the computational basis, determined by problem cost values and mixer-dependent walk counts. The statistical dependence between these classes provides a means of quantifying the available problem structure and identifying necessary conditions for exponential amplification. To assess the extent to which this structure can translate into algorithmic performance, we establish a mean-max non-separation bound relating the parameter-averaged probability of measuring th

ALT We review what it means for a relativistic particle to be localized and argue that the most useful approach is through local measurement. This perspective ties localization directly to relativistic causality and measurable outcomes in spacetime. Strict localization in quantum field theory is formalized by states that give the same expectation value as vacuum for all local observables outside some spacetime region. With this formalism, single photons cannot be strictly localized, but coherent states can. The structure and interpretation of local observables and local operator algebras are discussed in connection with the Reeh-Schlieder theorem. Since probabilities of local measurement outcomes cannot vanish in vacuum, particle detection events must be phrased carefully. Key characteristics of strictly localized states are surveyed alongside concrete strategies for constructing them. The relationship between localization, causality, and on-demand sources is analyzed, finding that strictl

ALT We propose distributed dual-comb spectroscopy, a quantum-enhanced sensing architecture that simultaneously exploits spatial- and spectral-domain entanglement to improve the extraction of global spectroscopic information across broadband frequency ranges. Our scheme consists of a network of Mach-Zehnder interferometers interrogating spatially separated samples, each driven by a classical frequency comb at the bright port. A single two-mode squeezed frequency comb is distributed through a passive beam-splitter array into K entangled combs, establishing multipartite correlations across sensors while preserving intrinsic spectral entanglement. The protocol is compatible with both heterodyne detection and division detection, and enables parallel estimation of weighted-average absorption features over multiple frequency components. Compared with spatially separable quantum strategies requiring K independently engineered nonclassical comb sources, our approach achieves enhanced signal-to-nois

ALT Coherence preservation and environmental renewal offer competing ways of controlling quantum memory and transport. We show that a seemingly natural protocol which exactly replaces the bath occupations while preserving arbitrary system–bath coherences need not correspond to a physical fermionic state. We instead construct a two-reservoir protocol with independent, number-conserving thermal attenuators, for which complete positivity and fermionic admissibility hold by construction. Physical attenuation necessarily modifies bath populations as well as cross correlations; the coherence control is not an independent hard-reset knob. Quadratic dynamics reduces the stroboscopic problem to an exact matrix fixed-point equation without a weak-coupling or Markov approximation. Analytically, coherence retention enhances the leading short-cycle transfer rate, including the complete-erasure limit; no general endpoint-vanishing theorem exists. An exact stationary continuity theorem forces the through

ALT Group IV color centers in diamond – silicon, germanium, tin, and lead-vacancy centers – are a promising platform for quantum networking. Typical Group-IV creation utilizes ion implantation during diamond growth that leaves the color centers with a broad depth distribution and damage-induced strain inhomogeneity. Deterministic placement and damage reduction in Group IV generation are essential for improving this platform. In this letter, we report on the localization of germanium-vacancy (GeV⁻) to a < 10 nm layer via the timed injection of GeH₄ during microwave plasma chemical vapor deposition. In this layer we have realized 17 ppm of Ge and a strain-free environment for the GeV⁻. Subsequent electron irradiation and annealing have generated a sheet density of 0.12 GeV⁻/μm². The minimal damage from color center generation mitigates spectral inhomogeneity and allows spectral resolution of isotopic clusters, with the best cluster having an inhomogeneous distribution of 2.14 GHz and an aver

ALT Pauli-based computation (PBC) is a measurement-based model of quantum computation that samples from output distributions of universal Clifford+T circuits. Here, we provide a normal form (NF) that completely characterizes its adaptive and entanglement structures. These insights unify PBC with one-way quantum computing as dual or `time-reversed' counterparts. We use the NF to advance strategies for distributed computation and investigate magic-state injection rates. We also demonstrate an exponential improvement in the detection of unnecessary magic-state qubits, allowing their efficient removal. Our NF further enables ahead-of-time circuit compilation using PBC, reducing CNOT gate count and quantum memory of random quantum circuits on average by 50% and 40%, respectively, beating other state-of-the-art compilers.

ALT Belief Propagation combined with Ordered Statistics Decoding (BP OSD) is an open-source decoding tool used widely within the community due to its versatility and ease of application to Quantum Low Density Parity Check (QLDPC) codes. However, the degeneracy of quantum codes has been observed to degrade the performance of BP OSD, particularly leading to error floors for low physical error rates. Here, we investigate the low-weight error configurations responsible for such failures in Bivariate Bicycle codes. We show that, at code capacity, BP OSD fails on errors whose weight is significantly smaller than d/2, arising from global symmetries of the decoding graph that prevent the convergence of parallel BP. Furthermore, our analysis reveals new pitfalls that can arise when analysing the performance of BP OSD in the rare events regime, such as loss of ergodicity in splitting methods and numerical instabilities in the decoder. We show how to mitigate these failure mechanisms by modifying the

ALT We consider the discrimination of two quantum channels acting on bosonic modes, with a probe state of fixed mean photon number and no ancilla. We prove that pure probes are optimal: for every mixed probe there is a pure probe with exactly the same mean photon number that performs at least as well. The result holds for arbitrary channels and for every figure of merit built from the Chernoff quantities \Tr[ρ₁^sρ₂¹-s], including the quantum Chernoff exponent, as well as for the single-shot error probability. The proof relies on a decomposition of any state of mean photon number \nb into pure states of mean photon number exactly \nb, which extends a matrix rank-one decomposition of Huang and Zhang to density operators of infinite rank.

ALT Fault-tolerant syndrome extraction is fundamental to stabilizer-code-based quantum error correction, yet existing general protocols incur substantial costs in either circuit depth or width. In this work, we design ancilla stabilizer states for a general transversal circuit to construct a family of fault-tolerant syndrome-extraction gadgets that interpolate between Shor and Steane syndrome extraction for any stabilizer code. The result is a configurable trade-off between circuit depth and width.

ALT Numerically simulating quantum many-body systems is one of the central challenges in modern physics, as the exponential growth of the Hilbert space with system size renders large-scale exact solutions intractable. Over the past decade, generative artificial neural networks have emerged as powerful wave function ansätze that have powered advances in finding ground state representations, reconstructing quantum states from data, and modeling dynamics in quantum many-body systems. While recurrent neural networks (RNNs) are computationally efficient, the recurrent nature can limit their capacity to capture long-range correlations. Transformer models with their underlying self-attention mechanism excel at capturing these long-range correlations, but incur increased computational requirements, restricting applications to small physical systems. In this work, we address these limitations by exploring the multi-layer perceptron (MLP) mixer model as a wave function ansatz. By mixing information

ALT AI agents are increasingly capable of constructing quantum algorithms and proofs, yet machine-checked proofs alone cannot guarantee that the intended problem is solved or that resource claims match the verified computation.Here we introduce Lean-QuantumAlg, a Lean 4 framework for trustworthy AI-assisted development of quantum algorithms.Its Algorithm-Solves-Problem contract binds correctness, success probability, borrowed-state restoration and quantum and classical resource bounds to a single execution, while separating the guarantees that Lean checks from the problem specifications and execution models that humans review. We demonstrate the framework on nine AI-formalized quantum algorithms, from Grover search to quantum attacks on RSA-2048 and P-256, with less than 1% of each algorithm's imported source code requiring statement-level human review once the shared framework has been audited. By integrating reusable mathematical foundations, certified algorithmic primitives and executio

ALT A two-level emitter chirally coupled to a waveguide imprints a π conditional phase on a two-photon pulse, a key component assumed in quantum photonic neural network architectures, but whether it survives the pure dephasing of a solid-state emitter is unknown, since no two-photon scattering treatment includes it. We derive the dephased two-photon amplitude in closed form and validate it against an independent Fock-state master equation. The conditional phase is pinned at exactly π at every dephasing rate examined: dephasing destroys the amplitude carrying the nonlinear phase rather than rotating it. The one- and two-photon channels are not attenuated equally, so dephasing does not simply scale the node down but reweights it between photon-number sectors—an error no phase setting can train away. The standard factorization of two-photon correlators, exact for arbitrary loss, fails at first order in γᵩ, discarding 16–81% of pairs over γᵩ/γ=0.1–1.

ALT We prove a conjecture of Yu, Lai, and Oh: their rounded family of strengthened quantum Hamming bounds, which interpolates between Hamming-type bounds and the Singleton bound, holds for arbitrary exact quantum subspaces of dimension K>1. The result covers every integer local dimension p≥2, every integer t≥1, both distances 2t+1 and 2t+2, and every interpolation parameter e∈{0,…,t}. Yu, Lai, and Oh proved these bounds for pure codes and for general codes of distance three or four; the case e=0 contains the ordinary quantum Hamming bound for general codes, recently proved by Zhang and Chen. More generally, for p≥3, we prove the inequality Kf(0)≤ pⁿEf(X), where XsimBin(n,1-p⁻²), for every real polynomial f of degree at most D, with 2≤ D<d, that is nonnegative on {0,…,n} and positive at zero; here n and d are the code length and distance.

ALT We propose a quantum architecture that achieves addressable and parallel universal fault-tolerant logical in high-rate codes. The codes are obtained from the flexible concatenation of small-distance high-rate self-dual CSS codes. Addressable and parallel universal logic on the resulting K logical qubits is injected by fault-tolerantly preparing and then consuming diverse logical K-qubit CSS stabilizer states and logical |H〉\ᵒᵗⁱᵐᵉˢᴷ global magic states. Flag-at-origin is used to prepare the stabilizer resource states while a concatenated cultivation protocol prepares the global magic states. These resource states are consumed by Steane-QEC or Knill-QEC teleportation gadgets, which simultaneously perform quantum error correction. Any quantum algorithm with T-depth D_T can be executed by consuming 12D_T or fewer resource states. We benchmark the fault-tolerant preparation of the resource states for several two-level concatenations of the [[k+4,k,2]] H codes and the Hamming [[15,7,3]] code