Papers

Photonic cluster states are fundamental resource for measurement-based quantum computing (MBQC), which is a promising approach for scalable quantum computing. These highly entangled states enable computation with applying local measurements rather than gate operations, which makes them essential for fault-tolerant quantum computing. Generation of the photonic cluster states requires high-quality entanglement and stability, which can be done by making use of cavity quantum electrodynamics (cavity QED), which is embedding quantum dots (QDs) into photonic microcavities. This method enables controlled single-photon emission and the entanglement of them, helping with key challenges in generating photonic cluster states. Enhancing the generation of the photonic cluster state requires improvement in the quality factor (Q-factor) and therefore, cooperativity of cavity and QD systems. A high Q-factor helps with reduction in photon loss and decoherence, ensuring more stable and high-fidelity quantum states. It also enables better light-matter interactions, improving cluster state quality. Cooperativity, which is a measure for the light-matter coupling strength relative to dissipation, directly impacts photon emission efficiency. Optimization of these parameters improves entanglement generation, which is essential for producing high-quality photonic cluster states. Therefore, optimized cavities are essential for improving the generation of the photonic cluster states. Scalability is also an important parameter for the generation of the large-scale cluster states used in quantum computing. In this paper, after reviewing MBQC, cluster states, and the generation of the photonic cluster states, we investigate the deterministic generation of the photonic cluster state resource for the purpose of MBQC, and highlights the importance of the inverse design techniques for this goal.

Quantum convolution provides a discrete-variable analogue of classical convolution, with the mean state capturing the stabilizer structure preserved under repeated convolution. We establish a finite-step entropy hierarchy generated by compatible stabilizer dephasings. Along every compatible isotropic flag, the entropy increases toward the mean-state entropy ceiling, while the relative-entropy distance to the mean state decomposes exactly into successive coherence losses and a terminal classical nonuniformity. Optimizing over compatible subspaces yields an intrinsic entropy profile of the state. For quantum convolutional channels, Weyl covariance reduces the one-shot classical communication problem to minimal output entropy. A spectral-transfer argument shows that suitable stabilizer inputs reproduce stabilizer-measurement distributions of the environment as channel-output spectra. This gives a computable Holevo lower bound over all complete stabilizer measurements; its compatible restriction is characterized by the entropy hierarchy and refines the previous mean-state bound of Bu, Gu, and Jaffe. The bound is exact for stabilizer-diagonal environments, for which the Holevo capacity is strongly additive, and yields a single-letter formula for a nonstabilizer qutrit family. The same family also exhibits a coexistence region with simultaneously positive classical and quantum communication rates

We explore coherent ergotropy extraction in quantum batteries from a resource-geometric point of view. For an initial state $\rho$, we quantify the coherent extraction process by the coherent ergotropy $\mathcal{E}_c(\rho)$ and the coherent extraction distance $D_c^{\rm ext}(\rho)$ between the active state $\sigma_\rho$ and the passive state $P_\rho$. This defines the geometric power capacity $\Pi_c(\rho)=\mathcal{E}_c(\rho)/D_c^{\rm ext}(\rho)$, which measures the coherent ergotropy released unit minimal unitary distance. We prove that, for any driving Hamiltonian satisfying $\|V_t\|\leq\nu$, the actual coherent discharging power is bounded by $P_c^{\rm ext}(\rho;V_t)\leq \nu\Pi_c(\rho)$, showing that $\Pi_c(\rho)$ is a capacity under unit driving norm rather than the power of a particular protocol. General bounds on $\Pi_c(\rho)$ are derived by combining relative entropy bounds on coherent ergotropy with geometric bounds on the coherent extraction distance. We also formulate coherence measure induced bounds and protocol-corrected capacities involving the effective speed of a given Hamiltonian. Qubit and qutrit examples demonstrate that $\Pi_c(\rho)$ captures a resource-geometric feature of coherent discharging beyond coherent ergotropy or coherence measures alone.

We introduce and study a periodically kicked version of a one-dimensional spin-$1/2$ Ising model with contiguous $p$-body interactions. At specific interaction strengths of the model, we establish an exact Floquet interaction $\textit{order-range}$ mapping: the Floquet evolution operator of the $p$-body Ising model is exactly mapped to a two body Ising model with interactions having maximum range $p-1$ and exactly determined couplings. Upon further tuning the kicking strength, the mapped model becomes dual-unitary, thus providing an explicit family of $p$-body dual unitary models. We then determine exact entanglement dynamics of the $p$-body model for a class of solvable initial states at all times. We further illustrate the nontrivial structures that can emerge from the $\textit{order-range}$ mapping using a minimal example of $p=3$ and generalize it for all odd $p$. These findings provide a systematic route to constructing and studying $p$-body dual-unitary Floquet models.

We investigate the geometric quantum discord of bipartite Werner states influenced by Hawking radiation in the quantum atmosphere of a Schwarzschild black hole. We find that the geometric quantum discord in the physically accessible region exhibits a nonmonotonic behavior: it first decreases and then increases as the normalized radial distance increases, while the discord in the physically inaccessible region shows the exact opposite trend. A pronounced extremum of geometric quantum discord occurs precisely at the position corresponding to the peak intensity of Hawking radiation. Furthermore, we find that the Hartle Hawking constant and the event horizon radius exert opposite effects on the strength of quantum correlation redistribution: a larger Hartle Hawking constant enhances the redistribution effect, whereas a larger event horizon radius suppresses it.

We develop a quantum model for the rotational dynamics of a freely floating levitated ferromagnetic gyroscope (LFG), emphasizing the interplay between intrinsic spin $\boldsymbol{S}$, mechanical angular momentum $\boldsymbol{L}$, and magnetic torque. The conserved total angular momentum projection along the $z$-directed magnetic field $\boldsymbol{B}$, $J_z=S_z+L_z$, is quantized, leading in the small-libration-amplitude limit to discrete precessional states $|m\rangle$ (eigenstates of $J_z$ with eigenvalues $J_z = m\hbar$) and librational harmonic oscillator states $|n\rangle$ ($n=0,1,2,\ldots$). The discreteness of the energies and dynamical variables is governed by the quantum precession scale $\Omega_Q=\hbar/I$, where $I$ is the moment of inertia of the LFG. We find that the phenomenon of LFG precession persists into high-field regimes where the magnitude of the rotational angular momentum associated with precession exceeds the total intrinsic spin. We analyze the complementary quantum limits of localized semiclassical LFG orientation wave packets and exact $J_z$-eigenstates $|m\rangle$, clarifying the relation between classical precession signals and the underlying quantized spin-rotor dynamics. We further show that radio-frequency fields can drive $\Delta m = \pm 1$ and $\Delta n = \pm 1$ transitions, enabling ladder spectroscopy, tilt-angle control, and sideband-like coupling between precession and libration. The coupled dynamics also exhibit branch-point magnetic resonances where precession and librational motion become strongly coupled. These results establish a framework for using LFGs not only as ultrasensitive torque and magnetic-field sensors, but also as controllable mesoscopic quantum systems. The techniques developed here may be applied to searches for exotic, beyond-the-standard model spin-dependent interactions, ultralight dark matter, and spin-gravity couplings.

Nanophotonic platforms have multiple properties and features desirable for producing correlated photon pairs. In these platforms, spontaneous parametric down-conversion (SPDC) and spontaneous four-wave-mixing (SFWM) have been used to achieve photon pair production. By placing the nonlinear region in a resonant cavity, the source obtains an enhanced nonlinear interaction and naturally filters out photons by frequency according to the cavity linewidth. Among various platforms, X-cut thin-film lithium niobate (TFLN) stands out for its strong second-order optical nonlinearity ($\chi^{(2)}$) and access to a strong platform for modulating light. Although previously demonstrated, present sources are limited in their photon pair channel availability, limiting the potential of quantum applications in quantum information processing, communication, and sensing that can scale in robustness by having access to multiple photon pair channels. To this end, we demonstrate a photon pair source on X-cut TFLN with 80 measured photon pair channels spanning the C and L optical bands with a frequency spacing of 49.5 GHz between photons. We characterize the second-order correlation function and pair generation rate (PGR) of 80 channels, the highest number of channels demonstrated to date, and achieve a pair generation of 125.7 kHz / {\mu}W after accounting for the cavity's escape efficiency. We also demonstrate heralded single photon operation by calculating a heralded auto-correlation dip of 0.0544 $\pm$ 0.0054 with 2.2 mW of on-chip pump power. These findings demonstrate the promise of X-cut TFLN as a strong platform for quantum optical applications.

Black-hole hair can affect boundary mixed-state entanglement through local stress-energy and through topological information invisible to the classical metric. We separate these channels for a Nielsen–Olesen vortex on a nonrotating BTZ black hole. A superselection theorem shows that Shannon sector entropy cancels from the Markov gap, while standard $U(1)$ symmetry-resolved reflected entropy in a thermal $U(1)_k$ CFT is equipartitioned at leading order, excluding a universal $\log|n|$ term in the imbalance-resolved gap. We therefore define a Wilson-threaded reflected moment in a probe $U(1)_k$ Chern–Simons completion coupled to the compact vortex-flux class. In a reflected-replica sector with linking number $\nu$, its normalised phase is $2\pi\kappa pn\nu/k$, where $\kappa\in\mathbb Z$ is the mixed topological coupling; for $\gcd(\kappa\nu,k)=1$, a discrete Fourier transform reconstructs $n\bmod k$. The RT connectivity transition switches the specified linked contour on or off, whereas the independent scale $\ell_\star r_+/L^2=1.128378\ldots$ determines the direction of the vortex-induced shift of that transition. The charged-moment modulus and the ordinary Markov gap remain geometric observables and are computed from a horizon-anchored Einstein-Abelian-Higgs solution with a complete first-variation kernel including the motion of the entanglement-wedge cross-section endpoints. This phase and modulus separation distinguishes topological hair from gravitational dressing without assigning an unsupported winding-dependent entropy.

Optimal Polynomial Intersection (OPI) is a structured optimization problem for which Decoded Quantum Interferometry (DQI) attains a satisfaction guarantee governed by the semicircle law. Sun and Wootters recently showed that, for balanced OPI over prime fields, a Fourier-defined distribution $P_u$ gives a strict worst-case improvement from limiting rate $0.6225$ onward and asymptotically perfect solutions from rate $0.7496$ onward, and asked whether $P_u$ can be sampled efficiently. We answer this question for Reed–Solomon OPI parameters satisfying their exponent condition strictly below the dual Johnson radius. Under coherent membership-oracle access, we give a bounded-error polynomial-time quantum sampler for $P_u$. The ideal circuit samples $P_u$ exactly conditioned on success, while a finite-precision implementation achieves any prescribed inverse-polynomial total-variation error. Consequently, every fixed limiting rate $0.6225\le r<1$ admits a strict worst-case improvement over the DQI semicircle value, and every limiting rate $r\ge 3/4$ admits solutions of satisfaction $1-o(1)$ with high probability. The algorithm coherently sums the amplitudes of all low-weight errors in each syndrome class using deterministic complete list decoding. Complete Reed–Solomon list decoding and the Sun–Wootters denominator estimate make the list size and postselection overhead polynomial. In concurrent and independent work, Horinaga and Yamakawa obtain worst-case OPI algorithms over prime-power fields and exact satisfaction at every fixed rate strictly above $3/4$.

Recent work has demonstrated non-diffractive topological spin textures (Skyrmion- and meron-like) that persist in the core of diffracting relativistic twisted fermion beams [1]. Here we present numerical simulations of an analogous photonic system: Laguerre-Gaussian (LG) twisted photon packets coupled to a gauged Hopf lattice with discrete flux flywheels. Our results reveal emergent behavior of the same qualitative class, including persistent core features under propagation, mean survival approx 0.150 at critical lambdat = 2 clustering tightly with the mystery scale e^{-2} approx 0.1353 and residual R approx 0.1375, golden-angle correlations in the OAM mode ladder, and topological residuals with long-lived structure. Multi-l simulations further exhibit z-resolved flux transfer and twist dynamics that play a role analogous to probability-current continuity in the fermionic setting. These findings suggest photonic platforms as accessible analogs for exploring topological textures in structured waves, and they formalize a concrete computational bridge between relativistic twisted matter waves and topological photonics.

Bateman's dual oscillator embeds a damped harmonic oscillator and an independent anti-damped adjoint coordinate in a conservative doubled system. We develop a split-quaternionic formulation that remains consistent from the classical equations through ordinary complex canonical quantization. The doubled dynamics is written as a two-sided hypercomplex evolution whose conserved indefinite quadratic form is the split norm, while the sign of the generator square unifies the underdamped, overdamped, and critical regimes. The Bateman Lagrangian is recovered as a real scalar action on the split-complex configuration subalgebra. After quantization, operator-valued split quaternions belong to the complexified algebra $\mathbb C\otimes_{\mathbb R}\mathbb H_s\simeq M_2(\mathbb C)$. Noncommuting mechanical components require a symmetrized quantum split norm, which exactly reproduces the symmetrically ordered canonical Hamiltonian. Null idempotents resolve the crossed canonical structure of the doubled phase space. In particular, damping yields $[m\dot{\widehat y},m\dot{\widehat x}]=\mathrm{i}\hbar m\gamma$ and a Robertson–Schrödinger uncertainty relation. The limit $\gamma\to0$ retains the doubled positive/negative geometry; the ordinary single-oscillator Heisenberg relation is recovered only after selecting the positive normal mode, or by undoubling before quantization. The scalar split action gives the exact quadratic propagator and Gaussian evolution. A formal trace over the auxiliary coordinate is finally compared with high-temperature Caldeira–Leggett dynamics, clarifying that the doubled model is a coherent zero-noise embedding rather than a microscopic reservoir theory.

We study the two-step Floquet dynamics of the chiral $J_1$-$J_2$-$K$ Heisenberg model on the $4\times4$ torus, alternating its non-chiral Heisenberg part $H_{AF}$ and its chiral plaquette part $H_K$, at a parameter point where the static model hosts a quasi-degenerate, spectrally isolated chiral-spin-liquid (CSL) topological doublet. The one-period propagator is computed exactly in all symmetry sectors. Decreasing the frequency, the doublet survives the drive far beyond the frequency $\omega_{res}\simeq 11.5 J_1$ at which folded states first cross it in quasienergy: the time-averaged energy of the Floquet eigenstates, which orders the folded spectrum, shows that the doublet remains the isolated bottom of the spectrum down to $\omega\simeq 6J_1$, while stroboscopic time evolution over thousands of periods shows no heating for $\omega\gtrsim\omega_{res}$ and only slow absorption below. The quasienergy resonances of the folded regime are invisible in the average energy, identifying them as parametrically weak avoided crossings. We argue that this mechanism, stability controlled by local energy scales rather than by the extensive many-body bandwidth, is of the type expected to survive in the thermodynamic limit, where a prethermal Floquet CSL should persist for $\omega$ above a threshold set by local scales, with heating times exponentially long in $\omega/J_1$, a conjecture that larger clusters can now test. Consistently, the optimal $D=3$ chiral PEPS of the static problem still describes the driven doublet deep in the folded regime, with an essentially unchanged local tensor. Finally, we show that the drive is realizable on existing quantum simulators, via an explicit digital pulse sequence of XY-type two-spin gates on the four bond colours of the square lattice, with an infidelity of $1.5\times10^{-5}$ per period.

Holography is a central concept at the intersection of gravity, condensed matter theory, and quantum information, linking the interior bulk of a system to its boundary. A model realizing key features of holographic systems is the holographic pentagon code by Pastawski et al. Here we experimentally implement instances of the holographic pentagon and heptagon codes with trapped ions and test their properties: For the pentagon code, we recover logical bulk qubits from their nearby boundary and test the Ryu-Takayanagi entanglement area law. For the heptagon code, we show that the transversal Hadamard gate native to the constituent Steane codes induces a single-qubit, correctable error in the holographic code. Our implementation paves the way towards the use of holographic quantum codes for quantum information processing.

Superconductor-semiconductor Josephson junction arrays are a uniquely tunable platform for studying collective quantum phenomena, particularly in the regime where localized Andreev bound states can hybridize across the lattice when the physical separation between adjacent junctions is smaller than their coherence length ($\xi_{\text{ABS}}>d_{\text{JJ}}$). Here, we investigate three distinct Al-InAs Josephson junction arrays: a square array and super-honeycomb array fabricated within this ${\xi_{\text{ABS}}>d_{\text{JJ}}}$ regime, as well as a larger-spacing super-honeycomb control device designed such that $\xi_{\text{ABS}}\lesssim\!~d_{\text{JJ}}$. Under an out-of-plane field, critical current peaks emerge at rational filling factors, reflecting stable vortex configurations in the lattices. In the super-honeycomb lattice, vortices localize to distinct non-identical plaquettes at different filling factors, as predicted by frustrated XY model simulations. A rotating in-plane field yields periodic critical current oscillations that reflect the Rashba spin-orbit coupling inherent to the InAs quantum well. Surprisingly, at $f = 1$, the closely spaced super-honeycomb array exhibits a distinct critical current minimum as the magnitude of the in-plane field increases, a signature absent in the square array and large-spacing super-honeycomb array. These results indicate that this signature is jointly influenced by the unique geometry of the super-honeycomb vortex lattice and by long-range inter-junction hybridization.

Bond reconstruction in vacancy-related structures affects their formation energies, symmetries, and electronic and optical properties. Using density functional theory, we investigate bond reconstruction mechanisms of monovacancies and vacancy aggregates in monolayer silicon carbide. Multiple bond descriptors reveal that isolated monovacancies undergo both in-plane reconstruction and out-of-plane distortion, which together shape their stability and electronic structure. For compact vacancy aggregates, we show that bond reconstruction acts as a key stabilization mechanism. However, in carbon monovacancy, reconstruction suppresses optical activity. In contrast, a highly stable aggregate composed of three carbon vacancies surrounding a silicon vacancy emerges as a promising infrared color-center candidate, combining a triplet ground state with a favorable Debye-Waller factor of the emission. These results highlight the role of bond reconstruction in defining the quantum properties of vacancy defects in two-dimensional silicon carbide.

Molecular materials that enable coherent control over an electron's spin state at room temperature are promising candidates for quantum technologies, including quantum sensors and ultra-low noise microwave amplifiers, known as masers. Host-guest molecular crystals enable independent control of spin-active guests and their local environments to enhance molecular spin properties and so improve device performance. Using electron paramagnetic resonance and optically-detected magnetic resonance, we demonstrate the ability to tune triplet population, depopulation, and spin-lattice relaxation by modulating host-dependent lattice rigidity and vibrational coupling to significantly reduce the operating requirements for building useful masers. Importantly, the most rigid host, picene, reveals the ability to slow spin-lattice relaxation without lengthening triplet lifetime, though at the cost of strain-induced line width broadening and reduced triplet spin polarisation. We also find that deuteration reduces the triplet resonance line width and vibrationally-mediated triplet depopulation. Consequently, we find that perdeuterated pentacene in perdeuterated p-terphenyl is the most viable candidate for building a continuous wave maser. This work demonstrates host-guest engineering as an important and practical method for tuning the spin-dependent performance of room-temperature molecular quantum technologies.

We consider a formal model of quantum circuit description languages (QCDLs) in which semantically meaningful programs correspond to computable unitary matrices. We show that any semantically universal QCDL – that is, any QCDL able to describe all computable unitary matrices, which in turn form the set of matrices we can meaningfully represent on digital hardware – cannot have a semi-decidable set of semantically meaningful descriptions. In particular, no such language admits a compiler that reliably recognizes all valid program descriptions. This result stands in contrast to classical programming languages. While compilation in languages such as C or C++ may itself involve non-terminating computations, the set of semantically meaningful programs remains recursively enumerable, since successful compilation provides a witness of validity. The essential difference lies in the nature of the semantic domains: classical languages describe partial recursive functions, whereas QCDLs describe total unitary operators. Our analysis establishes a fundamental limitation of quantum circuit description languages and highlights a structural distinction between classical and quantum models of computation at the level of formal language theory.

We demonstrate a novel method for remote open-path Fourier-transform infrared spectroscopy with undetected photons. Similar to previous quantum spectroscopy works, a mid-infrared spectrum is reconstructed by detecting a near-infrared radiation only, thus bypassing important limitations of infrared detectors. Our study however relies on the co-propagation of the photon-pair and the pump-laser over the same optical path, which allows the probing of the open atmosphere over long distances. By sending the photons over unprecedented distances of up-to 43.4m in the outdoor atmosphere, we were able to detect butane released in the open-path, as well as natural atmospheric methane, thus demonstrating the first use of infrared spectroscopy with undetected photons for atmospheric measurements.

Diverging timescales are the hallmark of critical dynamics and the bottleneck to their classical and quantum simulation. To tame this, we compress a spacetime tensor network: temporally into semigroup influence matrices and spatially via matrix-product states. Benchmarking on the two-impurity Anderson model with its four fermionic species, we compute spectral functions to map the evolution from a Kondo resonance, across a non-Fermi-liquid quantum critical point, and into a gapped singlet phase. Resolving transient through asymptotic dynamics in sudden quenches and Kibble-Zurek ramps, we obtain the universal two-channel-Kondo exponent. Together, these results establish multibath influence matrices as a practical tool for real-time dynamics in strongly correlated multi-orbital systems.

The EWF-(FCI,SQD) method, a wave-function-based embedding approach combining full configuration interaction (FCI) and sample-based quantum diagonalization (SQD), is a promising new tool for the simulation of molecular systems. However, applications of EWF-(FCI,SQD) have so far been limited to single-point calculations, whereas the study of complex chemical processes requires the ability to explore potential energy surfaces. In this work, we demonstrate geometry optimization with EWF-(FCI,SQD), scaling our simulations to molecules as large as menthone and benzidine within the STO-3G basis set. Without fragmentation, these systems comprise 73 and 82 molecular orbitals respectively, presenting an intractable Hilbert space for conventional exact or high-level subspace solvers and establishing a clear necessity for fragmentation-based methodologies. The underlying fragment SQD simulations in the EWF-(FCI,SQD) geometry optimizations use up to 70 qubits. The resulting geometries show exceptional accuracy relative to the classical reference, with deviations below 4 picometers.

We show that no stabilizer state in a discrete realization of a local quantum field theory can flow in the continuum to the vacuum or to any state that resembles the vacuum at short distances. The argument rests on the fact that the entanglement spectrum is flat for stabilizer states but non-flat for cyclic and separating states in a local QFT as a consequence of the type III$_1$ nature of the von Neumann algebras associated with arbitrary subregions. Our result implies that simulating physically relevant QFT states necessarily requires quantum resources beyond stabilizer states and Clifford operations. We comment on the implications for holography.

Real-space geometric curvature in magnetic thin films introduces a controllable mechanism for tailoring the pathways of superconducting steady-state Josephson currents via the proximity effect. We present a generalized Green's function method for calculating diffusive transport in arbitrarily curved surfaces, and show how the competing mechanisms of curvature and distance regulate conversion between different superconducting pairings in a proximity-coupled ferromagnet. We show how this dictates the distribution of current density, with the possibility of curvature-controlled current density manipulation, induced eddy currents and current reversal.

Every two-qubit measurement basis composed of maximally entangled eigenstates can be transformed into the Bell basis via local unitary operations. For higher dimensions, in contrast, there exist inequivalent bases composed of maximally entangled eigenstates. Here, we provide a single-parameter family of two-qutrit maximally entangled measurement bases, and demonstrate that none of the bases are equivalent to each other under local unitaries. These bases are constructed from the continuous family of symmetric informationally complete sets of states in dimension three. By studying the local unitary bases that generate the family of two-qutrit maximally entangled measurement bases, we construct the first examples of wild error bases in the smallest dimension where these can exist. Finally, we discuss how distinct measurements in the family lead to differences in performance in several scenarios relevant in quantum information.

Quantum many-body Hamiltonians with two-body interactions can be represented by graphs, with sites as nodes and two-site couplings as edges. We investigate how the geometry of these graphs affects transport and entanglement growth. To do so, we study dynamics for quantum hopping on a random graph model with an effective range parameter. Tuning it, we interpolate between nearest-neighbor and all-to-all graphs, identifying a new localization regime that is robust in both single-particle and finite-density cases. This provides a model of Anderson localization induced by structural disorder, with implications for amorphous materials and tunable-range analog quantum simulators.

Floquet driving underlies Hamiltonian and gate engineering, and produces dynamical orders with no equilibrium counterpart. These phenomena are, however, transient in well-isolated systems. We show that statically coupled dissipative auxiliaries cool the system toward low-energy states of the Floquet-engineered Hamiltonian, stabilizing orders in the steady state. The excess energy density is controllably small at high drive frequency and weak coupling and is captured by rate theory based on Fermi's Golden Rule. We numerically confirm robust cooling in a Floquet-engineered transverse-field Ising chain in both phases, and demonstrate discrete time-crystalline order, with a period-doubled magnetization response, in the steady state of a long-range Ising chain. Our results provide a rare analytical handle on the steady states of driven dissipative systems.

Open-shell $3d$ transition-metal complexes pose a stringent challenge for correlated electronic-structure methods because near-degenerate metal $d$ orbitals give rise to competing spin states and oxidation-state-dependent charge transfer, while solvation can reshape the relative stability of the resulting electronic configurations. Building on prior demonstrations of open-shell sample-based quantum diagonalization (SQD) for light-atom systems and, separately, closed-shell SQD coupled to the integral-equation-formalism polarizable continuum model (IEF-PCM), we combine these capabilities through an open-shell SQD–IEF-PCM framework and apply it to the octahedrally coordinated $\mathrm{[Co(H_2O)_5CO_2]^{2+/3+}}$ complex, spanning the Co(III) singlet and quintet and Co(II) doublet and quartet states along a metal–ligand dissociation coordinate. Using quantum samples collected on an IBM Heron processor and active spaces of up to 50 qubits, SQD closely reproduces coupled-cluster and heat-bath configuration-interaction benchmarks within the same active spaces in both gas phase and implicit solvent; for high-spin quintet $\mathrm{[Co(H_2O)_5CO_2]^{3+}}$, it additionally resolves an avoided crossing associated with internal charge transfer that is absent in the corresponding singlet and in the lower oxidation state, while IEF-PCM suppresses this crossover by preferentially stabilizing the dissociation channel leading to neutral CO$_2$. To our knowledge, this work provides the first hardware demonstration of SQD for an open-shell 3d transition-metal complex with discrete metal-centered d-orbital chemistry, and the first application of open-shell SQD in a dielectric continuum, establishing a quantum-centric framework for transition-metal chemistry in regimes where spin-state energetics, charge transfer, and environmental response are strongly coupled.

It is well known that classical analog circuits and systems benefit from the powerful Thevenin and Norton theorems. These theorems enable rigorous and exact mathematical simplification and representation of the effect of the rest of a system on the part we want to focus on. We show that there are corresponding versions of a "Quantum Norton Theorem" that enable exact simplification and reduction for quantum circuits and systems, not just for one port, but also for multiport and even open quantum systems. We demonstrate the method on two level systems, chains, system environment partitions, Lindblad examples, and Grover search. The Grover examples show how the reduced network isolates the bright pole governing ideal search and exposes how diagonal disorder transfers spectral weight into dark poles that degrade performance. By partitioning finite dimensional Schrodinger dynamics into retained and eliminated sectors, we show that Gaussian elimination gives an exact reduced equation in which the eliminated subsystem appears as a dynamical self energy and a source term. In the circuit representation, these terms become the Norton admittance and Norton current source seen by the retained quantum port. The same Schur complement construction extends to multiport reductions, composite system environment partitions, density matrix dynamics, and Lindblad evolution in Liouville space.

Covariance dynamics on the positive-definite cone are commonly described by gradient flows, which encode dissipative relaxation but obscure the underlying phase-space structure. We construct a finite-dimensional Hamiltonian lift of covariance dynamics on Sym$^+_n$ equipped with the Bures–Wasserstein metric. The natural mechanical Lagrangian yields canonical momentum $\Pi=\tfrac12 L_\Sigma[\dot\Sigma]$, where $L_\Sigma$ is the Lyapunov operator, and explicit Hamiltonian $\mathcal{H}(\Sigma,\Pi) = 2{\rm tr}(\Pi\Sigma\Pi)+V(\Sigma)$. Adding Rayleigh dissipation recovers the Bures–Wasserstein gradient flow in the overdamped limit. For a spectral-floor and trace-control potential, the quadratic fluctuation Hamiltonian around the isotropic equilibrium separates trace and traceless modes; the baseline stiffness diverges as $(s-\nu)^{-2}$ as the equilibrium covariance approaches the floor. The construction identifies a conservative parent system for constrained Bures–Wasserstein covariance relaxation and fixes the local stiffness scale induced by the spectral floor.

For centered bosonic Gaussian states, the covariance pullback of the Bures cometric differs from the lift-normalized classical covariance Fisher–Rao cometric by a state-independent bilinear form. Under the canonical identification of symmetric covariance covectors with $\mathfrak{sp}(2N,\mathbb{R})$, this form is the trace form and hence a fixed multiple of the Killing form. We prove that, within the normalized symmetric Petz family, Bures is uniquely selected by requiring such an additive state-independent symplectic correction. We determine the full Williamson-frame spectrum and show that a boundary stratum with $m$ pure modes has an $m^2$-dimensional cometric kernel isomorphic to $\mathfrak u(m)$, while the pure Gaussian orbit remains nondegenerate. For radial one-mode estimation, ideal heterodyne detection accesses the exact fraction $(\nu-\hbar/2)/(\nu+\hbar/2)$ of the SLD quantum Fisher information. Its vanishing boundary limit reflects finite heterodyne information relative to a divergent radial quantum Fisher information, not zero measurement information. Finally, a minimal Schur realization fixes the auxiliary inertia and identifies the second Schur complement as the true covariant vertical block.

Adversarial collaborations have become increasingly prominent in empirical science, where proponents of competing theories jointly design experiments capable of discriminating between them. Much less attention has been given to theoretical disputes that cannot readily be resolved by experiment. We distinguish theoretical adversarial collaboration from its empirical counterpart and propose a five-step template for conducting it. The procedure is designed to move disputants beyond familiar critique-reply-rejoinder exchanges by requiring sustained clarification, supervised steel-manning of the target theory, and the collaborative development and refinement of objections. Its condition for success is that the collaboration produce insights that substantially exceed the existing literature: either novel, non-obvious arguments show that the theory can meet the objections, or the theory's advocate concedes that new conceptual resources or revisions are required. The template was developed through reflection on, and implemented in, our own adversarial collaboration in philosophy and foundations of physics. We offer it here as a general framework for constructive and publishable progress in philosophy, foundational science, and other areas of inquiry in which disputes cannot readily be resolved by experiment.