Papers

We show that private correlations in a bipartite quantum state constitute a metrological resource for distributed sensing assisted by a possibly noisy channel from one party to the other. We begin with an example with distillable secret key but poor locally accessible sensing performance and show that an assisting channel substantially improves its performance. We then show that any shared state yielding positive private information can serve as a sensing resource after appropriate local coherent processing, and derive a quantitative lower bound on the locally accessible sensing capability after assistance. We further show that classical correlations alone provide no analogous guarantee. Finally, in a channel formulation, we show that a channel with positive private information allows nonzero locally accessible sensitivity when paired with a suitable assisting channel.

We study local marginals in one-dimensional translation-invariant quantum systems that may hide finite-period structure. Given an $n$-site reduced density matrix, we ask whether it can be obtained by repeating a finite $p$-site block state along the chain and averaging over the $p$ lattice translations. This defines a symmetrized block-product periodic marginal problem, which provides a route both to diagnosing hidden periodic order from local data and to upper bounding ground-state energy densities of infinite translation-invariant local Hamiltonians. We develop two complementary methods. The first is a semidefinite-programming relaxation based on block permutation symmetry and positive partial transpose constraints, which outer-approximates the convex hull of such marginals and yields certified infeasibility tests. The second is a symmetrized matrix product state ansatz, which constructs explicit block-product periodic states and gives variational upper bounds. We benchmark the framework on the Majumdar-Ghosh model, transverse-field Ising, XX, XXZ, and contextuality-related spin models. The results show that the method captures the expected finite-period structure in exactly solvable cases and gives systematically improving variational energies as the period and bond dimension increase. We also formulate a periodic-NPA relaxation for translation-invariant contextuality witnesses and recover the known quantum limits in the tested examples.

The redistribution of the wave feature, particle feature, and mixedness is investigated for two-qubit isotropic states in Schwarzschild spacetime under Hawking radiation and environmental decoherence. It is shown that Hawking radiation changes their relative weights among different horizon regions rather than simply suppressing them. The analysis is further extended to phase damping, phase flip, and bit flip channels. Phase damping monotonically suppresses the wave feature and enhances mixedness, phase flip produces a symmetric death-and-revival behavior of the wave feature, and bit flip mainly reshapes the particle feature and mixedness through diagonal population redistribution. However, although Hawking radiation and channel noise affect the distribution of wave feature, particle feature, and mixedness in the subsystems, the triality relation among them still holds and remains unaffected by thermal and environmental noises.

This thesis studies exact, deterministic preparation of arbitrary dense n-qubit states, the data-loading step in quantum signal and image processing. It derives two syntheses built on the Digital Signal-induced Heap Transform (DsiHT): the QsiHT Fast Path Real Synthesis and the QsiHT Fast Path Complex Synthesis. Both are benchmarked against ten configurations spanning the UCR, isometry, multiplexor, Schmidt/SVD, QSD, and heap-transform families. Several of those are realizations through Qiskit builders or compiler optimization, not from-scratch reimplementations. The n=3 noisy comparison spans ibm_fez, ibm_kingston, and ibm_marrakesh, three 156-qubit IBM Heron r2 processors, where single-submission nine-method jobs permit within-session family-wide Benjamini-Hochberg-corrected comparisons. The frontier-versus-QSD separation reproduces within one calibration on every device, but the within-frontier order does not reproduce across devices or calibration days. A deep-circuit n=8 run on ibm_fez shows the executed-count ordering re-emerge outside the run-to-run spread on the complex target. Depth was not isolated from mapping, gate composition, calibration, or session effects. All methods are exact to machine precision and differ only in cost. Under noise the coarse error tier tracks the executed (routed) two-qubit count, separating the Theta(2^n) frontier from QSD's Theta(4^n) and nothing finer. Both syntheses realize the deployed Qiskit StatePreparation floor of 2^n-n-1 CNOTs, undercutting every other from-scratch method on the as-built CNOT axis. The Real Synthesis serves real (sign-bearing) targets and holds the lowest classical build cost among the exact loaders at large register sizes, through one fast Walsh-Hadamard pass. The Complex Synthesis serves arbitrary complex targets and ties Qiskit's StatePreparation for the lowest simulated sampled error.

Let $\mathcal H$ be a finite-dimensional complex Hilbert space, and let $w(P,\mathsf M)$ be a normalized probability weight assigned to an outcome projection $P$ as it occurs in a projective measurement $\mathsf M$. For fixed $P$, let $G_P\cong\mathcal U(P^\perp)$ be the group of unitaries acting identically on $\operatorname{ran}P$ and arbitrarily on $P^\perp$. We classify the $G_P$-orbits of projective measurements containing $P$: two measurements lie in the same orbit exactly when the multisets of ranks of their complementary outcomes agree. The orbit with profile $\lambda=(r_1,\ldots,r_k)$ is a compact homogeneous space of real dimension $(d-\operatorname{rank}P)^2-\sum_j r_j^2$. On maximal rank-one measurements there is one orbit, so context independence is equivalent to $G_P$-invariance, with equality of the corresponding uniform defects; invariance under two-level complementary unitaries already suffices. For arbitrary projective measurements, every context containing an outcome $P\neq I$ coarsens to the unique binary context $\{P,I-P\}$. Consequently, refinement consistency alone is equivalent to context independence. The finite orbit space carries a natural rank-profile refinement graph, whose diameter is $d-\operatorname{rank}P-1$ when $P\neq I$. We prove a stability theorem that compares the binary-coarsening path with a shortest path in this graph followed by one complementary unitary. In dimension at least three, Gleason's theorem converts the maximal-context invariance condition and the all-context refinement condition, on their respective domains, into the Born form $\operatorname{Tr}(\rho P)$. The results are structural characterizations, not independent physical derivations of context independence.

We introduce a programmable Heisenberg-limited bosonic quantum sensor based on a nonlinear quantum energy pump, implemented with a Kerr-nonlinear resonator coupled to multiple high-Q microwave terminal resonators. For parameter estimation encoded in an arbitrary number-conserving Hamiltonian acting on the terminal modes, we analytically construct optimal sensing protocols that attain the maximal quantum Fisher information, including initial-state loading, probe preparation, and readout. For diagonal multiparameter signals, we further show that the full phase-sensing quantum Fisher information matrix can be obtained from correlations of locally measured physical terminal works, providing a signal-free calibration of the metrological resource. We numerically demonstrate the construction and its robustness using realistic circuit-QED parameters while including experimentally relevant imperfections.

Multiparameter estimation remains a fundamental challenge in quantum estimation theory because the optimal measurements associated with different parameters are generally incompatible. In this work, we develop a Bayesian framework for the simultaneous estimation of multiple parameters. Our approach builds on Personick's method, in which the estimation problem is reduced to a set of Lyapunov equations whose solutions define optimal observables for the individual parameters. Since these observables generally do not commute, we construct a convex combination of the solutions, parameterized by a set of variational parameters. The spectral decomposition of the resulting operator defines a parametrized projection-valued measure. The resulting projective measurement determines the likelihood function, from which the minimum mean-square error estimators and the corresponding Bayesian mean-square errors are obtained, following standard Bayesian procedures, as functions of the variational parameters. To determine their optimal values, we formulate a minimax optimization problem based on the normalized Bayesian mean-square errors, introducing a min-max normalization procedure that enables a meaningful comparison of estimation errors associated with different parameters. This optimization yields a variationally optimized projective measurement for simultaneous Bayesian estimation. Two qubit examples, involving phase estimation and the estimation of parameters defining convex combinations of unitary operations, demonstrate the construction of optimized projective measurements and the corresponding minimum mean-square error estimators within the proposed framework for finite data sets.

We study incomplete sets of orthogonal stabiliser states that cannot be extended by a further stabiliser state orthogonal to all of its members. Such sets are the stabiliser analogue of unextendible product bases (UPBs), and we thus call them unextendible stabiliser bases (USBs). Leveraging the symplectic geometry underlying the $n$-qudit Pauli group in prime local dimension, we explicitly construct USBs for systems of four qubits and three qudits of odd prime local dimension. Moreover, we show that these are the respective minimal qubit, respectively qudit numbers for which such bases exist, and that USBs exist for all $n\geq4$ qubit and for all $n\geq3$ odd-prime-dimensional qudit systems. Finally, we compare the resource-theoretic aspects of USBs with those of UPBs. We establish that, analogous to the case of UPBs, the orthogonal complement of every unextendible stabiliser set is a stabiliser-free subspace, and its normalised projector is necessarily magic; moreover, it is bound magic in odd prime dimension, yet need not be for qubits. We also show that USB unextendibility alone imposes no uniform quantitative obstruction to discrimination by stabiliser operations.

Erwin Schrödinger is often portrayed as a reactionary who resisted the indeterminism introduced by quantum mechanics, but on closer inspection his views on determinism prove to be more complex and more radical.

We study the best separable state problem (BSS), which asks for the maximum acceptance probability of a quantum measurement over unentangled states. In classical terms, the goal is to maximize $\langle(x \otimes y), M (x \otimes y)\rangle$ over unit vectors $x,y$ where $0 \preceq M \preceq I$; we call this value $\mathrm{BSS}(M)$. We study $\mathrm{BSS}$ in the "perfect completeness" regime, where given $M$ such that $\mathrm{BSS}(M) = 1$ the goal is to find the best possible solution $x,y$ – this generalizes the problem of finding a rank-one matrix as close as possible to a given subspace of $\mathbb{R}^{n \times n}$ guaranteed to contain a rank-one matrix. The strongest known algorithmic guarantees for this problem are: (1) an algorithm which finds a solution with value $1-\varepsilon$ in time $\exp(\sqrt{n} (\log n)^{O(1)} / \varepsilon^2)$, due to Barak, Kothari, and Steurer, and (2) an algorithm which finds a solution with value $q/n$ in time roughly $n^{O(q)}$, due to Bhattiprolu, Ghosh, Guruswami, Lee, and Tulsiani. We give a much simpler approach to rounding the SoS relaxation, generalizing the canonical "global correlation rounding" technique, and obtain a better running time. Given $M$ with $\mathrm{BSS}(M) = 1$, our algorithm finds a solution with value $1-\epsilon$ in time $n^{O(\sqrt{n/\varepsilon})}$, and a solution of value $q/n$ in time $n^{O(\sqrt q)}$. Using the same techniques, we prove a new variant of the "pinning lemma", a measure-decomposition theorem widely used in LP/SDP rounding, high-dimensional probability, and statistical physics, which we believe is of independent interest.

Pure-state entanglement rests on a single algebraic backbone: majorization of the Schmidt spectrum governs state conversion under local operations and classical communication, and constrains entanglement monotones. Here we establish a corresponding majorization law for fermionic non-Gaussianity, the resource that elevates free fermions to universal quantum computation. Under any fermionic Gaussian protocol with pure state outcomes, the Williamson spectrum of a pure state's Majorana covariance matrix is weakly majorized by its ensemble average. This spectral law mirrors that of entanglement theory. It turns computable non-Gaussianity quantifiers such as fermionic antiflatness and occupation entropies into strong monotones for fermionic non-Gaussianity, and delivers necessary conditions and converse bounds on state conversion under Gaussian protocols. When fermion parity is conserved, no catalyst can remove a majorization obstruction—unless it carries parity coherence—and asymptotic interconversion is irreversible already for pure states. All relevant quantities are accessible from two-point Majorana correlators, turning the theory developed here into experimentally observable properties of quantum matter, testable on present-day quantum devices.

Negative stochastic entropy production is commonly called an apparent violation of the second law. In general quantum-trajectory dynamics, however, the physical entropy production $\sigma$ need not obey a forward detailed fluctuation theorem. A general arbitrary-coupling formulation identifies a dynamical-asymmetry term $\sigma^\ast$ that completes it into $\Omega=\sigma+\sigma^\ast$, whose mean is $\langle\Omega\rangle=\Sigma+\Sigma^\ast$. We prove that the likelihood-ratio sign is optimal among reversal-odd trajectory observables and use this fact to transfer an established sharp fluctuation-theorem floor to the tie-corrected physical sign statistic $\Pi_\sigma=\Pr(\sigma<0)+\Pr(\sigma=0)/2$. When $\Pr(\sigma=0)=0$, the result reads $\Pr(\sigma<0)\ge[1-\langle\Omega\rangle/g(\langle\Omega\rangle)]/2$, where $g$ is the inverse of $a\mapsto a\tanh(a/2)$. The physical integral fluctuation theorem simultaneously suppresses large negative events, producing a quantitative “frequent but mild” law, while the sign imbalance lower-bounds the hidden mean $\Sigma^\ast$. We formulate the measured-record protocol explicitly and illustrate and numerically audit the tie-corrected theorem in random finite-coupling collision models and a coherently driven qubit interacting with thermal ancillas.

Projected ensembles—the collections of conditional pure states induced on a system by measuring an entangled environment—have become central objects in quantum science, underlying deep thermalization, quantum state designs, the emergence of classicality, and exhibiting interesting phase transitions. Here we develop a general and exact theory of their dynamics, yielding a systematic approach to their dynamics and equilibrium and non-equilibrium stationary states. We derive an exact continuity equation on quantum state space for the projected ensemble, together with microscopic kinetic equations and analytical expressions for the probability flux and source terms generated by the system-environment interaction. The resulting dynamics admits a classical representation: isolated systems obey Hamiltonian transport and Liouville's theorem, while open systems are described by a kinetic theory of probability transport. The stationary continuity equation provides a general characterization of equilibrium and non-equilibrium stationary projected ensembles, which can be analyzed through the method of characteristics. The theory provides an analytical framework for studying the emergence, structure, and timescales of equilibrium and non-equilibrium stationary projected ensembles, with applications ranging from deep thermalization and the emergence of classicality to random quantum-state generation and quantum device benchmarking.

We reveal long-lived memory effects in the defect bath of a superconducting transmon qubit through electric-field tuning of two-level system (TLS) defects coupled to the qubit. Using a fast TLS mapping method we observe several hysteretic effects in the TLS environment with memory timescales of the order of seconds, far beyond the lifetimes of individual TLS defects. The observations can be explained by TLS coupling to electric field-polarised charge fluctuators in the defect bath. Our method enables detailed mapping of the dynamics of the bath's coupled microscopic degrees of freedom and the associated memory effects which can introduce temporally correlated noise. This information may be used to improve qubit-stabilisation and quantum error correction protocols.

We construct a toy model of an evaporating black hole using approximately local degrees of freedom acting on “overlapping" qubits in which a version of black hole complementarity arises naturally. The operators corresponding to the radiation and the interior are identified as two distinct representations of the same fundamental algebra, thereby preventing the exact factorization of the Hilbert space into interior and exterior and avoiding the conventional no-cloning violations. We show how this toy model captures several qualitative and quantitative features of black hole evaporation and how the ability to account for this “overlap" in the entropy calculation leads to the recovery of a Page curve.

Practical implementations of quantum error correction (QEC) require rapid measurement and continuous processing of the syndrome information in order to prevent a backlog of unprocessed data. While “static” QEC is theoretically well understood via mappings to equilibrium statistical mechanics models, such an understanding of “real-time” QEC is currently lacking. Here, we study the kinetics of sliding window decoding (SWD), an implementation of real-time decoding that acts on temporally local windows of noisy syndrome information and commits to corrections irreversibly at a nonzero rate. We propose an effective description of SWD in terms of a stochastic kinetic process, where $\mathbb{Z}_2$-charged point particles undergo parity-conserving reaction and diffusion. This model describes dynamics at length and time scales large compared to the window size $W$, whereas physics at scales smaller than $W$ leads to nontrivial $W$-dependent scaling of the effective parameters. We identify the rate of decoding $1/W$ as a relevant perturbation to the decodable phase. We also show broad applicability of our results by changing many microscopic details of SWD without affecting the effective description.

In this paper, we describe the fundamental operating mechanisms of optical interferometry using quantum memory and entanglement. We show how these remove the optical delay line bottleneck. Quantum memory is not without its own set of challenges, some of which include very small bandwidths as well as limitations in storage time. We examine the influence of timing artifacts on memory photon capture probability and interferometric complex visibility. We highlight keystone areas of technology that require further development and are essential to realizing these opportunities, as well as ongoing work to overcome these challenges.

Superradiant (SR) lasers store optical coherence in the atomic medium rather than the cavity field, but the incoherent drive that sustains inversion imposes a trade-off: local pumping yields coherent light at a rate that grows linearly with the atom number $N$, heating the medium through photon recoil, whereas fully collective pumping removes this scaling but limits the emission to partial coherence. We interpolate between these limits employing a spatially correlated pump on a chain of $N$ two-level atoms, with rates decaying with distance between atoms as a power law of exponent $\alpha$. To study systems beyond the reach of exact solutions, we employ the Truncated Wigner Approximation (TWA), whose independent trajectories are ideally suited to GPU parallelism. Harnessing this, we perform a full scan of the steady-state observables for up to $10^4$ atoms at a computational cost that is practical. Our findings indicate that ultra-narrow emission persists for all $\alpha$, while the coherence improves as the pump becomes shorter ranged, with $g^{(2)} \to 1$ surviving at least down to $\alpha \approx 1$, indicating that fully coherent light thus does not require local pumping. The drive strength needed for lasing is reduced by a factor $N^{1-\alpha}$ for $\alpha < 1$, and by $\log N$ as $\alpha \to 1$, parametrically suppressing recoil heating; notably, $\alpha = 1$ matches the far-field envelope of dissipative couplings in free space. The correlation range of the pump thus acts as a knob trading drive intensity, and the heating it causes, against optical coherence.

We study the recursion coefficients of orthogonal polynomials and their associated Krylov dynamics in random matrix models with high-degree and possibly asymmetric polynomial potentials. We develop a moment recursion method that, when combined with the recursive algorithm, provides an efficient construction of the recursion coefficients. We also obtain their large-$n$ asymptotic behavior for general asymmetric potentials; for $Nw_d=1$, the leading asymptotic form of $R_n$ reproduces Freud's conjecture. We apply this framework to an asymmetric quartic potential and to the double-scaled Sachdev-Ye-Kitaev (DSSYK) model. In both models, the recursion functions capture the overall qualitative behavior of the recursion coefficients, and the gradient catastrophes of the recursion functions are associated with “chaotic” transition regions in the recursion coefficients. For the quartic potential, such regions can occur in both $R_n$ and $S_n$, whereas the DSSYK model can exhibit multiple transition regions in $R_n$, with the recursion function remaining accurate in the smooth intervals between them. Finally, we compute the corresponding spread complexity and find that transition regions do not qualitatively modify its behavior, while a two branch structure produces early time oscillations followed by monotonic growth.

Product codes are an important class of quantum error-correcting codes constructed from multiple input codes, which can give rise to asymptotically good quantum low-density parity check codes. In previous work, we showed how the product between two codes can be physically implemented by coupling layers of the first code using checks of the second code. In this work, we further unify product code constructions with coupled-layer constructions of phases of matter by introducing coupled-layer codes. The essential strategy is to condense general excitations created by Pauli operators among multiple decoupled layers of the first code. The condensation is specified by an excitation algebra, which encodes the excitations, along with an algebra-preserving map. This coupling between layers generalizes the notion of gauging in physics as well as the mapping cone in homological algebra, and can be used to produce non-CSS codes. As examples, we show how coupled-layer codes reproduce the X-cube and Chamon models. We further generalize the balanced product code by allowing a unitary transformation in addition to a group action by free permutation and describe its corresponding coupled-layer construction. In particular, we show how balancing by a ZX-duality can reproduce non-CSS codes such as the fermionic toric code and the 3-fermion Walker-Wang model in 3D.

Standard pseudo-random generators have weaknesses that have led to the development of quantum random number generators (QRNGs). However, common QRNG validation methods, whether based on quantum indeterminism or statistical tests, are insufficient to guarantee high-quality randomness. In contrast, a mathematical theory based on the Located Kochen-Specker Theorem proves that 3D QRNGs produce maximally unpredictable outputs without using entanglement, and both theory and experiments have supported their security. The paper focuses on a practical photonic implementation of a 3D QRNG that is easier to deploy than cryogenic superconducting implementations. As any physical implementation is subject to various measurement errors, it is important to study theoretically and experimentally the type and role of errors in 3D QRNGs. In this paper, we will model the photonic 3D QRNG as an open quantum system, constructed as an arrangement of imperfect beam-splitters with a range of losses based on the fidelity of its components, and we will show that under certain conditions, the process remains within the scope of the Kochen-Specker Theorem, which guarantees maximum unpredictability.

We establish a global, worst-case non-identifiability theorem for periodically driven finite-dimensional quantum systems. On the unrestricted smooth periodic Hamiltonian class, we show that the period-averaged Fubini-Study metric component of a fixed initial state cannot, in general, be reconstructed from exact one-period propagators indexed by every starting time and external parameter. Thus, even complete starting-time-resolved endpoint data are insufficient to determine this intra-period geometric quantity. The obstruction is characterized exactly. The starting-time-indexed endpoint data determine the conjugation path of the monodromy, but not its particular unitary lift. On each fixed-monodromy slice, the observational fibres are precisely the right orbits generated by smooth parameter-dependent based loops taking values in the pointwise centralizer of the monodromy. The Fubini-Study functional is not invariant under this fibre action and therefore does not factor through the endpoint observation map. An explicit real-analytic two-level witness demonstrates the obstruction within a commuting, one-generator Hamiltonian family, so neither non-Abelian time ordering nor Floquet-logarithm ambiguity is required. A continuous family of Hamiltonians produces identical starting-time-indexed one-period endpoint data while yielding different, and on the unrestricted class arbitrarily separated, period-averaged Fubini-Study geometry. Non-identifiability persists under any prescribed uniform bound on the parameter derivative of the Hamiltonian. The result is a deterministic global statement, not a claim of generic non-identifiability or experimental impossibility. It identifies a precise information gap between complete one-period endpoint data and full intra-period dynamics: the missing information is the unitary lift of the observed monodromy path rather than ordinary scalar phase freedom.

Coherent energy backflow and non-Markovian oscillations limit energy retention and degrade extractable work (ergotropy) in open many-body quantum batteries. Here, we present a catalyst-mediated charging protocol for a collective spin-array quantum battery coupled to a laser-driven charger. Using the open-system Lindblad master equation, we examine the energy transfer dynamics when both charger and battery are symmetrically coupled to an off-resonant auxiliary catalytic mode. Numerical simulations reveal that while unassisted bipartite setups exhibit pronounced backflow oscillations and poor energy retention, catalytic mediation quenches transient oscillations and accelerates energy injection. The auxiliary system operates as an energy-invariant conduit, maintaining a constant energy expectation value $\langle H_C(t)\rangle \approx \langle H_C(0)\rangle$ and negligible transient population throughout the evolution. Microscopically, virtual excitations of the catalyst generate an effective complex inter-subsystem coupling $J_{\text{eff}}$, which induces an underdamped-to-overdamped dynamical crossover and introduces selective coherence damping. This mechanism prevents population depletion in the battery, stabilizing the population inversion and significantly increasing the asymptotic steady-state ergotropy with increasing battery size $N_B$. These findings clarify the dissipative dynamics of catalyst-mediated energy transfer and provide a practical scheme for improving storage stability in modern quantum hardware platforms.

Quantum coherence underlies collective quantum phenomena and emerging quantum technologies. Quantum gas microscopes have transformed quantum simulation by providing projective snapshots of many-body states with single-atom resolution, but spatially resolved measurements of off-diagonal correlations have remained elusive. Here, using the Talbot effect, we introduce a quantum coherence microscope that maps off-diagonal correlations onto site-resolved density signals with near-single-site resolution. We use this technique to locally probe the superfluid-Mott transition in a layer of a three-dimensional optical lattice and to measure coherence beyond nearest neighbors in an engineered potential landscape. By mapping off-diagonal correlations onto density signals through controlled Talbot evolution, this work opens new possibilities for accessing observables beyond the density basis through tailored matter-wave evolution and recapture.

The boundary quantity that captures the growth of black-hole interiors quantified by holographic complexity remains unknown beyond 2d dilaton gravity. We provide a critical analysis of a partition-function construction of Krylov spread complexity for thermofield-double states that provides a dimension-independent boundary reconstruction from semiclassical holographic partition functions, while developing the present dynamical and bulk construction for the BTZ saddle. In the double-scaled Sachdev-Ye-Kitaev model, where exact and semiclassical results can be compared, we show that the classical limit is reliable only when taken after the complexity has been reconstructed; taking this limit at the level of individual Lanczos coefficients discards essential information. Applying the construction to a large-central-charge two-dimensional conformal field theory above the Hawking-Page temperature dual to a Bañados-Teitelboim-Zanelli black hole, we find an intermediate departure from early-time quadratic growth followed by behavior compatible with a return toward asymptotically quadratic growth, rather than the linear late-time behavior of the volume and the standard finite-functional complexity = anything class. We then match this boundary behavior to a generalized complexity = anything bulk object built from an infinite series of extrinsic-curvature invariants. The construction provides a systematic route from black-hole thermodynamics to Krylov dynamics and can naturally be extended to higher-dimensional holographic black holes.

Two-dimensional translation-invariant topological CSS codes on qubits are known to be locally equivalent, after coarse-graining, to stacks of toric codes. However, existing constructions generally break more translation symmetry than is required to remove anyon-permuting translations, leaving open whether any further obstruction exists. We prove that no such obstruction occurs: after passing to the maximal anyon-preserving superlattice, every such code admits a local unitary decoupling into toric codes and product states. We further provide an efficient algorithm for explicitly constructing the decoupling map, together with bounds on the required supercell size and operator spreading. The decoupling requires no additional ancillas in generic cases and extends to finite systems with suitable boundary conditions.

Koszul-complex stabilizer models unify the toric-code hierarchy and bivariate-bicycle codes in one homological framework. To study translation-symmetry-enriched topological (SET) phases in these models and, more generally, in translation-invariant Calderbank-Shor-Steane (CSS) codes with stabilizer maps $(\varphi_X,\varphi_Z)$, we introduce the associated topological superselection profile $\mathscr S_\sigma:=\tau_{\geq1}\mathbf R\!\operatorname{Hom}_R(\overline{\operatorname{coker}\varphi_\sigma},R),\ \sigma=X,Z$. Its cohomology layers $E_\sigma^\ell:=H^\ell(\mathscr S_\sigma)\cong_R\operatorname{Ext}_R^\ell(\overline{\operatorname{coker}\varphi_\sigma},R)$ encode sectors, fusion, and translation action. When finite, the $\ell=1,2,\ldots$ layers describe pointlike, looplike, and higher-dimensional excitations; $\mathscr S_\sigma$ retains inter-layer gluing. For regular Koszul models, we compute $E_\sigma^\ell$ explicitly, find $\mathscr S_\sigma$ single-layer, and obtain finite-size $Z$-logicals from $\operatorname{Tor}$. Single-layer means that at most one positive-degree layer $E_\sigma^\ell$ is nonzero. Our matrix-level Schanuel-lemma method proves rigidity: under a finite-resolution hypothesis, the nonzero layer and degree uniquely determine a topological CSS code's translation SET order at the stable translation-invariant Clifford level. For prime qudits the hypothesis is automatic, and a finite layer's translation kernel gives the exact minimal coarse graining to a toric-code stack. We realize admissible single-layer data. Beyond this regime, split and nonsplit extensions of 3D qubit toric codes yield eight models sharing all identical $E_\sigma^\ell$ layers with trivial translation action but having distinct size-dependent ground-state degeneracies, hence distinct translation SET phases. Thus inter-layer gluing carries SET data invisible to individual layers.

Learning algorithms for structured quantum unitaries and Hamiltonians have primarily considered classes of processes that are local or sparse in the Pauli basis. We turn our attention to learning $n$-qubit quantum unitaries $U$ and Hamiltonians $H$, given query access to $U$ or the unitary evolution of $H$, that may be dense in the Pauli basis but still admit concise Clifford decompositions. Specifically, we consider unitaries (or Hamiltonians) of the form $U = \sum_i \alpha_i C_i$ over Cliffords $C_i$ with bounded Clifford extent $\sum_i |\alpha_i|$. To extract this Clifford structure, we introduce an agnostic tomography protocol for Clifford unitaries that given query access to an unknown unitary $U$ with optimal Clifford fidelity $\textsf{opt}$, outputs a Clifford unitary witnessing fidelity $\geq \textsf{opt} - \varepsilon$ for some error $\varepsilon > 0$, in time $\textsf{poly}(n,(1/\varepsilon)^{\log(1/\varepsilon)})$. We then apply this protocol to obtain tomography protocols for unitaries and Hamiltonians that have bounded Clifford extent. This extends learnability of Hamiltonians from those with sparse Pauli decompositions to those that are dense (i.e., has sparsity $\Omega(2^n)$) in the Pauli basis but are Clifford structured.

Silicon T centers are promising spin-photon interfaces in solid-state platforms for telecom-compatible, scalable quantum information technologies. A major challenge for T centers in nanophotonics is spectral diffusion, where fluctuations in the local electric-field environment from surface and bulk charge states broaden the optical transition and reduce photon indistinguishability. Strategies that directly suppress spectral diffusion are therefore critical for improving T-center-based quantum photonic devices. Here, we use atomic-layer-deposited Al2O3 to passivate the silicon surface and demonstrate a systematic narrowing of T center optical linewidths. Across our measurements, Al2O3 passivation reduces the T center emission linewidth by up to 57%. Complementary above-bandgap illumination and spectral hole burning measurements show that the remaining linewidth contains a significant spectral-diffusion component caused by adjacent charge traps, while placing an upper bound of approximately 75 MHz on the homogeneous linewidth. This work provides a CMOS-compatible path toward generating indistinguishable photons from silicon T centers for scalable quantum photonic applications.

Nonlinear stochastic differential equations describe dynamics under uncertainty, but their nonlinear coefficients and noise averaging complicate quantum representations. We develop a Kolmogorov–Lindblad mapping that encodes their probability laws as the position diagonals of trace-one quantum density operators. For each Brownian realisation, a stochastic flow transports the initial ensemble; the square-root Jacobian makes its action on half-densities unitary. Averaging the resulting pure-state projectors gives a Lindblad equation with Hermitian jump operators. Its diagonal reproduces the Fokker–Planck density, while forward and backward intertwining identities recover bounded observables and time correlations independently of the initial coherences. A Galerkin approximation obtained by projecting the Stratonovich generators preserves the Lindblad structure. We give a residual-based error estimate and conditional quantum costs that display the dimension dependence of approximation constants, operator normalisations, state preparation and readout. Numerical experiments for double-well Langevin dynamics and noisy Lorenz–63 show rapid convergence of selected statistics at fixed dimension. The construction provides an exact bridge from flow-regular nonlinear diffusions to quantum channels; any computational advantage additionally requires controlled approximation and coherent access for the chosen problem family.