Papers

We present the algebraic structure of bosonic quantum error-correcting codes on genus-two Riemann surfaces. We explicitly construct the code words as automorphic forms and analytically generate the full tower of code spaces at all weights. We prove a fundamental no-go theorem: for any genus greater than one, the stabilizer group is non-amenable, forcing a strictly positive spectral gap in the stabilizer Hamiltonian. Consequently, no normalizable quantum state can satisfy all stabilizer conditions. This sharply contrasts with standard Gottesman-Kitaev-Preskill (GKP) codes, where the amenability of the stabilizer group $\mathbb{Z}^2$ permits approximate code words with arbitrary precision.

Multi-photon dissipation – a key resource for bosonic qubits – is usually realized by parametrically pumping a Josephson coupler at the cost of spurious nonlinear terms. Here we instead engineer it using a dc-voltage-biased SQUID, such that these parasitic terms average out. We activate the conversion of one, two, or four photons of a high-Q mode into a single photon of a lossy mode. We characterize the two-photon dissipation by Wigner tomography, establishing dc-biased junctions as a resource for reservoir engineering and a viable route to cat-qubit stabilization.

Generative models have become central across science and industry, from image and text synthesis to the design of molecules and materials. Quantum generative models are considered one of the most promising applications for quantum computers, since a quantum circuit naturally produces samples from the distribution it encodes, and for suitable circuits that distribution is believed to be hard for any classical computer to reproduce. A leading strategy trains these models on a classical computer and reserves the quantum device for generating samples at deployment. This is possible when the training loss can be evaluated on a classical computer. A prime example is the maximum mean discrepancy (MMD$^2$), a moment-matching loss that compares the model and the data through their Pauli-$Z$ correlations. Research so far has asked whether such models can be trained and whether their sampling is hard; whether minimizing such an objective yields a model that generalizes, rather than one that merely reproduces the training statistics, remains poorly understood. We benchmark thirteen quantum and classical generative models by direct sampling on two application-inspired datasets: first a cardinality-constrained dataset at up to $30$ qubits and second a dataset of genomic single-nucleotide variants, whose valid set is the observed data. Models that converge the loss to the same value differ widely in how much of the unseen valid set they cover. These results indicate that a converged moment-matching loss is not a reliable measure of generalization, and that a train-classical, deploy-quantum workflow has to measure generalization by sampling the trained model, a step that at the sizes of interest is believed to require the quantum device.

We obtain a certified randomness protocol in the quantum random oracle model. The protocol is non-interactive and publicly verifiable with a classical verifier, and is based on Yamakawa and Zhandry's proof of quantumness [JACM'24]. We prove unconditional security of this protocol against adversaries making subexponentially-many adaptive quantum queries to the random oracle. Prior work on certified randomness relative to a random oracle additionally assumed the Aaronson–Ambainis conjecture or proved security only against low query-depth adversaries.

Exceptional points (EPs) can induce strongly amplified responses to weak perturbations, but enhanced spectral sensitivity in conventional non-Hermitian systems does not necessarily translate into improved quantum-limited sensing because of the associated gain and loss noise. Here, we investigate a tunable EP sensing platform based on the intrinsic non-Hermitian Bogoliubov dynamics of a spin-orbit-angular-momentum-coupled Bose-Einstein condensate. Starting from a fully Hermitian microscopic Hamiltonian, we derive a Bogoliubov dynamical matrix that exhibits parity-time (PT) symmetry, with EPs tunable through the Raman coupling and interaction parameters. We identify multiple EPs and map their trajectories and associated stability landscapes, revealing strong quantum Fisher information enhancement when the EPs are approached from the PT-symmetric stable regime. We further find that the gap-opening rate around a second-order EP provides a useful relative indicator for comparing the sensing performance of EPs, while higher-order EPs are not necessarily accessible from the stable regime. Moreover, two second-order EPs can be tuned to overlap, allowing their sensing contributions to add and yielding a linear enhancement of the total quantum Fisher information. Finally, we show that a spin-density measurement can approach the quantum Fisher information limit, providing an experimentally accessible route to tunable EP-enhanced quantum sensing in Bose-Einstein condensates.

Exchange-based semiconductor qubits encompass a broad family of encodings constructed from singlet- and triplet-like spin states, several of which are compatible with operation at zero applied magnetic field. Their reliable operation requires characterization of environmental noise, residual idle interactions, and exchange-dependent decay, but this characterization often relies on multi-axis control calibration or deliberately engineered magnetic-field gradients. A simpler zero-applied-field diagnostic is particularly valuable for hybrid semiconductor-superconductor systems, in which magnetic fields can degrade superconducting components. Here, we use the intrinsic magnetic-field gradient produced by residual nuclear spins in isotopically enriched Si/SiGe to implement exchange oscillations between two quantum dots as a characterization tool without a micromagnet, dynamic nuclear polarization, or prior multi-axis calibration. Using Carr-Purcell-Meiboom-Gill exchange sequences, we extend the singlet coherence from $T_2^*=1.17\pm0.02~\mu$s to $T_2^{\mathrm{CPMG}}=74.8\pm1.8~\mu$s with $N=70$ refocusing pulses. The oscillation phase resolves residual exchange in the tens-of-kilohertz regime and enables it to be mapped across the $(1,1)$ charge cell. These results establish intrinsic-gradient exchange oscillations as a simple, more relevant zero-field diagnostic for exchange-only and related semiconductor qubit encodings that is amenable to rapid, high-throughput device characterization.

We derive state-dependent bounds on the difference between two quantum evolutions generated by unbounded Hamiltonians sharing a common form domain. The main technical tool is a second integration by parts, performed at the level of sesquilinear forms rather than at the operator level, which removes the need for a common invariant operator domain. The resulting estimate involves the norm of the time-integrated difference of the two generators, rather than the integral of its norm, and is therefore sensitive to the averaging effects produced by fast-oscillating terms. As an application we prove a quantitative bound on the rotating-wave approximation for spin-boson models with a structured boson field, described by an arbitrary massive dispersion relation on a general measure space and by a suitable class of form factors. The proof involves a careful analysis of the high-frequency scaling. The bound holds on a dense subspace of states, is fully explicit, and all the constants entering it depend only on the parameters of the model and not on the frequency scale, so that the approximation becomes exact in the limit of large frequency.

We develop a Heisenberg-picture tensor-network formulation of collision-free Gaussian Boson Sampling, providing a direct Fock-space expression for output probabilities in terms of experimentally accessible quantities. The resulting representation naturally recovers the Hafnian structure while revealing the decomposition of GBS probability into a phase-insensitive contribution and a hierarchy of interference sectors associated with pairs of perfect matchings. As an application, we investigate phase diffusion and show how it progressively suppresses many-body interference, driving the output statistics toward a classical dimer-model regime. Our results establish a transparent framework for connecting experimentally characterized phase fluctuations with the loss of quantum interference in photonic quantum sampling experiments.

We give a deterministic realization of the finite-dimensional quadratic certificate underlying Collins's mixed-unitary proof of minimum-output-entropy nonadditivity. For every fixed integer $K\ge 2$ and rational $\eta>0$ satisfying $\log K>2(3+\eta)^2$, a deterministic polynomial-time algorithm, for every sufficiently large target size $N$, outputs $K$ permutations on $N'=N+o_{K,\eta}(N)$ points. Restricting their permutation matrices to the nontrivial standard representation yields real orthogonal Stinespring blocks and a channel $\Phi_{N'}:M_{N'-1}(\mathbb{C})\to M_K(\mathbb{C})$ such that \[ 2H_{\min}(\Phi_{N'}) -H_{\min}(\Phi_{N'}^{\otimes 2}) \ge \frac{\log K}{K} -2\log\left(1+\frac{(3+\eta)^2}{K}\right) >0. \] The construction combines Haagerup's length-two inequality with the simultaneous deterministic spectral approximation of O'Donnell and Wu. We further show that the constant $3$ is asymptotically sharp on the relevant Hermitian zero-diagonal coefficient class and that the finite spectral transfer is nearly saturated, thereby isolating the finer geometry of the full output body as the natural next level of refinement beyond the scalar-radius method. Finally, a standard covariant extension converts the same deterministic entropy gap exactly into self-tensor superadditivity of the one-shot Holevo quantity.

The generalized Bethe ansatz framework formulated in [P. R. Pasnoori, Phys. Rev. B 112, L060409 (2025)] provides a unified framework to find exact solutions to quantum many-body systems with time-dependent coupling strengths with periodic boundary conditions. In this work we extend this framework to the case of open boundary conditions where in addition to the time-dependent interactions in the bulk, the boundary conditions are explicitly time-dependent. We show that for integrable time-dependent bulk coupling strengths, the generalized Bethe ansatz framework provides the time-dependent boundary conditions compatible with integrability and reduces the time-dependent Schrodinger equation to a set of matrix difference equations called the boundary quantum Knizhnik-Zamolodchikov (BqKZ) equations. The solution to the BqKZ equations provides the explicit form of the exact wavefunction. We further show that the RG invariants of the corresponding static model identify with the dynamical invariants in the time-dependent model.

The long-time state of a non-Hermitian system is determined by the eigenvalue with the largest imaginary part. In interacting many-body systems this eigenvalue usually cannot be tracked analytically, and the character of the state it selects is unknown. We construct a non-Hermitian spin ensemble of $L$ spins with exactly $k$-local all-to-all interactions, in which this dominant eigenvalue can be tracked analytically from the clean limit into the disordered regime. Disorder produces a competition between an isolated spectral outlier and the edge of a many-body spectral bulk. We study three cases: purely anti-Hermitian disorder, purely Hermitian disorder, and mixed disorder of equal strength. For purely anti-Hermitian and mixed disorder, we show that when the bulk overtakes the outlier in imaginary part, the dominant eigenstate switches from an outlier state with low entanglement and magic (nonstabilizerness) to a bulk state with substantially larger entanglement and magic, with both changing at the same threshold. For $k \gg \sqrt{L}$ the bulk has a sharp spectral edge and the transition thresholds follow in closed form, while for $k \ll \sqrt{L}$ spectral tails broaden the transition into a crossover. Purely Hermitian disorder provides a contrasting case with no outlier-to-bulk switching. Finally, we map the non-Hermitian evolution exactly onto postselected trajectories of a monitored quantum system, connecting this spectral mechanism to measurement-induced transitions.

We design low-complexity, fault-tolerant decoders for quantum low-density parity-check (QLDPC) codes with the goal of reducing decoding latency. We target two major bottlenecks of decoding under the circuit-level noise model: (i) post-processing via order-statistics decoding (OSD), and (ii) the large number of auxiliary variable nodes commonly introduced to represent CNOT-induced correlations during syndrome extraction. Our key observation is that propagating CNOT faults (hook errors) create stabilizer-induced trapping sets (TSs) that are intrinsic to hypergraph-product (HGP) and lifted-product (LP) constructions. Therefore, instead of modeling each such fault with an explicit correlation node and relying on OSD to clean up the resulting failures, we design message-passing decoders that resolve the corresponding stabilizer-induced TSs directly. We obtain these decoders by deriving QLDPC decoders from decoders for the parent classical LDPC codes and using them collectively to correct broad families of stabilizer-induced TSs. For CNOT faults that manifest primarily as syndrome errors, we show that their effect is equivalent to a data error together with syndrome-bit measurement errors. Consequently, given repeated measurements and a decoding graph that already includes nodes representing syndrome-bit errors, no distinct variable node is needed for each CNOT fault. Using a phenomenological Tanner graph with nodes representing only data errors and syndrome-bit errors, simulations on the LP codes show a reduction in, or comparable, logical error rates relative to BP+OSD, at substantially lower decoding complexity.

Fault-tolerant quantum computation requires robust protection of encoded quantum information. In this work, we develop a representation-theoretic framework for constructing protected logical qudits in finite-group Kitaev quantum double models. By introducing $\varepsilon$-stable irreducible representations, we establish a necessary and sufficient existence criterion and derive ribbon–projector commutation relations that yield a $d$-dimensional protected logical subspace. We apply this construction to symmetric and alternating groups, obtaining logical qubits for $S_n$ ($n\ge 3$) and a logical qutrit for $A_4$. Moreover, the family $(\mathbb Z_2)^d\rtimes\mathbb Z_d$ realizes protected logical qudits of arbitrary dimension $d\ge 2$. Finally, for $D(A_4)$, we describe a scheme for universal logical qutrit computation using ribbon-based logical operations.

Thermodynamics is operational in the sense that the very concept of thermal equilibrium depends crucially on the choice of observables, while the amount of extractable work is defined relative to the allowed operations. Here we show that isolated quantum many-body states admit a thermodynamic hierarchical structure of observables and allowed operations, where the same state can be thermal at one level of the hierarchy and athermal at another. Enlarging the set of allowed operations therefore renders such hidden athermality a potential resource for work extraction; the resulting work gain is bounded in terms of the difference between the entropy densities of the two levels. This entropy difference takes the form of the mutual-information density. We establish the bounds for three extensions of operational access: increased spatial resolution, increased duration of control, and nonlocal connectivity, which provide access to position-state Holevo information, correlations between neighboring regions and spatially nonlocal correlations, respectively. Thus the difference between entropies at different levels of the thermodynamic hierarchy governs the bound on the work gain associated with moving to a less restricted level.

Quantum signal processing (QSP) provides a simple and efficient framework for implementing polynomial transformations using quantum circuits. Its classical design stage leads to a constrained minimax approximation problem: find a polynomial of prescribed parity that approximates a target function uniformly on a fitting set while remaining bounded in magnitude by one on the domain $[0,1]$, which can be viewed as a semi-infinite constraint. Discretization converts the problem into a linear program, but feasibility at a set of finitely many sampled points does not ensure feasibility on the whole domain, especially when an optimal approximant reaches the boundary of the feasible set. We investigate two approaches to address this difficulty. A Remez exchange method combined with active-set constraint enforcement is efficient on many tested instances, but its stability depends on the target and problem geometry. We then introduce nonlinear Fourier retraction, which uses QSP completion and phase synthesis to turn a nearly feasible polynomial into phase factors for a feasible QSP polynomial without increasing the degree. Across representative problems, retraction largely preserves approximation accuracy and remains effective on instances where the Remez heuristic is unstable. The resulting workflow connects classical minimax approximation and semi-infinite optimization with nonlinear Fourier analysis, and is implemented in the qsppack software package.

We theoretically investigate the inter-sideband phase coherence within the resonance fluorescence spectrum of an acoustically modulated quantum dot using a filtered-field formalism for a Mach-Zehnder configuration. We demonstrate that geometric slant of the interferograms provides an indicator of phase coherence that is resilient to environmental white noise. Specifically, noise-induced spectral diffusion reduces the global fringe intensity, while leaving the characteristic inclination strictly invariant. Our findings establish a framework for verifying single-photon coherence between spectral sidebands, essential for frequency-bin encoding and scalable quantum networking in realistic, noisy solid-state architectures.

We reformulate the relaxation problem in statistical mechanics by making explicit what are the operational objects subject to relaxation: the local time statistics of the recorded signal $Z(t)$. These local time statistics are simply the estimated histograms of observations $\{Z(t_i)\}_{i=1}^M$ performed at uniformly random times $\{t_i\}_{i=1}^M$ by a clockless observer. The subject of prediction is a belief about a future fresh out-of-sample reading of a measurement outcome whose distribution is inferred from the mathematical model believed to be true. For finite bounded systems of $N\ge 1$ degrees of freedom global irreversible relaxation of predictions can occur but special initial conditions exist. The form of the predictions depends on certain loss functions whose choice is up to the particular observer. Finally, entropy is given a learning interpretation as mutual information between the observer and the unknown past of the system under consideration and, in complete generality, its stationary value depends on the information available.

Markovian open quantum systems are well modeled by the Lindblad Master Equation (ME) $\frac{\mathrm{d}}{\mathrm{d} t} \rho_t = \mathcal{L} \rho_t$, where $\mathcal{L}$ is a linear (super-)operator and $\rho_t$ is the system state, a positive matrix. When designing or characterizing a quantum system, one is usually interested in the steady state $\rho_\infty$ (such that $\mathcal{L} \rho_\infty = 0$), the first few excited states, and trajectories $t\mapsto \rho_t$. In finite dimension, $\rho_t$ is an $n\times n$ matrix, $\mathcal{L}$ thus typically costs $n^4$ to store explicitly as a dense matrix, and $O(n^6)$ to diagonalize or invert exactly, making standard linear algebraic techniques expensive for large systems. However, $\mathcal{L}$ usually costs only $O(n^3)$ to apply. This makes iterative methods appealing, but they do not work without a good preconditioner. In this article, our main observation is that a part of the Lindblad equation, corresponding to the so-called no-jump evolution $\mathcal{S}$, can be inverted efficiently. Using this inverse map, we introduce an auxiliary completely positive trace-preserving (CPTP) map $\Phi$ whose fixed point is directly related to $\rho_\infty$, all the other eigenvalues having smaller magnitude. The map $\Phi$ is thus well suited to iterative methods, and $\rho_\infty$ can be found in a few Arnoldi iterations. Using the same inverse map $\mathcal{S}^{-1}$ as preconditioner, we compute the low-lying spectrum efficiently via shift-invert Arnoldi, and, as a proof of concept, build an implicit time integrator that is competitive on stiff systems in the low-precision regime. For the steady-state and low excited states problems, our methods scale like $O(n^3)$ per iteration and offer state-of-the-art performance on CPU and GPU.

Practical robust self-testing of multipartite entanglement has so far been restricted to small-scale systems due to error bounds that degrade severely with system size. In this work, we establish multipartite self-testing with robustness independent of the size of the quantum network. We derive a fully analytic, device-independent self-testing bound for $n$-qubit Greenberger-Horne-Zeilinger (GHZ) states. The bound scales linearly with the observed violation error and lies universally within a constant factor of two from a theoretical upper bound. Furthermore, the operator-inequality framework reduces the verification of the conjectured optimal bound to a highly efficient numerical check, which we perform up to $n=100$. Consequently, GHZ entanglement can be certified under a fixed noise level in arbitrarily large systems, enabling scalable device-independent verification.

Localization-delocalization transitions have recently been proposed for building a class of efficient quantum many-body critical sensors. This work scrutinizes metrological performances of such devices by focusing on the Aubry-André-Harper model that supports a localization-delocalization transition at finite strength of the onsite potential. We identify a metrological quantum-to-classical crossover driven by the interplay between noise and system size, whereby quantum-enhanced scaling of the quantum Fisher information persists only up to a finite, noise-dependent characteristic system-size. We first consider thermal noise and show that, at and near the localization-delocalization transition, the quantum Fisher information exhibits quantum-enhanced scaling for small systems but the system is stripped of this advantage beyond the characteristic crossover length. The crossover length decreases with increasing temperature. We then consider imperfections in the lattice hopping strengths and find a qualitatively similar crossover. There, the quantum-enhanced regime, identified with super-extensive scaling, gives way to an extensive scaling-a classical-limited weaker form-at sufficiently large system sizes. Thus, distinct noise mechanisms lead to a common limitation on the scalability of quantum-enhanced sensing: increasing the probe size beyond a noise-dependent limit can destroy the metrological quantum advantage.

Local constraints govern the low-energy physics of frustrated matter, but familiar ice-type rules constrain flux-like quantities and are insensitive to handedness. Here we show that handedness itself can be imposed as an exact local quantum constraint without selecting an axis in spin space. We construct positive-semidefinite, SU(2)-invariant parent Hamiltonians whose complete zero-energy space on a tetrahedron has a prescribed chirality sign, rather than selecting a particular chiral wave function. For spin-1/2 the local term is a rank-one projector onto a chiral tetrahedral singlet, while for arbitrary spin it factorizes as $B^\dagger B$ through a singlet-annihilation operator, with a completely characterized kernel given by the span of the globally rotated chiral color-ice states. For coherent states, the same zero-energy condition becomes an $S$-independent nonlinear constraint in which three spin directions determine the fourth through a Möbius transformation; compositions of these maps define constraint holonomies on extended lattices. Connecting the same local constraint in different ways produces qualitatively different collective regimes: corner-sharing lattices retain exponentially large quantum ground-state kernels, with rigorous lower bounds exceeding conventional ice benchmarks; edge-sharing lattices support subdimensional plane or line zero modes; while triangular constructions suppress nonuniform coherent deformations and contain the complete Anderson tower of tetrahedral magnetic order at exactly zero energy. Two inequivalent triangular coverings further show that harmonic zero-mode counting does not determine the size of the quantum kernel. These results establish a tractable setting in which local handedness, nonlinear constraint geometry, and quantum degeneracy can be disentangled and related directly to the connectivity of the constraint network.

Linear quantum repeater chains based on Werner-state purification (the BBPSSW protocol) and entanglement swapping (the BDCZ scheme) are fundamental to entanglement distribution in quantum networks. However, they operate under a stringent operation reliability threshold and rely on resource-intensive recurrence purification rounds, each consuming two entangled pairs to probabilistically produce one. In the literature, hyperentanglement has been proposed to exploit multiple degrees of freedom (DOF), such as polarisation and spatial modes, to encode independent entangled states within a single photon pair. This has led to the definition of DAEPP (DOF-Assisted Entanglement Purification Protocol), which we propose to integrate with the BDCZ scheme, resulting in a chain protocol that we call DAHR (DOF-Assisted Hyperentanglement Repeater). The DAEPP step distils the fidelity of a DOF by consuming other(s). In this work, we propose and analyse a DAHR variant which integrates DAEPP at every segment of an end-to-end path combined with BDCZ. We derive a closed-form end-to-end fidelity recursion that embeds single-segment DAEPP into the BDCZ scheme and give a strict resource lower bound for any BDCZ baseline utilising BBPSSW purification to match DAHR's per-segment effective fidelity. At a representative asymmetric operating point informed by prior experiment, we show numerically that matching DAHR's single-photon-pair performance requires two to three rounds of BBPSSW purification. Additionally, below a critical operation reliability, no amount of BBPSSW rounds matches DAHR's one DAEPP round performance.

Neutral atom qubits are one of the leading approaches for implementation of a large scale quantum computer. The original proposals for neutral atom qubits were formulated more than 25 years ago, with first demonstrations of a universal gate set following 10 years later. In the last few years the performance and scale of neutral atom qubit arrays has developed at a rapid pace leading to demonstrations of quantum algorithms, and logical qubits for fault tolerant error correction. This contribution reviews the physics of the neutral atom approach, surveys current capabilities, and provides an outlook for future progress.

In the early nineties, the introduction of turbo codes revolutionized classical error correction. The idea was mainly applied on two types of codes: convolutional turbo codes and turbo product codes. The first type of codes was adapted to quantum error correction which initiated the theory of quantum serial turbo codes. In this paper, we present a theory for quantum block turbo codes, the quantum analog of the second type of turbo codes. We describe their iterative decoding algorithm and simulate their performances on a depolarizing channel for different constituent codes.

The dynamical Lie algebra (DLA) governs the controllability, expressibility, and simulation complexity of a quantum system. Explicitly computing it has been a major computational bottleneck: brute-force Lie closure scales exponentially in the number of qubits $n$. Many applications, however, consult only the isomorphism type of the DLA. We introduce PauLie, an open-source framework that decides this isomorphism type for DLAs generated by arbitrary Pauli strings, building on the anticommutation-graph reduction of Aguilar et al. PauLie runs in $O(n|\mathcal{G}|\max(n,|\mathcal{G}|))$ time, where $|\mathcal{G}|$ is the number of generators, turning DLA classification into a routine preprocessing step. We demonstrate its use as a structural oracle for routing Lie-algebraic simulation and Cartan decomposition, diagnosing barren plateaus in variational quantum algorithms, and engineering universal Pauli string generator sets with optimal generation rate.

Breakpoint graphs originate in comparative genomics, where their alternating cycles encode relationships between genomes. We study a constrained class of three-colored breakpoint graphs associated with permutations and develop cycle-refined generating functions for two extremal families. These families have a natural topological interpretation: their canonical surfaces are, respectively, the sphere and the projective plane. The spherical family is characterized by noncrossing configurations, while the projective-plane family admits a different decomposition involving a distinguished family of Möbius ladders. The resulting generating-function equations retain the full cycle structure but nevertheless admit substantial reductions. This leads to explicit Catalan-weighted evaluations, polynomiality results for refined cycle statistics, and a connection between a natural diagonal specialization and noncrossing trees. The two topological families exhibit markedly different combinatorial mechanisms, providing complementary examples of how local transformations of breakpoint graphs can control refined permutation enumerations. As a further application, the same Catalan-weighted sums arise in asymptotic unitary-Weingarten expansions for entanglement of random Gaussian states in linear optics. The combinatorial results determine the leading and constant-order moment polynomials entering the Rényi entropy expansion, with the projective-plane contribution giving the finite-size constant correction.

A Majorana field cannot be split into two spatial pieces, but a propagating Majorana can be truncated by a time-dependent shutter. We study this truncation for the two chiral components of a massless Majorana field in one spatial dimension, modeling the shutter as a smooth time-dependent $SO(2)$ rotation of the two components. Although orthogonal at the level of the real field algebra, this rotation does not preserve the positive- and negative-frequency splitting that defines the Fock vacuum, so the in-vacuum becomes a fermionic squeezed state in outgoing modes. At any finite infrared regulator, a single incident Majorana is then a single outgoing quasiparticle on top of this squeezed vacuum. The squeezed background carries a universal soft response: its anomalous Bogoliubov kernel falls as the inverse sum of the two frequencies at low energy, so the anomalous Hilbert–Schmidt norm grows logarithmically with the infrared cutoff, with a coefficient fixed by the asymptotic shutter mismatch. The vacuum overlap exhibits a Fermi-edge type orthogonality exponent which, for the rotation-angle lift $\Delta\theta$ with $|\Delta\theta|<\pi$, is exactly $(\Delta\theta/2\pi)^2$, in analogy with the Fermi-edge singularity and the Kondo and Luttinger-liquid problems. We prove local equivalence non-perturbatively for the squeezed-vacuum factor under a compact-support hypothesis, and give an exact local pullback identity for the full one-quasiparticle state on the even CAR algebra; combined with wavepacket-localization assumptions, these yield the expected local vacuum and one-Majorana descriptions. We verify profile independence using a smooth switching family and contrast the temporal benchmark with a number-conserving beam-splitter benchmark whose entropy is bounded by $\log 2$.

A quantum state is called flat if it is proportional to a projector. There has been recent interest in studying antiflatness, the property of diverging from flat states, and establishing a resource theory for it. Identifying the free operations (the Flatness-Preserving Operations (FPOs)) remained an open problem. For this purpose, we first discuss Orthogonality-Preserving Operations (OPOs), of which trivial examples are unitary operations in an isolated system. More generally, we give a simple proof that all OPOs are isometric embeddings consisting of combinations of unitaries/isometries and appending a fixed state. We then show that all FPOs are either constant maps to some fixed flat state or a special case of an OPO, where the appended fixed state must be a flat state. We also show that the only possible flat convex combinations of flat states are those of orthogonal flat states with weights given by their purities.

The contact process is a paradigmatic example of nonequilibrium dynamics, with broad applications ranging from chemistry to sociology. Its quantum counterpart, the quantum contact process (QCP), extends the classical model to include coherent processes. Despite sustained interest, the nature of the transition in the one-dimensional (1D) QCP remains debatable. Here, combining Liouvillian spectral analysis, the tensor jump method, exact quantum jump Monte Carlo, and truncated Wigner simulations, we show that 1D QCP undergoes a continuous absorbing-state phase transition, with critical exponents distinct from the classical case. We further find Liouvillian gap closes well below the critical point, highlighting that spectral gap analysis alone cannot distinguish a phase transition from metastability in the QCP. Crucially, the 1D QCP is weakly entangled, yet even this weak entanglement is indispensable for capturing the correct critical behavior, whereas semiclassical methods artificially stabilize the active state and predict a spurious first-order transition. Our work establishes the quantum origin of the phase transition in the 1D QCP and underscores the essential role of entanglement in dissipative quantum many-body systems.

Quantum cooling is important for reliable quantum computation but involves a trade-off between cooling performance and implementation resources. Although reservoir memory can improve particular aspects of cooling performance, the associated resource cost, particularly for circuit implementation, remains insufficiently understood. Here, we investigate how reservoir memory affects the trade-off between cooling performance quantified by the cooling-step count and geometric implementation cost in single-qubit heat-bath algorithmic cooling. Using a pseudomode mapping, we represent the non-Markovian damped Jaynes–Cummings dynamics by a repeated collision circuit and evaluate its geometric implementation cost. Using matrix-based simulations and an implementation on the ibm_kawasaki Heron r2 processor, we identify a trade-off: suppressing reservoir memory reduces the cooling-step count but generally increases the geometric protocol cost. Our work provides a resource-based perspective on reservoir engineering for algorithmic cooling.