Papers

We propose candidate lower bounds on the real Grothendieck constants $K_{\mathrm G}(d)$ and their infinite-dimensional limit $K_{\mathrm G}$ using rotationally invariant cubic kernels. For the continuous construction, we identify an explicit threshold above which hemispherical binary strategies are unstable under cubic boundary deformations. Supported by numerical evidence, we conjecture that hemispherical strategies are globally optimal at this threshold. This conjecture would imply $K_{\mathrm G}\geq9\pi/16\simeq1.767146$, improving the rigorous lower bound $6\pi/11\simeq1.713596$. We also construct finite symmetric coefficient matrices from unit vectors in dimensions up to $24$. Large-scale see-saw optimization supports the continuous predictions and suggests improved lower bounds on $K_{\mathrm G}(d)$ in the studied dimensions from $4$ to $24$, conditional on the conjectured binary optima being exact. Selected matrices also yield finite-setting candidate dimension witnesses when interpreted as bipartite correlation Bell functionals. If the corresponding binary upper bounds hold, these witnesses would certify a local Hilbert-space dimension of at least five for each party.

Zero-knowledge proofs (ZKPs) enable the verification of a statement without revealing any information beyond its validity and constitute a fundamental primitive in cryptography and information theory. However, existing constructions rely on computational assumptions and are predominantly confined to bipartite settings, leaving their information-theoretic realization in bipartite or network scenarios largely unexplored. Here we develop a framework for zero-knowledge verification based on the indistinguishability of quantum states under operational constraints. Exploiting the fundamental limitations imposed by local operations, we show that a verifier is inherently restricted from extracting information about the underlying state while retaining the ability to verify correctness. We construct explicit protocols for multiparty quantum networks that achieve information-theoretic security, ensuring that no subset of collaborating parties can gain knowledge beyond the validity of the statement, independent of their joint computational power.

A longstanding conjecture in quantum complexity theory asserts that, under the uniform input distribution, quantum query algorithms can be polynomially simulated by classical query algorithms. More precisely, the acceptance probability of any quantum query algorithm can be approximated, on average over uniformly random inputs, by a classical query algorithm, with only polynomial query overhead. The conjecture is central to understanding whether exponential quantum advantages for decision problems necessarily rely on additional structure. We study analogues of this conjecture under other natural input distributions and prove that they are all equivalent to the original uniform-distribution conjecture. We first consider the product distribution $\mu_p$, where the input bits are independent Bernoulli variables with fixed bias $p$. We show that for every fixed $p \in (0, 1)$, quantum query algorithms under the $\mu_p$ distribution admit polynomial-overhead classical simulations if and only if the same holds under the uniform distribution. Second, we consider the distribution $\nu_p$ that is uniform over the slice of strings with Hamming weight $\lfloor pn \rfloor$ and prove a similar equivalence for the $\nu_p$ distribution and the uniform distribution. The Aaronson-Ambainis conjecture is a stronger statement that implies the above-mentioned conjecture and is formulated in terms of bounded low-degree polynomials on the Boolean hypercube. It asserts that under the uniform distribution, any such polynomial with nonnegligible variance must have an influential variable. We formulate analogues of this conjecture, where the underlying distribution is a biased product distribution or a uniform distribution over a slice, and prove that all these variants are equivalent to the original Aaronson-Ambainis conjecture.

Scalable fault-tolerant quantum error correction based on Gottesman-Kitaev-Preskill (GKP) codes requires finite-rate outer codes that can exploit analog GKP information under realistic circuit noise. However, quantum low-density parity-check (qLDPC) outer codes have not been systematically compared as candidates for circuit-level GKP concatenation. Here, we benchmark BB and tricycle codes using a unified simulation framework that progresses from code-capacity noise to repeated noisy syndrome extraction and schedule-resolved displacement propagation. Across all three noise models, analog-informed belief-propagation with ordered-statistics decoding (BP-OSD) yields higher finite-size crossing estimates than hard-decision decoding. In the full circuit model, the analog-informed crossings are \(\sigma_{\mathrm{th}}\simeq0.212\) for the selected BB sequence and \(0.142\) for the tricycle sequence, corresponding to squeezing requirements of approximately \(10.46\,\mathrm{dB}\) and \(13.94\,\mathrm{dB}\), respectively. These results show that analog GKP information continues to improve decoding under circuit-level noise. Under the common simulation assumptions used here, the selected BB sequence also yields a higher finite-size crossing estimate than the selected tricycle sequence.

A reduced ordered decision diagram is the minimal automaton of a function on words of fixed length: its nodes are the residuals, and reduction is the Myhill–Nerode quotient. We study what happens when that quotient is coarsened by a group. Fix a group $G$ acting on residuals, merge two nodes when their residuals lie in one $G$-orbit, and record the group element on the edge. For functions $\{0,1\}^n\to\mathbb{C}$ and $G$ the Pauli group this is the Local Invertible Map Decision Diagram. We take $G$ from the two-parameter family generated by $C^{\leq k}R_q$, the phase rotation of order $q$ with up to $k$ control qubits, with and without the bit flip $X$. We show that this gives exponential succinctness improvements compared to Pauli-LIMDD, and we determine the succinctness order of the family completely. The separating objects are hypergraph states, which can always be efficiently represented by some member of the family. We settle the tractability of five queries and eight transformations, which is invariant across the family, and shows the same behavior as Pauli-LIMDD. We give a five-rule reduction system whose normal forms are unique for every member of the family, and we show that this canonical form is computable in polynomial time in the size of the LIMDD. We show that, when coarsening beyond the (anti-)diagonal groups, the calculation of a minimal sized normal form turns out to be non-local and it might to rebuild the whole diagram.

We study the problem of learning a local Lindbladian in the presence of state-preparation-and-measurement (SPAM) noise. Although recent work has developed scalable learning algorithms under idealized access assumptions, SPAM can make distinct Lindbladians experimentally indistinguishable, thus making part of the Lindbladian fundamentally unlearnable. We give a sharp characterization of this obstruction for bounded-degree local Lindbladians. We identify a family of locality-preserving gauge transformations that commutes with trusted single-qubit control, and use it to classify Lindbladian components. For the generically gauge dependent components, we construct Lindbladians to show that they can have $\Omega(1)$ uncertainty independent of system size, even after imposing complete positivity. We complement this characterization with SPAM-robust algorithms for learning every universally gauge-invariant component. Our algorithms use only trusted single-qubit operations, require neither ancillas nor entangling control, and use $\widetilde{\mathcal O}\left(\epsilon^{-2}\log(N/\delta)\right)$ experiments and total evolution time for constant locality and degree. Our guarantees allow global SPAM to become arbitrarily far from ideal as $N$ grows, requiring only nonvanishing local visibility. We also establish sufficient conditions for boundary-induced gauge invariance of additional Hamiltonian coefficients under physical positivity constraints, though learning these additional parameters in general remains an open problem. More broadly, our gauge-aware framework and SPAM-cancellation techniques offer a practical toolkit for the scalable characterization of open quantum systems.

Time-multiplexed (TDM) photonic reservoirs are usually judged by their scores on a few datasets, which say little about a chip's overall performance, and designed by enumerating candidate circuits and simulating each one, which is inefficient and gives no guarantee of finding a good structure. For a time-unrolled passive linear network with data-modulated gates or sources and a ridge readout, we derive an exact bridge from the task to the prediction risk in three steps. (i) Task features: the finite-shot risk depends on the time series only through finitely many statistics of its training windows and their correlations with the target, selected by the encoding and the optical paths. (ii) Encoding: every output moment is a polynomial in the features of the data-modulated sites, with degree and support bounded by tuples of optical paths. Gate encoding reads the characteristic function and creates interactions across time lags; squeezing encoding reads the moment-generating function and displacement encoding low-order moments, and with quadrature receivers they yield only additive and linear models, respectively, for every topology. (iii) Readout: for homodyne, heterodyne and photon-number receivers the risk closes exactly, and its dependence on the number of shots is an explicit sum over signal-to-noise modes; threshold clicks admit finite-dictionary approximations with certified error. Parts of the network that share no light carry independent states, which a receiver combines only through measurement events that join them. Checks on seven datasets confirm every exact statement to machine precision. The three steps thus yield a useful space of candidate TDM architectures, pruned by exact statements rather than by trial simulation, which can in future guide the selection of TDM chips for target requirements.

A Clifford template is a finite ordered family of repeatable Clifford operations, and an instantiation specifies how many times each operation is applied. The Clifford template compilation problem asks how to choose these repetition numbers so that the template realizes a target transformation of Pauli operators. This problem arises, for example, when searching for logical operations in quantum error correction using only Clifford operations permitted by physical or fault-tolerance constraints. Although forward Clifford dynamics is efficiently classically simulable, this inverse problem has sharp complexity transitions. For commuting templates with unrestricted integer exponents, feasibility lies in $\mathrm{NP}\cap\mathrm{BQP}$ and a constructive quantum algorithm returns a particular solution together with the full exponent-relation lattice; already at $k=1$, recovering the repetition number contains finite-field discrete logarithm over $\mathbb{F}_{2^r}^{\times}$. In general, restricting every exponent to $\{0,1\}$ removes the Abelian-group closure and makes feasibility NP-complete for variable $k$, even for exactly commuting CNOT-only operations and X-type Paulis. For commuting self-inverse Clifford actions, both binary feasibility and recovery of one solution are classically polynomial-time solvable, but imposing a bound on the total repetition count is NP-complete, even for CNOT-only operations. These results reveal a rich complexity landscape within Clifford template compilation, spanning classically tractable cases, problems admitting quantum polynomial-time algorithms, and NP-complete variants.

We introduce a technological capability scale that ranks civilizations by the control operations they can perform per second. A control operation is defined as setting one binary degree of freedom of matter to a specified value, whatever its previous state. Building on constructor theory, we sort them into construction and its special cases on information media, namely processing, storage and transfer. The index $\Xi = K + B$ adds to the Kardashev index $K$ an efficiency index $B$ of energy per operation, measured from the thermal floor at the microwave background temperature. The Kardashev scale gives the ceiling for resets of thermally random bits with heat radiated into the present sky, and the Barrow scale gives the floor, which for such a reset is the thermal floor at the heat-rejection temperature at every level. Since 1950 the energy per logic operation has fallen 11.7 orders of magnitude, around 5 through miniaturization. Humanity, at $K = 0.73$, computes with CMOS logic gates at $B = -0.78$ in primary energy. We describe the ultimate technology, at $\Xi = 7.58$, which would dissipate the conjectured largest power $c^5/4G$ into an uncharged, non-rotating black hole near its largest mass in de Sitter space.

The complex spacing ratio is the complex displacement from a reference eigenvalue to its nearest neighbor divided by the corresponding displacement to its next-to-nearest neighbor. Its statistics provide a useful diagnostic of spectral correlations and nonintegrability in open quantum systems. Here, starting from the exact joint eigenvalue probability densities, we derive finite-$N$ complex-spacing-ratio distributions for the Gaussian ensembles of non-Hermitian random matrices in classes AI$^{\dag}$ and AII$^{\dag}$, realized by complex symmetric and complex self-dual random matrices, respectively. In class AII$^{\dag}$, we obtain an exact algebraic expression for arbitrary $N$ and explicitly evaluate the distributions and representative moments for $N=3, 4, 5, 6$. In class AI$^{\dag}$, although the joint density retains a noncompact integral over nonunitary eigenvector degrees of freedom, we analytically derive a normalized one-dimensional integral representation for $N=3$ and determine the asymptotic behavior, including a logarithmic correction to the cubic level repulsion and a nonanalytic contribution to the angular density. We further confirm these analytical results through direct numerical diagonalization of non-Hermitian random matrices.

Vector-vortex photons, characterized by a nonseparable coupling between polarization and orbital angular momentum (OAM), offer opportunities for optical manipulation, quantum communication, nuclear photonics, etc. However, their generation in the $\gamma$-ray regime remains challenging. Here, we put forward a novel method to generate vector-vortex $\gamma$ photons via nonlinear Compton scattering in elliptically polarized laser pulses. We reveal that tailoring laser ellipticity directs the multiphoton absorption to coherently populate OAM modes with opposite winding numbers, $\pm \ell$, tied to orthogonal circular polarizations, producing nonseparable spin-OAM photon states. For a linearly polarized laser of moderate intensity (dimensionless amplitude $a_0 \sim 1$), the mode-pair concurrence–a 0-to-1 measure of spin-OAM entanglement–reaches unity for MeV $\gamma$ photons, realizing maximally nonseparable radial- or azimuthal-type vector-vortex states. The laser amplitude further controls the accessible OAM spectrum. Our method offers a route to MeV vector-vortex photons, opening a new avenue for nuclear-scale structured photonics and high-energy quantum information.

We numerically study laser deceleration, cooling and trapping of host fast ortho-positronium (Ps) bunches as produced in silica microchannel targets using positron bunches from a Surko trap. While Doppler laser cooling routinely allows to cool neutral atom species below milli-Kelvin kinetic temperatures, the fast ground state annihilation and the high recoil shift to line-width ratio in Ps pose new challenging limitations on timing and the required laser power. Earlier theoretical work and first experiments already exhibit viable prospects for radiation pressure cooling to create unprecedented cold and dense Ps ensembles. Our extended numerical studies confirm very good prospects to simultaneously decelerate, cool and optically trap Ps atoms in a standard Doppler cooling geometry on the $1^3\mathrm{S}$–$2^3\mathrm{P}$ transition. Including the full Zeeman state manifolds and adding additional transverse lasers on the $2^3\mathrm{P}$–$3^3\mathrm{D}$ transition improves timing and final temperature to allow for optical trapping at the end. The required laser powers and geometry parameters to implement effective slowing and trapping within a time frame, where the majority of atoms is not annihilated, is in reach of current technology of $\mathrm{mJ}$ energy pulses of approximately $100\ \mathrm{ns}$ duration. Future extensions to collectively enhance cooling and trapping in optical cavities or hollow-core fibres should finally allow fast preparation of ultra-cold Ps systems as future basis of superradiant lasing and Bose–Einstein condensates.

Quantum circuit Born machines (QCBMs) built with instantaneous quantum polynomial (IQP) circuits have loss functions that can be efficiently estimated classically, but require quantum computers during inference. Thus, classical computers can train large IQP QCBMs that exceed the qubit numbers of available quantum hardware. This motivates research into how qubit-limited quantum computers can be used to sample from larger IQP QCBMs. Leveraging insights from classical simulation of noisy IQP circuits, we propose a deployment protocol for IQP QCBMs that injects noise at the logical level to probabilistically decompose the original circuit into smaller clusters that can be sampled on qubit-limited quantum processors. We also apply lightweight resampling of known noisy qubits to mitigate the impact of the introduced error. Numerical simulations of our protocol applied to shallow IQP QCBMs and IBM Heron experiments deploying a 316-qubit IQP circuit onto 156-qubit hardware show that mitigation improves the similarity of the empirical distribution to the target distribution. The proposed deployment protocol also crucially preserves correlation structures more accurately than a classical baseline that has accurate single-qubit marginals.

Identifying regimes in which interacting fermionic systems admit efficient classical simulation is a crucial task in quantum many-body physics. In this work, we rigorously establish the Gaussianity and classical simulability of sufficiently weakly interacting fermions. For the Gibbs state of a local interacting fermionic Hamiltonian $H=H_0+V$ at any finite temperature and in any spatial dimension, where $H_0$ is quadratic and $V$ is the interaction term, we show that there exists a positive interaction strength below which the Gibbs state is a convex mixture of fermionic Gaussian states. Moreover, based on this structure, we construct a polynomial-time classical sampler for the Gibbs state via Metropolis updates on a tree whose leaves are Gaussian states.

In this paper, we prove that the Mean-Field Approximate Optimization Algorithm (MF-AOA), a quantum-inspired classical algorithm of the Quantum Approximate Optimization Algorithm (QAOA), is unable to give arbitrary near optimal solution for problems exhibiting the Overlap Gap Property (OGP). We show this by relating the MF-AOA to finite-memory Approximate Message Passing (AMP) algorithms, which are known to be limited in performance by the OGP. Thus, our paper argues that problems exhibiting the OGP are one such instance where the QAOA can outperform the MF-AOA and AMP algorithms in general. We supplement this by numerically simulating the performance of the QAOA on instances of Max-$4$-XORSAT that exhibit the OGP and find that the QAOA is able to surpass the barrier, while our finite-size scaling analysis favors a super-polynomial over a polynomial depth dependence. In addition, we observe a non-differentiable point in the performance of the QAOA near by the OGP barrier, where the optimal QAOA parameters change from an adiabatic to a non-adiabatic schedule.

Designing quantum codes with both transversal non-Clifford gates and good error-correcting parameters is an important goal in fault-tolerant quantum computation. Here, we construct an explicit family of binary CSS codes with constant rate and linear distance that admit fully addressable transversal $T$ gates. Specifically, any prescribed tensor product of logical powers of $T$ is implemented by a tensor product of physical powers of $T$, without any subsequent correction. Our construction combines algebraic-geometry codes with suitable binary embedding to obtain generalized divisibility of binary codes. This divisibility then enables fully addressable transversal $T$ gates. Furthermore, we formulate the minimum binary embedding length problem as a minimum-weight problem over an affine space and numerically improve the constants in the asymptotic rate and relative-distance bounds.

The exact classical simulation of non-integrable quantum systems rapidly becomes intractable beyond small system sizes, yet its role is central to predicting many-body dynamics. Approximate methods alleviate this cost but typically lack rigorous guarantees on their deviation from the exact result. For the infinite-temperature correlation function, we derive a rigorous error bound for approximating the full dynamics within a computable finite-sized region. Applied to autocorrelations, this finite-region approach is especially accurate across one-dimensional systems and beyond, and can further provide rigorous error bounds for other approximate methods, demonstrated here for matrix-product-operator simulations.

The Landau-Lifshitz-Gilbert (LLG) equation provides the fundamental description of dissipative magnetization dynamics. A recently proposed quantum analog, the quantum Landau-Lifshitz-Gilbert (QLLG) equation, extends this framework to quantum spin systems. However, whether the QLLG equation recovers the LLG equation in the classical large-spin limit for interacting spin systems remains an open question. Here, we demonstrate this connection by deriving the LLG equation as the classical large-spin limit of the QLLG equation. We establish this correspondence analytically and verify it numerically for an interacting spin system. These results provide a quantum-to-classical description of dissipative spin dynamics, offering a microscopic foundation for the LLG equation. From numerical calculations provided here, we also conclude that quantum effects become much less noticeable for systems with larger number of spins in the Hamiltonian.

Decoded quantum interferometry (DQI) and its Hamiltonian extension (HDQI) prepare states whose amplitudes are low-degree polynomials of an objective, using Fourier transforms and coherent decoding. We recast this approach as quantum state transduction through algebra homomorphisms. We transfer an efficiently preparable operator state of a degree-$D$ polynomial in a source Hamiltonian $H_A$ to the corresponding polynomial state of a target Hamiltonian $H_B=\pi(H_A)$, where $\pi$ is a unital $*$-homomorphism between the finite-dimensional source and target $C^*$-algebras. The transduction uses operator Fourier transforms and relative decoding to recover source operators rather than individual term-selection labels. The relative distance $d_{\mathrm{rel}}$ is the first degree at which source and target traces disagree. We prove that $2D<d_{\mathrm{rel}}$ is equivalent to preserving all inner products between degree-$D$ polynomials. Moreover, $d_{\mathrm{rel}}\ge d_{\mathrm{ord}}$, where $d_{\mathrm{ord}}$ is the ordinary distance used in (H)DQI, and we give families with $d_{\mathrm{ord}}=O(1)$ but $d_{\mathrm{rel}}=\Theta(n)$ and efficient decoders. Our framework replaces the complicated pilot state preparation by the more modular task of preparing a source polynomial state. DQI and HDQI arise as relation-free special cases. The framework accommodates nonuniform coefficients and noncommuting interactions and extends to fermionic, qudit, and bosonic systems, with applications to approximate optimization and Gibbs sampling. As evidence of advantages, for a nonlinear pairwise variant of optimal polynomial intersection where constant $d_{\mathrm{ord}}$ limits DQI-style preparations, relative decoding yields an ideal quantum score of 0.643 versus 0.606 for the best tested classical heuristic, a gap exceeding 3 percentage points.

Dephasing can sharpen the activation of a dissipative quantum neuron, but a stationary response does not determine how much input information its output delivers per unit time. For a single qubit with partial-reset updates at rate $\nu$, we derive the threshold response bandwidth and the exact local Fisher information rate of the complete record from repeated projective readouts, including their backaction. Near the activation threshold, the rate obeys $\mathcal R\leq\nu(1-s)(1+s)^2/2\leq16\nu/27$, where $s$ is the retained amplitude of each update. For every fixed finite Markovian dephasing rate, optimization over the readout interval and $s$ gives the same supremum, approached at $s=1/3$ with arbitrarily rapid ideal readout. A finite measurement dead time instead selects a finite optimal interval, which we obtain by a dimensionless two-parameter optimization. The ideal bound is saturated by a classical two-state jump process: quantum coherence changes finite-cadence performance but cannot raise the optimized bound. These results separate noise-enhanced activation from the operational information throughput of a quantum neuron and provide a hardware-aware benchmark for finite-time quantum neural processing.

The combination of quantum sensing with quantum computing to provide an enhancement over conventional quantum sensing has recently emerged as a promising potential application of quantum computing that could give advantages without needing large-scale or fault-tolerant hardware. In this work, we report an experimental demonstration of a recent theoretical proposal to repurpose Grover's search algorithm to improve the ability to detect signals with unknown frequency within a large detection bandwidth. Our experiments were based on a system comprising a single superconducting qubit coupled to a single superconducting cavity, highlighting the modest hardware requirements for realizing the protocol. We found that Grover-based sensing was able to outperform the natural non-Grover baseline for our experimental platform for detection bandwidths $>$10~MHz, with an advantage that empirically grew superlinearly with the bandwidth beyond that break-even point. The use of the Grover-based protocol reduced the amount of signal that needed to be sensed to make an accurate detection decision by more than 10$\times$ for choices of larger detection bandwidth and higher desired detection accuracy. Our results provide a proof-of-principle validation that Grover-based quantum computational sensing can be realized in near-term hardware and provide a metrological advantage well beyond break-even in spite of the additional protocol complexity.

Enantiomer-specific state transfer (ESST) based on electric-dipole transitions has attracted considerable interest in the studies of manipulating molecules with electromagnetic fields. It also holds promise as a powerful tool for enantiomer detection and separation. To date, experimental demonstrations of ESST have focused mainly on molecules in the lowest rotational angular-momentum states, namely, $J=0$ and $J=1$. Realistic molecular samples, however, may contain appreciable populations in higher-$J$ rotational states, making it desirable to develop ESST schemes applicable to such states. Nevertheless, one cannot derive such schemes via a simple and straightforward extension of existing low-$J$ schemes, because higher-$J$ manifolds contain more magnetic sub-levels and involve more complicated networks of electric-dipole transitions. Here, we propose an ESST scheme for chiral molecules involving the $J=1$ and $J=2$ rotational states. Specifically, our scheme is based on enantiomer-specific pumping driven by three linearly polarized microwave fields and one laser beam. Under this scheme, one enantiomer is pumped into an enantiomer-specific dark state within a sub manifold with $J=1,2$, whereas the other enantiomer is dissipatively pumped out of this manifold. Our strategy can be extended to systems involving rotational states with even higher angular momenta.

The Learning With Errors (LWE) problem is a fundamental assumption in post-quantum cryptography. Regev established a quantum reduction from LWE to the Dihedral Coset Problem (DCP). Later, Brakerski et al. introduced the Extrapolated Dihedral Coset Problem (EDCP), proving its equivalence to LWE. However, unlike DCP, EDCP no longer admits a coset structure. This limits the direct application of techniques for hidden subgroup problems. In this work, we introduce the Cyclotomic Coset Problem (CCP), a cyclotomic generalization of DCP that preserves an exact hidden-subgroup structure. Let $\zeta_p$ be a primitive $p$-th root of unity, let $\pi=\zeta_p-1$, and write $q=p^t$ and $L=t(p-1)$. We work over $R_q=\mathbb Z_q[\zeta_p] \cong \mathbb Z[\zeta_p]/(\pi^L)$, where the isomorphism follows from the total ramification identity $(p)=(\pi)^{p-1}$. We exploit the resulting $\pi$-adic ideal chain to construct a quantum sieve that successively reduces phase states modulo $\pi^{L},\pi^{L-1},\ldots,\pi$. For every fixed prime $p$ and modulus $q=p^t$, our algorithm solves the CCP in time and sample complexity $2^{O_p(\log n\log q)}$, using polynomial quantum space. The sieve also applies to uniform EDCP and Gaussian S|LWE>, yielding quasi-polynomial time algorithms for all the above problems when $q=\text{poly}(n)$. This extends the power-of-two EDCP sieve of Bai et al. (CRYPTO 2025) to a cyclotomic setting. However, we emphasize that our result does not, by itself, yield a quasi-polynomial-time algorithm for standard LWE, because the currently known reduction produces only a limited number of approximate CCP states.

Models of quantum systems faithfully map system parameters to observations, but the inverse problem of parameter inference from measurement data presents a fundamental challenge: computationally intractable likelihoods due to an exponentially large Hilbert space. Here, we introduce simulation-based quantum system inference, a unified, likelihood-free framework that learns parameter posteriors directly from classical simulation data. The central idea is to pair polynomial-cost classical simulators, such as Pauli propagation and tensor networks, with normalizing flows or other neural density estimators for accurate, reusable inference. A single model, trained once, maps any new measurement record to its posterior in one forward pass—turning per-experiment inference into a fixed, up-front cost. We numerically demonstrate the framework's versatility across Pauli noise learning, quantum error mitigation, quantum state tomography, and Hamiltonian learning, with examples involving 81-qubit shallow circuits and 735-parameter inference. In each case, the approach yields accurate estimates of identifiable parameters, while posterior uncertainty provides additional diagnostics of non-identifiability and indicates where further characterization is needed. Our framework reduces data-acquisition requirements in quantum experiments and accelerates parameter inference, providing a practical route to characterizing and improving large-scale quantum systems.

Preparation contextuality is often manifested operationally through a quantitative advantage over preparation-noncontextual models in information-processing tasks, yet quantum theory typically falls short of perfect success. Here we introduce a parity-oblivious Hidden Matching task that instead yields an all-vs-nothing manifestation of preparation contextuality. Alice encodes an $n$-bit string so that her message reveals no information about any input parity other than the two-bit parities. Bob, given a perfect matching on the input positions, must output an edge of the matching together with the parity of its two bits. A quantum protocol using a single $\lceil\log_2 n\rceil$-qubit message satisfies the parity-obliviousness constraint and succeeds with certainty. We prove that no preparation-noncontextual model achieves perfect success for any even $n\ge6$. The result holds for arbitrary ontic state spaces and assumes neither outcome determinism nor measurement noncontextuality. For $n=6$ and $n=8$, the optimal noncontextual success probabilities are $4/5$ and $3/4$, respectively, while asymptotically the optimal noncontextual success probability is $1/2+\Theta(1/\sqrt n)$. Our asymptotic upper bound follows from a Fourier-analytic sum rule derived via hypercontractivity on the Boolean hypercube. The resulting separation is qualitative rather than merely quantitative: quantum theory achieves perfect success, whereas preparation-noncontextual models cannot. We aslo show that at $n=8$ the noncontextual bound remains $3/4$ even when Bob is restricted to just suitable $4$ of the $105$ possible perfect matchings, bringing the effect within experimental reach.

Classical simulation of quantum random access memory (QRAM) under noise can be accelerated dramatically by branch pruning: noise histories are sampled as trajectory ensembles, and good branches, whose routing paths avoid every sampled fault, need not be evolved because their final states are analytically predictable. Under amplitude damping this predictability is not automatic, because the no-jump operator $K_0$ acts on every branch at every time slice. Here we give a complete account of damping-channel predictability in bucket-brigade QRAM simulation, for both qutrit and qubit encodings. For the qutrit encoding, $K_0$ is diagonal in the node basis, and the wait state $|W\rangle$ is its fixed point, so a good branch follows the noiseless orbit up to a scalar attenuation. In the qubit encoding, phase-kickback memory fetching between two Hadamard walls makes $K_0$ no longer diagonal, yet the resulting structure is exactly solvable in closed form. Conditional on no jump, the in-branch infidelity of a good branch is second order in the damping rate $\gamma$, with coherent leakage $\sim n^2\gamma^2/4$ per data qubit, and the closed form captures it without approximation. We also revise the pruning criterion for the qubit encoding. The resulting algorithm evolves only the bad branches plus one reference branch and shares every other cost with the full evolution it replaces. It is validated by end-to-end benchmarks with pruned-over-full speedups up to $285\times$ and by trajectory-level tests confirming every closed form to machine precision.

A resonant classical field drives a two-level system coherently and, with ordinary relaxation, produces saturation rather than directional population transfer. Here we show that directionality emerges when the excitation source is retained as a quantum subsystem and subsequently traced out. We model the source as a single-excitation degree of freedom, or equivalently a stream of two-level ancillas, exchange-coupled to a target two-level system. The source first moment generates the usual coherent drive, while its second moments produce upward and downward dissipative channels. For a number-diagonal, fully excited source, the first moment vanishes and only the upward channel remains, yielding monotonic pumping of the target. The same structure follows from both an exact collision map and a fluctuation-regulated second-order quantum master equation. For exponentially decaying source correlations, the pumping rate shows a Lorentzian detuning dependence governed by the correlation time $\tau_c$, accompanied by a dispersive frequency shift. In the presence of thermal relaxation, the steady-state excited-state population can exceed the resonantly driven optical-Bloch limit of one half. Within the fluctuation-regulated master equation, this directional pumping arises as a drive-induced dissipative contribution whose strength and spectral response are controlled by $\tau_c$.

A measure of correlations for statistical systems is advanced, called correlation index. The measure is general, being applicable to quantum and classical, equilibrium and nonequilibrium statistical systems. After formulating the general notion of correlation indices for arbitrary trace-class operators, the calculation of the correlation indices are illustrated by several examples of density operators and reduced density matrices. The computation of the correlation indices for equilibrium systems is exemplified for bosonic systems with the Bose-Einstein condensate, superconducting systems, and for spin systems. Correlation indices for nonequilibrium systems are considered for nonlinear dynamics of spin and pseudospin systems.

A near-deterministic source of non-Gaussianity is the missing piece to reach universal and fault-tolerant quantum computing with continuous-variable optics. Due to a lack of strong non-linearities, the probabilistic photon-subtracted Gaussian states remain the most promising contender. In combination with Gaussian measurements and single-mode feed-forward operations, they have been shown to provide sufficient non-Gaussianity at high rates. However, these existing breeding protocols lack the necessary loss tolerance to be experimentally feasible. In this work, we introduce a mathematical formalism based on the application of a Gaussian blur and filter on the measured Fock Wigner function to describe general photon-subtracted Gaussian states. Within our representation, the initial squeezing, Gaussian measurements, and photon loss can all be understood as contributions to the total blurring and interchanged accordingly. We find that this intuitive approach can be used to find improvements to cat, cubic phase, and GKP state generation by compromising between success rates, feed-forward compatibility, and loss tolerance. In the case of multiple photon subtractions, this is achieved by introducing a hybrid setup variant bridging the gap between protocols based on breeding and post-selection. Finally, we establish a general lower bound on the resources needed to generate a given target state near-deterministically by introducing the expected Wigner logarithmic negativity as an additive monotone of non-Gaussianity.

Hybrid quantum systems combining discrete-variable (DV) and continuous-variable (CV) subsystems arise across a broad range of physical platforms and enable quantum information processing beyond purely qubit-based designs. Their classical simulation, however, is challenging since computational costs of both CV and DV systems exponentially increase. In this paper, we introduce a simulation framework for CV–DV hybrid systems based on linear combination of Gaussian (LCoG) decomposition. We decompose the hybrid density matrix into blocks in a DV basis and represent each block as an LCoG expansion. Within the representation, Gaussian operations on the bosonic subsystem independently act on each Gaussian function. We derive analytic formulas describing how complex Gaussian functions transform under controlled Gaussian operations. We further extend the framework to controlled Gaussian channels with state-dependent Gaussian noise. The method avoids a Fock-space truncation for the CV subsystem, and the cost of updating each Gaussian term scales polynomially with the number of modes. The framework provides a general computational tool for analyzing hybrid quantum algorithms, quantum simulation protocols, and non-Gaussian state generation schemes. As an example, we simulate Gottesman–Kitaev–Preskill (GKP) state generation based on a cavity-QED system.