Papers

Quantum state transfer (QST) via homogeneous spin chains plays a crucial role in building scalable quantum hardware. A basic quantum state transmission protocol prepares a state in one qubit and transfers it to another through a channel, seeking to minimize the time and avoid information loss. The fidelity of the process is measured by functions proportional to the transition probability between both states. We approach this optimization problem using constant magnetic pulses and two complementary strategies: deep reinforcement learning, where an agent learns pulse sequences through rewards, and genetic algorithms, which develop candidate solutions through selection and mutation. We analyze the efficiency of both methods and their ability to incorporate physical constraints.

Classical error-correcting codes are powerful but incompatible with quantum noise, which includes both bit-flips and phase-flips. We introduce Hadamard-based Virtual Error Correction (H-VEC), a protocol that empowers any classical bit-flip code to correct Pauli noise with the addition of only a single control qubit and two layers of controlled-Hadamard gates. Through classical post-processing, H-VEC virtually filters the error channel, projecting the noise into pure Y-type errors that are subsequently corrected using the classical code's native decoding algorithm. We demonstrate this by applying H-VEC to the classical repetition code. Under a code-capacity noise model, the resulting protocol not only provides full quantum protection but also achieves an exponentially stronger error suppression (in distance) than the original classical code. The improvements over the surface code are even more pronounced, while using far fewer qubits, simpler checks, and straightforward decoding. Considering circuit-level noise, we present a fault-tolerant protocol in which H-VEC can quadratically reduce the qubits needed for long-range surface code lattice surgery. There are some limitations to the technique, most notably that H-VEC introduces a sampling overhead due to its post-processing nature. Nonetheless, it represents a fundamentally novel hybrid quantum error correction and mitigation framework that redefines the trade-offs between physical hardware requirements and classical processing for error suppression.

The Clifford hierarchy is a fundamental structure in quantum computation whose mathematical properties are not fully understood. In this work, we characterize permutation gates – unitaries which permute the $2^n$ basis states – in the third level of the hierarchy. We prove that any permutation gate in the third level must be a product of Toffoli gates in what we define as staircase form, up to left and right multiplications by Clifford permutations. We then present necessary and sufficient conditions for a staircase form permutation gate to be in the third level of the Clifford hierarchy. As a corollary, we construct a family of non-semi-Clifford permutation gates $\{U_k\}_{k\geq 3}$ in staircase form such that each $U_k$ is in the third level but its inverse is not in the $k$-th level.

Quantum cryptographic definitions are often sensitive to the number of copies of the cryptographic states revealed to an adversary. Making definitional changes to the number of copies accessible to an adversary can drastically affect various aspects including the computational hardness, feasibility, and applicability of the resulting cryptographic scheme. This phenomenon appears in many places in quantum cryptography, including quantum pseudorandomness and unclonable cryptography. To address this, we present a generic approach to boost single-copy security to multi-copy security and apply this approach to many settings. As a consequence, we obtain the following new results: -One-copy stretch pseudorandom state generators (under mild assumptions) imply the existence of t-copy stretch pseudorandom state generators, for any fixed polynomial t. -One-query pseudorandom unitaries with short keys (under mild assumptions) imply the existence of t-query pseudorandom unitaries with short keys, for any fixed polynomial t. -Assuming indistinguishability obfuscation and other standard cryptographic assumptions, there exist identical-copy secure unclonable primitives such as public-key quantum money and quantum copy-protection.

In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The input and output to the quantum algorithm is represented by a set of boundary vertices, and the hyperedges act like switches, connecting the input vertex to the output that the algorithm computes. Apart from generalizing the graph composition framework, our new proposed framework unifies the quantum divide and conquer framework, the decision-tree framework, and the unified quantum walk search framework. For the decision trees, we additionally construct a quantum algorithm from an improved weighting scheme in the non-boolean case. For quantum walk search, we show how our techniques naturally allow for amortization of the subroutines' costs. Previous work showed how one can speed up “detection” of marked vertices by amortizing the costs of the quantum walk. In this work, we extend these results to the setting of “finding” such marked vertices, albeit in some restricted settings. Along the way, we provide a novel analysis of irreducible, reversible Markov processes, by linear-algebraically connecting its effective resistance to the random walk operator. This significantly simplifies the algorithmic implementation of the quantum walk search algorithm, achieves an amortization speed-up for quantum walks over Johnson graphs, avoids the need for quantum fast-forwarding, and removes the log-factors from the query complexity statements.

We pose and solve the problem of quantum filtering based on continuous-in-time quadrature measurements (homodyning) for the case where the quantum process is in a thermal state. The standard construction of quantum filters involves the determination of the conditional expectation onto the von Neumann algebra generated by the measured observables with the non-demolition principle telling us to restrict the domain (the observables to be estimated) to the commutant of the algebra. The finite-temperature case, however, has additional structure: we use the Araki-Woods representation for the measured quadratures, but the Tomita-Takesaki theory tells us that there exists a separate, commuting representation and therefore the commutant will have a richer structure than encountered in the Fock vacuum case. We apply this to the question of quantum trajectories to the Davies-Fulling-Unruh model. Here, the two representations are interpreted as the fields in the right and left Rindler wedges.

Dissipative quantum algorithms for state preparation in many-body systems are increasingly recognised as promising candidates for achieving large quantum advantages in application-relevant tasks. Recent advances in algorithmic, detailed-balance Lindbladians enable the efficient simulation of open-system dynamics converging towards desired target states. However, the overall complexity of such schemes is governed by system-size dependent mixing times. In this work, we analyse algorithmic Lindbladians for Gibbs state preparation and prove that they exhibit rapid mixing, i.e., convergence in time poly-logarithmic in the system size. We first establish this for non-interacting spin systems, free fermions, and free bosons, and then show that these rapid mixing results are stable under perturbations, covering weakly interacting qudits and perturbed non-hopping fermions. Further, we adapt the techniques from separable qudits to the fermionic setting and prove rapid mixing of the strongly-interacting regime of the Fermi-Hubbard model, for which we also explicitly evaluate the guaranteed parameter regimes. Our results constitute the first efficient mixing bounds for non-commuting qudit models and bosonic systems at arbitrary temperatures. Compared to prior spectral-gap-based results for fermions, we achieve exponentially faster mixing, further featuring explicit constants on the maximal allowed interaction strength. This not only improves the overall polynomial runtime for quantum Gibbs state preparation, but also enhances robustness against noise. Our analysis relies on oscillator norm techniques from mathematical physics, where we introduce tailored variants adapted to specific Lindbladians $\unicode{x2014}$ an innovation that we expect to significantly broaden the scope of these methods.

In this work, we develop new pulse designs and embedding strategies to improve the analog quantum subroutines of hybrid column generation (CG) algorithms based on neutral-atoms quantum computers (NAQCs). These strategies are designed to improve the quality and diversity of the samples generated. We apply these to an important combinatorial optimization (CO) problem in logistics, namely the fleet assignment. Depending on the instance tested, our quantum protocol has a performance that is either comparable or worse than the best classical method tested, both in terms of the number of iterations and final objective value. We identify the cause of these suboptimal solutions as a result of our quantum protocol often generating high-quality but degenerate samples. We address this limitation by introducing a greedy post-processing technique, Make\_Diff, which applies bit-wise modifications to degenerate samples in order to return a non-degenerate set. With this modification, our quantum protocol becomes competitive with an exact solver for the subproblem, all the while being resilient to state preparation and measurements (SPAM) errors. We also compare our CG scheme with a Gurobi solver and find that it performs better on over 50% of our synthetic instances and that, despite Gurobi having a more extensive runtime. These improvements and benchmarks herald the potential of deploying hybrid CG schemes on NISQ devices for industrially relevant CO problems.

We show that it is undecidable to determine whether the commuting operator value of a nonlocal game is strictly greater than 1/2. Specifically, there is a computable mapping from Turing machines to /boolean constraint system (BCS) nonlocal games in which the halting property of the machine is encoded as a decision problem for the commuting operator value of the game. As a corollary, there is a BCS game for which the value of the Navascués-Pironio-Acín (NPA) hierarchy does not attain the commuting operator value at any finite level.

Quantum entanglement remains a challenging concept to teach and visualise due to its microscopic and non-classical nature. We present innovative educational demonstration material consisting of electronic dice that simulate the properties of quantum entanglement through haptic interaction. The system uses displays, orientation sensors, and wireless communication to visualise key quantum mechanical principles such as superposition, measurement, and entanglement correlations. This analogy enables students to experience quantum phenomena through familiar objects, making abstract concepts more tangible. The dice support various educational scenarios, from basic entanglement demonstrations to more complex quantum key distribution experiments, and can be adapted for different educational levels from secondary school to undergraduate physics courses. Initial implementations demonstrate that the interactive nature of the Quantum Dice can help users develop an intuitive understanding of quantum mechanical principles. The low-cost, open source, and robust design makes Quantum Dice accessible to a wider range of educational institutions.

We present a new primitive for quantum algorithms that implements a discrete Hermite transform efficiently, in time that depends logarithmically in both the dimension and the inverse of the allowable error. This transform, which maps basis states to states whose amplitudes are proportional to the Hermite functions, can be interpreted as the Gaussian analogue of the Fourier transform. Our algorithm is based on a method to exponentially fast forward the evolution of the quantum harmonic oscillator, which significantly improves over prior art. We apply this Hermite transform to give examples of provable quantum query advantage in property testing and learning. In particular, we show how to efficiently test the property of being close to a low- degree in the Hermite basis when inputs are sampled from the Gaussian distribution, and how to solve a Gaussian analogue of the Goldreich-Levin learning task efficiently. We also comment on other potential uses of this transform to simulating time dynamics of quantum systems in the continuum.

The commutative depth model allows gates that commute with each other to be performed in parallel. We show how to compute Clifford operations in constant commutative depth more efficiently than was previously known. Bravyi, Maslov, and Nam [Phys. Rev. Lett. 129:230501, 2022] showed that every element of the Clifford group (on $n$ qubits) can be computed in commutative depth 23 and size $O(n^2)$. We show that the Prefix Sum problem can be computed in commutative depth 16 and size $O(n \log n)$, improving on the previous depth 18 and size $O(n^2)$ bounds. We also show that, for arbitrary Cliffords, the commutative depth bound can be reduced to 16. Finally, we show some lower bounds: that there exist Cliffords whose commutative depth is at least 4; and that there exist Cliffords for which any constant commutative depth circuit has size $\Omega(n^2)$.

We introduce a general corner transfer matrix renormalization group algorithm tailored to projected entangled-pair states on the triangular lattice. By integrating automatic differentiation, our approach enables direct variational energy minimization on this lattice geometry. In contrast to conventional approaches that map the triangular lattice onto a square lattice with diagonal next-nearest-neighbour interactions, our native formulation yields improved variational results at the same bond dimension. This improvement stems from a more faithful and physically informed representation of the entanglement structure in the tensor network and an increased number of variational parameters. We apply our method to the antiferromagnetic nearest-neighbour Heisenberg model on the triangular and kagome lattice, and benchmark our results against previous numerical studies.

A qubit, or quantum bit, is conventionally defined as "a physical system for storing information that is capable of existing in either of two quantum states or in a superposition of both". In this paper, we examine the simple question of whether two distinct levels, each consisting of multiply degenerate sub-states, could serve as a practical quantum bit. We explore this idea using a well-characterized atomic system of the kind employed in several quantum computing implementations. We approximate the atom as a two-level system without degeneracy lifting in the magnetic quantum number while using the angular momentum addition rules to select the desired state transition. We find that, in the continuous presence of the field, the atom still undergoes Rabi oscillations, which are suitable for quantum gate construction. In addition, we compute the average fidelity in quantum gate performance for a single degenerate atom and postulate the required form of two-atom interaction to construct a controlled Z gate.

Horn's problem is concerned with characterizing the eigenvalues $(a,b,c)$ of Hermitian matrices $(A,B,C)$ satisfying the constraint $A+B=C$ and forming the edges of a triangle in the space of Hermitian matrices. It has deep connections to tensor product invariants, Littlewood-Richardson coefficients, geometric invariant theory and the intersection theory of Schubert varieties. This paper concerns the tetrahedral Horn problem which aims to characterize the tuples of eigenvalues $(a,b,c,d,e,f)$ of Hermitian matrices $(A,B,C,D,E,F)$ forming the edges of a tetrahedron, and thus satisfying the constraints $A+B=C$, $B+D=F$, $D+C=E$ and $A+F=E$. Here we derive new inequalities satisfied by the Schur-polynomials of such eigenvalues and, using eigenvalue estimation techniques from quantum information theory, prove their satisfaction up to degree $k$ implies the existence of approximate solutions with error $O(\ln k / k)$. Moreover, the existence of these tetrahedra is related to the semiclassical asymptotics of the $6j$-symbols for the unitary group $U(n)$, which are maps between multiplicity spaces that encode the associativity relation for tensor products of irreducible representations. Using our techniques, we prove the asymptotics of norms of these $6j$-symbols are either inverse-polynomial or exponential depending on whether there exists such tetrahedra of Hermitian matrices.

In this paper we extend the applicability of Fox-Wright functions beyond mathematics, specifically in quantum physics. We focused our attention on a new application, on the connection between the Fox-Wright functions and the generalized coherent states formalism. We constructed the generalized coherent states in the Barut-Girardello manner, in which the Fox-Wright functions play the role of normalization functions, and we demonstrated that the Fox-Wright coherent states satisfy all general conditions imposed on the set of coherent states. In parallel, we examined the properties of both pure and mixed (thermal) Fox-Wright coherent states. All calculations were performed within the diagonal operators ordering technique (DOOT) using the Dirac's bra-ket formalism. Finally, we introduced some (specifically, integral) feedback elements that Fox-Wright coherent states induce in the theory of special functions, including a new integral representation of Fox-Wright functions.

The thermodynamic uncertainty relation quantifies a trade-off between the relative fluctuations of trajectory currents and the thermodynamic cost, indicating that the current precision is fundamentally constrained by entropy production. In classical bipartite systems, it has been shown that information flow between subsystems can enhance the current precision alongside thermodynamic dissipation. In this study, we investigate how information flow, local dissipation, and quantum effects jointly constrain current fluctuations within a subsystem of interacting quantum systems. Unlike classical bipartite systems, quantum subsystems can exhibit simultaneous state changes and maintain quantum coherence, which fundamentally alters the precision-dissipation trade-off. For this general setting, we derive a quantum thermokinetic uncertainty relation for interacting multipartite systems, establishing a thermodynamic trade-off between current fluctuations, information flow, local dissipation, and quantum effects. Our analysis shows that, in addition to local dissipation, both information exchange and quantum coherence play essential roles in suppressing current fluctuations. These results have important implications for the performance of quantum thermal machines, such as information-thermodynamic engines and quantum clocks. We validate our theoretical findings through numerical simulations on two representative models: an autonomous quantum Maxwell's demon and a quantum clock. These results extend uncertainty relations to multipartite open quantum systems and elucidate the functional role of information flow in fluctuation suppression.

We consider imaging of two partially coherent sources and derive the ultimate quantum limits for estimating the separation, location, relative intensity, and coherence factor. We show that super-resolution in the separation is achievable both in the presence of nuisance parameters as well as when some of the parameters are assumed known. Nuisance parameters restrict super-resolution to balanced sources, whereas for known parameters super-resolution persists over a broader range of relative intensities and is lost only for perfectly correlated sources, i.e., $\gamma=1$. The achievable precision is governed primarily by interference-induced photon statistics and depends strongly on the degree of coherence. In the sub-Rayleigh regime, the imaging problem reduces to an effective two-dimensional Hilbert space description, provided a consistent reference position is used, with all parameters encoded in a Bloch vector representation. Finally, indirect estimation schemes based on the purity of the image-plane state are generally suboptimal for all non-zero coherence and become valid only in the incoherent limit.

Noncommutativity of observables is a central feature of quantum physics. It plays a fundamental role in the formulation of the uncertainty principle for complementary variables and strongly affects the laws of thermodynamics for systems with noncommuting, that is, non-Abelian, conserved quantities. We here derive nonequilibrium generalizations of the second law of thermodynamics in the form of fluctuation relations, both for mechanically and thermally driven quantum systems. We identify a non-Abelian contribution to the energy and entropy balances, without which these relations would be violated. The latter term can be controlled to enhance both work extraction and nonequilibrium currents compared to what is obtained in commuting thermodynamics. These findings demonstrate that noncommutativity maybe a useful thermodynamic resource.

We designed a scheme for a neutral atom Rydberg blockade $C_Z$ gate based on the double sequence of adiabatic pulses applied symmetrically to both atoms and using counterdiabatic driving for Rydberg excitation. This provides a substantial reduction in the quantum gate operation time compared to previously proposed double adiabatic schemes, and makes our scheme competitive with modern time-optimal protocols for high-fidelity entangling gates with neutral atoms. Our approach creates a bridge between fully adiabatic and time-optimal gate schemes. The use of adiabatic passage reduces the sensitivity of gate fidelity to variations in laser intensity, while counterdiabatic driving provides short gate times. The intensity and phase profiles of the laser pulse acting on the atoms are described analytically depending only on the gate duration. We demonstrated the applicability of this scheme for single-photon and two-photon schemes of Rydberg excitation in rubidium and cesium atoms, and, for the first time, discussed the implementation of a $C_Z$ gate using three-photon excitation of rubidium atoms. In contrast to many modern $C_Z$ gate protocols, our scheme does not generate intrinsic single-qubit phase shifts, although they still appear in two-photon configuration. We also designed a numerically optimized amplitude-robust gate with an analytically defined phase profile of the laser pulse and compared its performance with the counteradiabatic gate scheme.

We study the two-dimensional $t$–$J$ model at finite temperature directly in the thermodynamic limit using purification represented by an infinite projected entangled-pair state (iPEPS). We reach temperatures down to $T/t=0.1$ and hole concentrations up to $1-n\simeq0.25$, and provide benchmark thermodynamic-limit results for the specific heat, uniform susceptibility, and charge compressibility. We identify a susceptibility maximum $T^\ast$ that tracks the buildup of short-range antiferromagnetism and a shallow compressibility enhancement upon cooling in the same doping window. To expose the underlying microscopic mechanism, we introduce dopant-conditioned multi-point correlators that quantify how holes reorganize nearby exchange: single holes weaken adjacent antiferromagnetic bonds, while nearest-neighbor hole pairs produce a cooperative response that reinforces antiferromagnetism on the parallel plaquette edge. Over the same parameter window, $d$-wave pairing correlations remain short-ranged. These results provide experiment-compatible thermodynamic-limit benchmarks and establish dopant-conditioned correlators as incisive probes of finite-temperature spin-texture reorganization in doped Mott insulators.

Secure key leasing (SKL) enables the holder of a secret key for a cryptographic function to temporarily lease the key using quantum information. Later, the recipient can produce a deletion certificate, which proves that they no longer have access to the secret key. The security guarantee ensures that even a malicious recipient cannot continue to evaluate the function, after producing a valid deletion certificate. Most prior work considers an adversarial recipient that obtains a single leased key, which is insufficient for many applications. In the more realistic collusion-resistant setting, security must hold even when polynomially many keys are leased (and subsequently deleted). However, achieving collusion-resistant SKL from standard assumptions remains poorly understood, especially for functionalities beyond decryption. We improve upon this situation by introducing new pathways for constructing collusion-resistant SKL. Our main contributions are as follows: - A generalization of quantum-secure collusion-resistant traitor tracing called multi-level traitor tracing (MLTT), and a compiler that transforms an MLTT scheme for a primitive X into a collusion-resistant SKL scheme for primitive X. - The first bounded collusion-resistant SKL scheme for PRFs, assuming LWE. - A compiler that upgrades any single-key secure SKL scheme for digital signatures into one with unbounded collusion-resistance, assuming OWFs. - A compiler that upgrades collusion-resistant SKL schemes with classical certificates to ones having verification-query resilience, assuming OWFs.

In this paper, we define and benchmark a hybrid quantum-classical machine learning pipeline by performing a binary classification task applied to a real-world financial use case. Specifically, we implement a Quantum Reservoir Computing (QRC) layer within a classical routine that includes data preprocessing and binary classification. The reservoir layer has been executed on QuEra's Aquila, a 256-qubit neutral atom simulator, using two different types of encoding: position and local detuning. In the former case, classical data are encoded into the relative distance between atoms; in the latter, into pulse amplitudes. The developed pipeline is applied to predict credit card defaults using a public dataset and a wide variety of traditional classifiers. The results are compared with a fully-classical pipeline including a Deep Neural Network (DNN) model. Additionally, the impact of hardware noise on classification performance is evaluated by comparing the results obtained using Aquila within the classification workflow with those obtained using a classical, noiseless emulation of the quantum system. The results indicate that the noiseless emulation achieves competitive performance with the fully-classical pipeline, while noise significantly degrades overall performance. Although the results for this specific use case are comparable to those of the classical benchmark, the flexibility and scalability of QRC highlight strong potential for a wide range of applications.

Conditional Value-at-Risk (CVaR) is a leading tail-risk measure in finance, central to both regulatory and portfolio optimization frameworks. Classical estimation of CVaR and its gradients relies on Monte Carlo simulation, incurring $O(1/\epsilon^2)$ sample complexity to achieve $\epsilon$-accuracy. In this work, we design and analyze a quantum subgradient oracle for CVaR minimization based on amplitude estimation. Via a tripartite proposition, we show that CVaR subgradients can be estimated with $O(1/\epsilon)$ quantum queries, even when the Value-at-Risk (VaR) threshold itself must be estimated. We further quantify the propagation of estimation error from the VaR stage to CVaR gradients and derive convergence rates of stochastic projected subgradient descent using this oracle. Our analysis establishes a near-quadratic improvement in query complexity over classical Monte Carlo. Numerical experiments with simulated quantum circuits confirm the theoretical rates and illustrate robustness to threshold estimation noise. This constitutes the first rigorous complexity analysis of quantum subgradient methods for tail-risk minimization.

In this paper, we investigate how to achieve strong optomechanical entanglement and mechanical squeezing in a membrane-embedded cavity optomechanical system incorporating a coherent feedback loop, where the membrane interacts with the cavity mode through both linear and quadratic optomechanical couplings. This hybrid optomechanical architecture offers a flexible tunability of intrinsic system parameters, thereby enabling controlled stiffening or softening of the mechanical mode through adjusting quadratic optomechanical coupling, as well as effective modulation of the cavity decay rate via feedback control. More importantly, the synergistic interplay effect allows for a strategic reconfiguration of the system's stability regime, which in turn permits the presence of significantly enhanced effective optomechanical coupling strengths before entering the unstable regime. Exploiting these unique features, we showcase that optomechanical entanglement can be substantially enhanced with positive coupling sign and suitable feedback parameters, while strong mechanical squeezing beyond the $3$dB limit is simultaneously achieved over a broad parameter range with negative coupling sign, reaching squeezing degree above $10$dB under optimized conditions. Our proposal, establishing an all-optical method for generating highly entangled or squeezed states in cavity optomechanical systems, opens up a new route to explore macroscopic quantum effects and to advance quantum information processing.

This thesis focuses on the Lie-theoretic foundations of controlled open quantum systems. We describe Markovian open quantum system evolutions by Lie semigroups, whose corresponding infinitesimal generators lie in a special type of convex cone - a Lie wedge. The Lie wedge associated to a given control system therefore consists of all generators of the quantum dynamical semigroup that are physically realisable as a result of the interplay between the coherent and incoherent processes the quantum system is subject to. For $n$-qubit open quantum systems, we provide a parametrisation of the largest physically relevant Lie algebra (the system algebra), in which these Lie wedges are contained: the Lindblad-Kossakowski Lie algebra. This parametrisation provides several useful benefits. First, it allows us to construct explicit forms of these system Lie wedges and their respective system Lie algebras. Second, we analyse which control scenarios yield Lie wedges that are closed under Baker-Campbell-Hausdorff (BCH) multiplication and therefore generate Markovian semigroups of time-independent quantum channels. Lie wedges of this form are called Lie semialgebras, and we completely solve this open problem by proving that Lie wedges specialise to this form only when the coherent controls have no effect on both the inherent drift Hamiltonian and the incoherent part of the dynamics. Finally, this parametrisation of the Lindblad-Kossakowski Lie algebra points to an intuitive separation between unital and non-unital dissipative dynamics, where the non-unital component of the dynamics is described by affine translation operations. These translation operators are then exploited to construct purely dissipative fixed-point engineering schemes to obtain either pure or mixed states as a system's unique fixed point.

Curved Boolean Logic (CBL) generalizes propositional logic by allowing local truth assignments that do not extend to a single global valuation, analogous to curvature in geometry. We give equivalent sheaf and exclusivity-graph semantics and a context-aware proof calculus that is conservative in the flat limit. We formalize CBL-SAT and basic complexity (NP-complete in general) and present operational operators (CBL-AC and CBL-CONS) that prune contradictions earlier on classical hardware. We model noise with iid, AR(1)-correlated, and adversarial bounded perturbations and provide permutation-based significance with Benjamini-Hochberg FDR control. A Colab-ready notebook (ancillary files) regenerates all figures and statistics. We position CBL relative to KCBS, CSW, and sheaf frameworks and outline links to SAT/CSP and robustness/adapter stability in large language models.

In this paper, for $\alpha\in(0,\infty)\setminus\{1\}$, $p>0$ and positive semidefinite matrices $A$ and $B$, we consider the quasi-extension $\mathcal{M}_{\alpha,p}(A,B):=\mathcal{M}_\alpha(A^p,B^p)^{1/p}$ of several $\alpha$-weighted geometric type matrix means $\mathcal{M}_\alpha(A,B)$ such as the $\alpha$-weighted geometric mean in Kubo–Ando's sense, the Rényi mean, etc. The log-majorization $\mathcal{M}_{\alpha,p}(A,B)\prec_{\log}\mathcal{N}_{\alpha,q}(A,B)$ is examined for pairs $(\mathcal{M},\mathcal{N})$ of those $\alpha$-weighted geometric type means. The joint concavity/convexity of the trace functions $\mathrm{Tr}\,\mathcal{M}_{\alpha,p}$ is also discussed based on theory of quantum divergences.

The semi-empirical Pariser-Parr-Pople (PPP) Hamiltonian is reviewed for its ability to provide a minimal model of the chemistry of conjugated $\pi$-electron systems, and its current applications and limitations are discussed. From its inception, the PPP Hamiltonian has helped in the development of new computational approaches in instances where compute is constrained due to its inherent approximations that allow for an efficient representation and calculation of many systems of chemical and technological interest. The crucial influence of electron correlation on the validity of these approximations is discussed, and we review how PPP model exact calculations have enabled a deeper understanding of conjugated polymer systems. More recent usage of the PPP Hamiltonian includes its application in high-throughput screening activities to the inverse design problem, which we illustrate here for two specific fields of technological interest: singlet fission and singlet-triplet inverted energy gap molecules. Finally, we conjecture how utilizing the PPP model in quantum computing applications could be mutually beneficial.

We present novel, exotic types of frame changes for the calculation of quantum evolution operators. We detail in particular the biframe, in which a physical system's evolution is seen in an equal mixture of two different standard frames at once. We prove that, in the biframe, convergence of all series expansions of the solution is quadratically faster than in `conventional' frames. That is, if in laboratory frame or after a standard frame change the error at order $n$ of some perturbative series expansion of the evolution operator is on the order of $\epsilon^n$, $0<\epsilon<1$, for a computational cost $C(n)$ then it is on the order of $\epsilon^{2n+1}$ in the biframe for the same computational cost. We demonstrate that biframe is one of an infinite family of novel frames, some of which lead to higher accelerations but require more computations to set up initially, leading to a trade-off between acceleration and computational burden.