Papers

Slater-type orbitals (STOs) provide the physically correct description of atomic wavefunctions but have been largely replaced by Gaussian-type orbitals in computational chemistry due to the lack of closed-form multi-center integrals. We present a systematic study of amplitude encoding of STOs on quantum computers using matrix product states (MPS). For one-dimensional orbital functions of the form $p_d(x) e^{-\zeta x}$, we derive analytical MPS constructions with constant bond dimension $\chi = d + 1$, requiring $O(n)$ classical and quantum resources for $n$-qubit registers with no grid sampling. We demonstrate a complete one-electron integral pipeline – overlap, kinetic energy, and nuclear attraction – in one dimension, validating the overlap and kinetic energy on IBM Heron processors at 5~qubits with 0.67% hardware-induced error using Zero-Noise Extrapolation. In three dimensions, we compute multi-center overlap integrals between 1s and 2s orbitals in Cartesian coordinates with 0.02% discretization error at 18~qubits. A systematic entanglement analysis reveals that the MPS bond dimension of three-dimensional STOs in Cartesian coordinates saturates with increasing grid resolution – reaching $\sim$138 for the hydrogen 1s orbital at 12~qubits per coordinate – establishing bounded encoding complexity rather than the exponential scaling initially expected. The SVD truncation threshold provides a practical resource parameter, reducing the bond dimension to 39 at threshold $10^{-6}$ with negligible accuracy loss. These results map the entanglement landscape for amplitude encoding of atomic orbitals and establish MPS-based state preparation as a viable path toward exact STO basis sets on quantum computers.

Variational quantum algorithms (VQAs) constitute a prominent paradigm for exploring the capabilities of near-term quantum computers. As the effectiveness of VQAs depends heavily on the design of variational quantum circuits, Quantum Architecture Search (QAS) has emerged as a critical research area to automate the discovery of high-performing circuit structures. This paper reviews key advancements in current research on QAS, including its core concepts, representative methodologies, applications, and emerging trends. The content is structured to ensure broad accessibility for a diverse audience of researchers while preserving the core principles of complex methodologies. In addition, we discuss remaining challenges and suggest potential research directions to offer perspectives on future exploration in this rapidly evolving field.

We take the non-relativistic limit $c\to\infty$ of the free Klein-Gordon field on static spacetimes at three levels: one-particle resolvents, quasi-free states and the time-zero net. After subtraction of the rest energy, the one-particle Hamiltonian is an explicit function of a Schrödinger-type operator whose potential on the Schwarzschild exterior is exactly Newtonian. On regular static stars it converges to the Newtonian Schrödinger operator in norm-resolvent sense at rate $c^{-2}$, with convergence of eigenvalues and an explicit first post-Newtonian correction. On the Schwarzschild exterior the Boulware one-particle spectrum has no eigenvalues for any $c$; the convergence is strong but not in norm, the limit selects the Friedrichs realisation of the gravitational hydrogen atom, and its bound states emerge by spectral concentration. The same holds on the Reissner-Nordström exterior. In all cases the rescaled two-point functions converge to those of the Schrödinger-Fock vacuum. The hydrogenic states are limits of resonances: in each partial wave there is exactly one near each hydrogenic level, its real part carries the first post-Newtonian correction, and its width, proportional to $c^{-(4l+3)}$, is the one found for gravitational atoms by matched asymptotics. At the level of nets the time-zero Weyl algebra is the same for every $c$, and the vacuum and the dynamics converge on it, yet for smooth metrics the algebra of each bounded region with smooth boundary is a type III$_1$ factor at finite $c$ and a type I factor with a pure product vacuum in the limit. What collapses is the entanglement of the vacuum; thermal states in flat space and on stars survive the limit. With positivity of the energy imposed modulo the central charge, the axioms of Galilean nets hold in the limit for every static star and for Schwarzschild, and the vacuum is not separating.

Quantum computing has advanced rapidly in recent years and has shown advantages in a variety of domains. In this paper, we investigate its potential for discrete simulation optimization in the fixed-confidence setting, a fundamental problem in the simulation literature. We first introduce a quantum simulation oracle that prepares a coherent superposition over all candidate solutions and provides the foundation for quantum algorithm design. Based on this oracle, we develop the first Grover-search-based quantum algorithm for discrete simulation optimization, called SOGAS. In particular, SOGAS uses a binary-search framework to progressively eliminate suboptimal solutions while carefully controlling the error probability, and eventually identifies a set of near-optimal solutions. We prove that SOGAS returns a near-optimal solution with probability at least the prescribed confidence level and achieves a quadratic speedup in the dependence of query complexity on the number of candidate solutions. Numerical experiments further show that SOGAS substantially outperforms classical benchmarks and provide empirical evidence for quantum advantage in discrete simulation optimization.

We ask in which states, and for which local algebras, Galilean quantum fields have the Reeh-Schlieder property. The nets are generated by time-zero canonical fields on spatial regions and by the dynamics. The Bargmann mass over the charge of the field is a number operator for the time-zero fields, bounded from below by positivity of the energy and boost covariance, and Chaiken's theorem gives Galilean Fock rigidity: these fields form a direct sum of Fock representations, and the time-zero annihilation fields annihilate every translation-invariant vector. If the vacuum is the only vector invariant under spatial translations (not implied by the usual uniqueness axiom), the vacuum sector of the observable net is one-dimensional. No vector of finite mass is cyclic or separating for an algebra of a spatial region at fixed time. In the vacuum of Bose gases with bounded or Coulomb-type pair potentials (with Buchholz's renormalised dynamics if not H-stable), the fields of any region over any time interval generate all bounded operators. By contrast, a KMS state is cyclic and separating for the algebra of every region $B\times I$ with temporal extent whenever the spatial algebras at all times generate the global algebra, as for free gases. For the free Schrödinger field in the vacuum, the thermal states of Bose and Fermi gases and the Fermi sea, fixed-time field algebras are type I factors, for which thermal vectors and the Fermi sea are separating but not cyclic, and every field algebra with temporal extent is the global one: type I in pure states, type III$_1$ in thermal states, with the grand-canonical dynamics as modular group. Galilean vacua are thus never separating for local algebras. For the free field the type of the algebras of regions with temporal extent depends on the state, and what is specifically relativistic is the locality of type III$_1$.

We ask which kinematical groups allow local algebras of canonical quantum fields to commute at unequal times. The Galilei group acts transitively on pairs of non-simultaneous events with a given time separation, so a Galilean-invariant commutation relation between sharp-time algebras at unequal times also holds at coincident positions; at arbitrarily short separations it contradicts the canonical commutation relations, with no spectral assumption. Under unitary Bargmann covariance and positivity of the energy modulo the central mass, the vacuum is annihilated by the annihilation fields, hence not separating for local algebras, and the vacuum two-point function of a canonical field factorises into the free Schrödinger propagator and the characteristic function of an internal-energy distribution. Sharp-time algebras at unequal times then commute only at a closed null set of time separations, bounded below by the Mandelstam-Tamm and Margolus-Levitin times and empty for sharp or generic internal energy; any finite set of separations occurs. Algebras of open spacetime regions containing time-smeared fields never commute. Positivity cannot be dropped: without it, commutation can hold at all separations beyond any given one. Among spatially isotropic homogeneous spacetimes with absolute time, only the galilean ones are transitive at fixed time separation, up to discrete exceptions in the two oscillating cases, realised by a harmonic trap in the Newton-Hooke one. Non-commutation transfers from the vacuum to every representation of a simple C*-algebra on which the dynamics acts by automorphisms, including free Bose and Fermi gases at all temperatures and the Galilei-covariant cutoff dynamics of interacting fermions of Narnhofer and Thirring; without such a vacuum representation it can fail even in thermal equilibrium.

Early fault-tolerant quantum computers are expected to support reliable but depth-limited quantum circuits, while classical computational resources remain available. These conditions have motivated hybrid coherent algorithms which use quantum simulation as a central algorithmic primitive. This trend calls for quantum-simulation methods that operate with shallow circuits and admit systematic improvements in gate-complexity scaling. Here, we introduce qSHIFT, an adaptive sampling protocol for simulating a Hamiltonian $H=\sum_{i=1}^{L}h_iH_i$. qSHIFT achieves gate complexity $\mathcal{O}_r\left((\lambda t)^{1+1/r}/\varepsilon^{1/r}\right)$, where $r$ is an algorithmic parameter, $\lambda=\sum_i |h_i|$ and $\varepsilon$ denotes the target precision. Relative to qDRIFT, increasing $r$ systematically improves the gate complexity for a given target precision without incurring extra quantum cost. Unlike Trotterization, the number of sampled gates is nominally independent of $L$. qSHIFT retains the elementary gate set of qDRIFT and, unlike qSWIFT, requires neither ancillary qubits nor controlled operations. The improved gate complexity scaling is obtained at the cost of a classical calculation involving $L^r$ coefficients at each adaptive sampling round.

Quantum simulations of scalar quantum field theories (QFT) provide important benchmarks for demonstrating quantum advantage. We revisit digitization in the occupation basis, which is typically hindered by unfavorable circuit depth scaling. We present an approach that achieves exponential reductions in circuit depth and significantly mitigates Trotter errors by diagonalizing field operators prior to their decomposition into Pauli strings. Focusing on a scalar QFT in 2+1 dimensions, we show that this method substantially reduces circuit depth and CNOT gate counts for time evolution. Using the Lorentzian energy-energy correlator as a benchmark observable, we find parameter regimes in which occupation-basis digitization converges more rapidly with respect to local truncation than the amplitude-basis approach of Jordan, Lee, and Preskill. These results provide both algorithmic advances and phenomenological benchmarks for studies of light-ray observables on near-term quantum devices.

Loading high dimensional distributions is an important task for utilizing quantum computers on applications ranging from machine learning to finance. The high dimensionality leads to a curse of dimensionality, representing a d-dimensional distribution with k resolution requires dk qubits and an unstructured parameterized circuit would express a unitary in an exponential operator space in the number of qubits, leading to vanishing gradients and poor convergence guarantees even at high depth. Vine copula decompositions are widely used to represent high dimensional distributions classically, showing high quality approximation in many important applications, such as financial modeling. We present Qvine, a vine structured ansatz for quantum circuits, that mirrors the vine decomposition to construct scalable quantum circuits with efficient trainability while achieving similarly high quality approximation for amplitude encoding distributions. For regular vines (R-vines), we show that the circuit depth scales at most quadratic in the dimension of the distribution, while for D-vines, as well as many practical R-vines, the circuit depth scales linear in the dimension. For 3-dimensional and 4-dimensional Gaussians and empirical joint stock price return distributions for selected stocks, our experiments show Qvines achieve high quality loading.

Quantum computing remains in the Noisy Intermediate-Scale Quantum (NISQ) era, with performance constrained by noise. Addressing this limitation requires hardware-facing capabilities beyond gate sequences: mid-circuit measurement and classical feedback for quantum error correction (QEC), precise timing for dynamical decoupling (DD), and pulse-level waveform access for calibration. OpenQASM 3 exposes these capabilities through a hardware-level programming interface. Despite rapid progress in large language models (LLMs) for code generation, datasets targeting these advanced features remain lacking. We introduce QASM-Eval, the first comprehensive dataset to train and evaluate LLMs on OpenQASM 3, targeting completion of hardware-facing constructs within a supplied program context. QASM-Eval comprises an expert-curated test set of 1,200 tasks and a training set of over 4,000 tasks, covering classical logic, timing scheduling, pulse control, and complex tasks inspired by quantum-control workflows. An extended verifier automatically checks syntax, quantum measurement distributions, and program timelines. Our evaluation identifies substantial headroom for OpenQASM 3 code generation and significant gains from targeted fine-tuning. Fine-tuned Llama-3-8B outperforms zero-shot GPT-5.6-Terra, while fine-tuned Llama-3-70B achieves 61.17% overall pass@1 and approaches few-shot-augmented GPT-5.6-Terra. QASM-Eval provides a benchmark and training resource for specification-guided code generation over the hardware-facing constructs of OpenQASM 3, supporting the development of LLM assistants for quantum programming. Data and code: https://github.com/fuzhenxiao/QASM-Eval

In this study, we present a quantum-statistical analysis of H$_2$ and LiH diatomic molecules within the Frost–Musulin potential framework. By combining the analytical bound-state approach to the radial Schrödinger problem with the near-equilibrium Pekeris representation, we obtain a validated rotation-vibration spectrum that reproduces a physically consistent ordering of energy levels. These bound states are subsequently combined with standard translational and rotational ideal gas contributions to construct the total partition function and the corresponding thermodynamic observables of the ground state. The resulting formulation captures the Gibbs free energy deviation function for both molecules with high quantitative accuracy and provides chemically plausible trends for heat capacity and enthalpy increase over a wide temperature range. At the same time, residual errors become increasingly pronounced in derivative-sensitive quantities, particularly at high temperatures; this indicates that the dominant limitations now stem not from the local bound-state spectrum itself, but from the neglect of inelastic rotational, continuity contributions and dynamics close to dissociation. Consequently, the present results define the potential model as a compact and analytically tractable representation of the bound region, recovering a significant portion of the observed thermochemistry whilst also delineating the regime where more comprehensive molecular statistical mechanics is required.

During a QEC cycle, quantum error decoding stands on the critical path. To enable fault tolerance on millions of qubits in real time, scalable decoding is necessary, which motivates this paper. Existing decoding algorithms (decoders), such as clustering, matching, belief propagation (BP), and neural networks, suffer from one or more of inaccuracy, costliness, and incompatibility, upon a broad set of quantum error correction codes, such as surface code and bivariate bicycle code. Therefore, there exists a gap between existing decoders and an ideal decoder that is accurate, fast, general, and scalable simultaneously. To move closer to the goal above, this paper contributes in three aspects, including decoder algorithm, decoder architecture, and decoding simulator. First, we propose Lottery BP, a lightweight decoder that introduces guided randomness to break the symmetric deadlock caused by quantum degeneracy during decoding. Lottery BP improves the decoding accuracy over BP by up to 6 orders. Second, we design a PolyQec architecture that implements Lottery BP as a local decoder and ordered statistics decoding (OSD) as a global decoder, exemplifying a hierarchical decoder architecture. PolyQec is configurable for surface code and X/Z check. Since Lottery BP boosts the local decoding accuracy, PolyQec invokes the costly global OSD decoder less frequently over BP+OSD to enhance the scalability, e.g., up to 4 orders of magnitude less for surface codes. Third, we develop Syndrilla, a modular PyTorch-based decoding simulator that enables fair, extensible decoder evaluation with unified accuracy and performance metrics. On GPUs, Syndrilla runs 1 order of magnitude faster than CUDAQX.

Antenna miniaturization remains a critical technological challenge across frequency scales - from microwave RF links in phones and wearables to VLF for underwater-to-air communications and ionospheric probing. At deeply subwavelength scales conventional antennas require complex and lossy matching circuits due to absent intrinsic material resonances, motivating resonant electrically small emitters (ESEs) like mechanical resonators and quantum emitters. Here, we extend the theory of electrically small antennas (ESAs) to this broader ESE class, deriving the fundamental efficiency limit for a unit volume emitter at given frequency and bandwidth. Our figure of merit (FOM) - quantifying proximity to this limit - enables direct comparison across ESE types, frequencies, bandwidths and scales. We demonstrate its utility using public data from ELF and VLF Navy facilities alongside two mechanical ESEs reported in literature. The measurements reveal that mechanical antennas operate near theoretical FOM limit, questioning claims of possible further orders-of-magnitude gains. A naturally resonant emitter is still subject to the Chu-Harrington limit (CHL) under its standard assumptions. Indeed, we derive novel CHL-dictated constraints on atomic ESE properties: lower bound on excited-state lifetime and an upper bound on transition dipole moment.

Transportation systems such as urban logistics, vehicle routing, and infrastructure planning require solving large-scale combinatorial optimization problems under complex constraints. Problems such as the vehicle routing problem (VRP), traveling salesman problem (TSP), and facility location problem (FLP) involve large discrete search spaces and the need to generate multiple feasible solutions in real time. In this work, we develop a hardware-grounded hybrid quantum optimization framework that uses Approximate Quantum Compilation (AQC) to compress early segments of digitized adiabatic evolution into shallow circuits. The compressed prefix is combined with variational layers, enabling a systematic study of how initialization, circuit depth, and expressivity interact on near-term quantum hardware. All experiments are performed on an IBM gate-based quantum computer, and circuits are evaluated as stochastic generators of candidate transportation plans. Results show that moderate prefix compression reduces two-qubit gate depth while maintaining or improving feasible solution discovery, particularly for routing problems. These benefits depend on compatibility between the compressed prefix and the variational ansatz: while standard QAOA effectively leverages AQC initialization, linear-chain QAOA shows limited improvement. Overall, this work demonstrates that hybrid AQC-QAOA methods provide a practical pathway for hardware-efficient quantum optimization, positioning quantum algorithms as candidate generators within transportation decision-making workflows.

One of the main difficulties in preparing many-body ground states is achieving the target state through simple counterdiabatic controls. For critical systems crossing a transition to a topological phase, this task becomes even more challenging due to the closing of the gaps in multiple symmetry sectors. This is the case of the Kitaev chain, whose transition between the trivial and topological phases involves states belonging to different symmetry sectors. In this work, we apply the recently introduced minimal action shortcut to adiabaticity (MA-STA) to a Kitaev chain and propose a multi-step strategy to obtain the optimal control protocol to drive the system across its different phases. Our results show that high fidelities can be achieved through the adapted MA-STA at time scales much shorter than those of linear ramp protocols. We also compare the performance of both controls in suppressing work fluctuations. These findings may guide the design of STA protocols in many-body systems where competing energy scales and symmetries shape the global dynamics.

We consider a many-body Hilbert space with a fixed global charge and show that the typical entanglement entropy of a subsystem, at the leading and subleading order in the thermodynamic limit, can be expressed in terms of a single quantity which represents the local thermal entropy at fixed charge density. We find a general formula which applies both to abelian U(1) symmetry and non-abelian SU(2) symmetry, including the case of a local Hilbert space which transforms under a general reducible representation of the symmetry group. We illustrate the general formula with model systems and discuss the relevance of the results as a probe of quantum chaos for physical Hamiltonians.

We study a minimal model of collective light emission from an incoherently driven ensemble of atoms where incoherent drive is applied to only a subset of the atoms and show that both the linewidth and the photon statistics can be controlled within a single framework. In this setting, collective dissipation induces correlations between the pumped and unpumped parts of the system, leading to interference between their emission contributions. By introducing a relative phase between these contributions and tuning the pump rate, we demonstrate that the properties of the emitted light can be varied over a broad range. In particular, the linewidth can be made either independent of system size or scale extensively with it, while the photon statistics can be tuned from antibunched or quantum to bunched. We further show that the role of the relative phase in controlling the interference can alternatively be played by the coherent interaction. By tuning the interaction strength together with the pump rate, one can access the same regimes as in the dissipation-only model. In addition, coherent interactions stabilize regimes of coherent emission with narrow linewidth, reminiscent of superradiant lasing. Our results illustrate how interference in partially driven collective systems provides a flexible mechanism for tailoring both spectral and statistical properties of light.

Quantum Machine Learning (QML) has recently emerged as a highly promising research frontier. Within this domain, Quantum Neural Networks (QNNs),characterized by Variational Quantum Circuits (VQCs) at their core and featuring layers of quantum gates optimized by classical algorithms, have garnered significant attention. However, a rigorous and exhaustive evaluation of their practical performance remains largely incomplete. In this study, we conduct a comprehensive comparative analysis of three prominent hybrid classical-quantum architectures: Quantum Convolutional Neural Networks (QCNN), Quantum Recurrent Neural Networks (QRNN), and Quantum Vision Transformers (QViT), focusing on the critical dimensions of generalization, accuracy, and robustness. Our findings provide novel insights that address previous evaluative gaps. Notably, while these models exhibit exceptional performance on low-feature datasets such as MNIST, their learning efficacy degrades significantly when transitioned to high-feature datasets. Furthermore, convolutional-based models like QCNN appear less effective on high-dimensional data than other machine learning architectures. Additionally, while all models are susceptible to adversarial noise, traditional architectures, such as recurrent and convolutional networks, demonstrate superior resilience. Conversely, in the presence of quantum noise, the transformer-based architecture proves its strength by maintaining high robustness against measurement noise, channel noise, and finite-shot effects, whereas other architectures suffer marked performance declines. These results provide a granular perspective on the current state of the field and underscore the critical importance of tailoring model selection to the constraints of contemporary Noisy Intermediate-Scale Quantum (NISQ) environments.

Tricationic protactinium monofluoride ($^{229}$PaF$^{3+}$) has been proposed as a candidate for probing physics beyond the Standard Model of particle physics. Since studies with $^{229}$PaF$^{3+}$ require significant experimental advances, we exploit the stable, valence-isoelectronic dicationic cerium monofluoride (CeF$^{2+}$) as a surrogate. Gas-phase fluorinated-cerium molecular ions are formed and identified using the Off-Line Ion Source and TITAN mass measurement facilities at TRIUMF. Quantum chemical calculations are performed on the electronic structure of CeF$^{2+}$, revealing a parallel to that of $^{229}$PaF$^{3+}$. Moreover, these calculations provide estimates on the sensitivity of CeF$^{2+}$ itself to various $\mathcal{P,T}$-odd properties. A brief discourse on the specifics of the quantum control of CeF$^{2+}$ is presented which anticipates future searches for symmetry violations.

Can quantum computers effectively simulate the propagation and scattering of electromagnetic waves in a classical plasma? This chapter introduces some of the basic concepts in mathematics and physics essential to answering that question. The numerical simulations of Maxwell equations for wave propagation in dielectrics are constrained by technological limitations of the present-day computers. In contrast, there has been ample fanfare around quantum computers and their potential to far exceed the performance of traditional computers. Whether the enhanced capabilities of a quantum computer can be put to use for simulating topics in classical physics is a source of intrigue and curiosity.

We present a variational algorithm for fault tolerant quantum computing to solve a system of linear equations which directly maximises the parameters of the target fidelity. This so-called measurement test algorithm can be applied to any computational task with a solution that is represented as eigenvector of a self-adjoint matrix. The solution is prepared as state of a register in the quantum computer by a von Neumann measurement of a corresponding observable, which is implemented using the phase estimation algorithm. The probability to project the system thus into the unknown target state, which equals the target fidelity, is measured in terms of relative frequencies and iteratively optimised to read out the target state. The new algorithm overcomes three issues of previous variational quantum algorithms: i) It does not rely on a decomposition in terms of Pauli strings and therefore can compute eigenvectors of dense matrices. ii) The accuracy is not limited by the condition number $\kappa$ of the matrix, provided a logarithmic number ($O(\log\kappa)$) of qubits is used to encode the eigenvalues and iii) the target fidelity $F_T = 1-\epsilon$ can be reached with an accuracy $\epsilon$ that scales with $1/N$ for $N$ measurements per iteration. We demonstrate this by numerical simulations for dense random real-valued $16\times 16$ matrices with non-vanishing determinant.

Zero-field (ZF) nuclear magnetic resonance (NMR) spectroscopy probes scalar J-couplings between nuclei while dispensing with large homogeneous magnetic fields, enabling low-cost and geometrically flexible detection, including through conductive enclosures. Despite these advantages, its broader use for chemical analysis has been limited by sensitivity and by the difficulty of predicting the dense spectral multiplets that arise at zero field. Here we demonstrate natural-abundance (1.1%) 13C ZF spectroscopy on off-the-shelf liquids using a compact commercial 87Rb magnetometer for the first time, without hyperpolarization or special sample preparation. Instrumental advances yield improved sensitivity, <250-mHz linewidths and >week-long stability, enabling isotopomer-resolved fingerprint spectra across a 13-molecule library, including the ability to discern rare (0.0121%) doubly 13C-labelled species. In parallel, we demonstrate vibrationally corrected density-functional theory (DFT) based prediction of ZF NMR spectra for chemically diverse molecules with few-hertz accuracy. Comparing experiment with these calculations renders residual deviations as chemically informative, reporting on hydrogen bonding, hydration and ion pairing at high ionic strength. Together, these results contribute towards DFT-assisted ZF NMR as a general platform for field-constraint-free molecular identification and for extracting transient solution-state structure from responsive J-coupling observables.

Approximate combinatorial optimization is a promising use case for quantum computers. The quantum optimization algorithms often employ a fixed ansatz that evolves an unbiased initial state towards states with better values of the optimand, then samples the states to determine an approximately optimal solution. However, promising alternative approaches have considered “warm-start" and sampling-based methods that instead begin from the best known solution, which can be directly optimized with the quantum computer and updated as new information becomes available, potentially outperforming the fixed ansätze. Here we use these ideas to design a nonvariational quantum algorithm for combinatorial optimization. At each step the algorithm begins with a state superposed around the best known solution, then drives it to lower energy using quantum imaginary time evolution. These nonvariational, initial-state-dependent circuits are determined using analytic equations that are evaluated using only a conventional computer. After implementing the circuits, the state is sampled, potentially obtaining a new best-known solution to use as the initial state at the next iteration. Using simulations of the algorithm solving MaxCut on 3-regular graphs with 30 or fewer vertices and a shot budget of 100 total shots, the approach obtains median solutions within 95% of the global optimum and finds optimal solutions in 11% or more of cases, significantly outperforming random and simplified classical search procedures. We discuss several future directions.

Broad claims about whether adaptivity helps in quantum state tomography can be misleading unless the state family, measurement architecture, and error metric are specified carefully. We study a restricted but physically important regime: single-copy quantum state tomography under local Pauli basis measurements, where the allowed measurement settings are tensor-product measurement operators built from local single-qubit Pauli operators, and performance is measured in trace distance with high probability in a minimax sense over a known structured family. We construct an explicit discrete prefix/tree family of states for which adaptive measurement selection achieves polynomial copy complexity, while every non-adaptive design requires exponentially many copies in the worst case. The adaptive upper bound comes from stagewise prefix recovery using hierarchical breadcrumb information revealed by partial prefix matches. The non-adaptive lower bound is based on a rare-prefix mechanism: every fixed design under-samples some deep prefix subset, and outside that subset the competing hypotheses induce identical one-shot laws, so only an exponentially small fraction of the measurement budget contributes to the KL divergence between the full data distributions. The result isolates a concrete regime in which adaptivity provably changes the sample-complexity scaling under the experimentally common local Pauli measurement architecture.

Variational Quantum Algorithms, including the Quantum Approximate Optimization Algorithm (QAOA), have shown promise in solving optimization problems but rely on costly variational loops that can themselves be hard optimization problems. Many methods have been proposed to mitigate this variational cost, with one of the most common being parameter transfer and concentration where variational parameters for one problem instance or for an average over problem instances can be used as a good set of parameters for another instance. Methods exist for reweighting these parameters based off graph degree and edge weights, but there has been little work on how to do this reweighting to handle higher locality problems where the graph structure turns into a hypergraph structure. In this paper, we analytically derive parameter reweighting rules to transfer parameters between different locality hypergraphs, resulting in a reweighting for the mixing terms in the Hamiltonian which have previously not been considered. These analytics rely on three cycle-free and low-circuit-depth assumptions, but numerics indicate that the results can be used even when these assumptions are not satisfied. The numerics obtain high quality results across a diverse set of hypergraphs with locality less than or equal to five, improving on previous relations that do not reweight the mixing terms.

We unveil that non-Abelian multigap band topology characterized by nontrivial Euler class invariants induces observable magnetononlinear Hall transport phenomena. We demonstrate these effects in a highly-tunable class of recently synthesized two-dimensional kagome N-heterocyclic carbene (NHC) metal-organic frameworks. We showcase the controllability of the nonlinear effect upon applying external voltage, changing temperature, and chemical substitutions that preserve the bulk topology and associated edge states. Our findings therefore reveal an uncharted presence of Euler class topology in metal-organic materials that can be experimentally deduced through measurable magnetotransport.

The conserved probability current of the Schrodinger field admits a dimension-dependent gauge representation that provides a convenient setting for comparing hydrodynamic, topological and infrared structures. We use this representation to develop a unified treatment of several deformations of the Madelung momentum. BF couplings incorporate electromagnetic interactions, Berry and spin connections, projected non-abelian adiabatic data, and intrinsic phase holonomy within the same framework. In $(2+1)$ dimensions, the Chern-Simons deformation can be reduced to a nonlocal functional of the wavefunction. Its Coulomb-gauge form separates into a phase-sensitive geometric contribution and a density-dependent dynamical contribution; we show explicitly how this separation changes under a general gauge transformation and recover the topological braiding phase in the well-separated adiabatic regime. For systems with a spatial boundary, we derive the equal-time symplectic structure, the associated surface charges, and their boundary algebra. Finally, after a nonlinear interaction produces the Bogoliubov acoustic branch, the radiative memory can be expressed in the dual two-form variables. Its zero-average component is generated by a residual large gauge transformation, whereas the monopole component remains independent global data. This provides a gauge-theoretic description of the memory/asymptotic-symmetry sector of the acoustic infrared structure.

Quantum noise is a central challenge in quantum computing across many applications. Extensive work has examined how qubits couple to their environment, leading to decoherence and irreversible relaxation. This work studies a continuous coherent noise model for quantum circuits and compares it with a discrete Pauli model. The focus is on small, coherent gate errors that accumulate across circuit depth. These errors are modeled as random rotations on the Bloch sphere using a von Mises-Fisher distribution. In the small-angle limit, the model reduces to an isotropic Gaussian distribution. We test the model on quantum error-correction circuits based on the [[5,1,3]] and [[7,1,3]] codes. A variant of Grover's search circuit with different qubit counts is also examined. To enable fair comparison, we introduce a model-independent matching scheme. Pauli and continuous noise channels are aligned using the binary entropy at readout. This isolates the effect of noise structure at fixed uncertainty. An approximate analytical method for the propagation of coherent errors is also developed. The method tracks error distributions both on Clifford and non-Clifford circuits without full Monte Carlo sampling. It reduces simulation cost while preserving accuracy for circuit-level error estimates. The approximation is validated against brute-force simulations, identifying its regime of validity with Clifford and non-Clifford circuits under error correction. Our results show that continuous coherent noise and Pauli noise lead to comparable logical-error trends in the stabilizer-code circuits studied here. This behavior is consistent with syndrome extraction projecting a general single-qubit error onto Pauli-error subspaces before recovery. They also show where simplified propagation models work well and where their accuracy is reduced.

We study a quantum mechanical system whose spectrum coincides with that of bilinear operators of the Sachdev-Ye-Kitaev model. The standard positivity-based quantum mechanical bootstrap is degenerate with respect to the boundary data: it does not distinguish the boundary conditions that select the SYK spectrum, and hence is insufficient to determine the eigenvalues. Instead, by considering fractional powers of operators, we obtain constraint equations that determine the spectrum without imposing positivity. The resulting roots converge to exact eigenvalues as the truncation order increases. We call this the direct bootstrap.

Topological defects play a fundamental role in the investigation of symmetries in quantum field theories. For conformal field theories in two space-time dimensions, it is possible to construct these defects using lattice models allowing ab-initio analytical and numerical computations of their characteristics. In this work, topological defects are investigated in non-unitary conformal field theories using appropriate variations of the restricted solid-on-solid models. The relevant impurity models and the corresponding defect operators are constructed for the lattice system. Numerical computations are performed for the energy spectrum, eigenvalues of the defect operators as well as thermodynamic characteristics and compared with analytical predictions. Finally, renormalization group flows between the different fixed points are analyzed using numerical methods.