Papers

Spatial and temporal correlations in quantum noise challenge the local Markovian models commonly used in quantum information processing. We develop a unified operational framework for quantifying temporal, spatial, and total spatiotemporal correlations in general quantum processes. Using process tensors, we define these quantities through optimal distinguishability from Markovian, spatially local, and fully uncorrelated processes. Optimization over admissible probing combs ensures monotonicity under every superprocess that preserves the corresponding free set, while Choi-state functionals and restricted probes provide accessible lower bounds. We establish hierarchy and interpolation relations among the correlation measures and derive dimension-dependent upper bounds on temporal correlations transmitted by quantum memories, with tighter bounds for classical memory, together with universal ceilings imposed by the system dimension. These bounds turn certified lower estimates into witnesses of minimum memory dimension, nonclassicality under a memory-dimension constraint, and inconsistencies in the assumed process model. We illustrate the results with effective superconducting-qubit models featuring \(ZZ\) and \(XY\) interactions, exhibiting saturation of classical-memory, quantum-memory, and system-dimension ceilings. These results pave the way toward practical approaches to characterizing and addressing spatiotemporally correlated errors in quantum devices.

We study the Quantum Approximate Optimization Algorithm with a Grover mixer and independently sampled cost and mixing angles. Under a lattice condition on the cost values carried by the initial state, we prove a depth-independent lower bound for the variance of the loss at every depth, together with the same bound for the derivative with respect to the final mixing angle. The estimate is instance-dependent and, for fixed locality, is inverse polynomial in the number of qubits for integer-valued local objective functions with uniformly bounded local terms, in particular for MaxCut. We also establish Grover-type reachability bounds showing that the depth required to approximate a prescribed carried eigenspace is bounded below by a constant multiple of the inverse square root of its initial probability.

Motivated by the Planckian thermalization rate $\Gamma \sim T$ observed in the two-body interacting SYK model, we study thermalization in the $q/2$-body case. Previous studies of such systems have established the notion of instantaneous thermalization to leading order in $1/q$. It was conjectured that the thermalization may still be Planckian but with a divergent rate $\Gamma \sim T q$, explaining the “instantaneous” part. For an analytically and numerically tractable system, we calculate the effective temperatures after a quench at time $t = 0$ and indeed find a Planckian rate, albeit with the unexpected decaying behavior $\Gamma \sim T q^{-1} $. This is contrasted with the behavior of the causal Green's function $\mathcal{G}(t_1, t_2)$, which instantly acquires a thermal form in the two-time plane block $t_1, t_2 > 0$. The resulting picture is that instant thermalization is a meaningful concept only for this block, while the off-diagonal blocks $t_1 \cdot t_2 < 0$ are inherently non-thermal at any $q$. Since the effective temperature is obtained from correlations spanning all blocks, it inherits a finite rate set by the off-diagonal. We illustrate this directly by studying the non-thermal correlations' time dependence.

Quantum machine learning offers a compelling representational perspective: angle-encoded states inhabit Hilbert spaces in which periodic similarities and interactions can be expressed naturally. Realizing this perspective for visual recognition remains difficult, however, because present quantum neural networks are constrained by limited qubit counts, costly circuit simulation and measurement, noise, and unstable optimization on noisy intermediate-scale quantum devices. We investigate whether useful structural ideas from quantum models can instead be realized as scalable classical Transformer operations. We introduce QiT, a Quantum-inspired Transformer for vision tasks with three components: (i) angle-inspired encoding that maps image tokens to learned trigonometric Hilbert-space features analogous to quantum rotation-based state encoding; (ii) self-attention over these periodic features, inducing a classical cosine kernel approximated to quantum fidelity kernels; and (iii) gated multiplicative emulation, a trainable classical surrogate for interaction terms found in variational circuits. All components are differentiable tensor operations, so QiT claims neither quantum computation nor quantum speedup and retains the $\mathcal{O}(N^2D)$ attention complexity of a standard Vision Transformer. Across image-classification benchmarks, QiT is competitive with a matched classical Transformer while avoiding the severe runtime cost observed for a small simulated quantum Transformer. QiT-B reaches 78.3% ImageNet-1K top-1 accuracy with 45.7M parameters and 11.5 GFLOPs. These results position QiT as a scalable baseline for isolating and evaluating quantum-motivated inductive biases in visual recognition.

We introduce a method to suspend an optical micromirror, with a total mass of \SI{30}{\micro\gram}, using superconducting magnetic levitation. The micromirror is formed on a silicon membrane, coated with a high-reflectivity dielectric stack and attached to superconducting microspheres. The object is stably levitated inside a magnetic quadrupole field at cryogenic temperatures. Magnetic feedback on the transverse motion is used to stabilize the position of the levitator within the trapping field, allowing to measure the axial displacement of the levitator using optical interferometry. The system reaches a sensitivity of order \SI{100}{\pico\metre/\sqrt{\hertz}} near the axial trap frequency of \SI{167}{Hz}. This approach enables free-standing mirrors with minimal dissipation and tunable oscillation frequencies, offering a platform for precision sensing and quantum cavity optomechanics in the microgram regime.

We combine the Briegel–Englert damping basis of a lossy cavity mode with the permutation-invariant Liouville basis of \(N\) identical, incoherently pumped two-level emitters. The resulting Liouvillian is exactly block tridiagonal in a single radial field index, with atomic blocks of dimension \(\binom{N+3}{3}\). The stationary state follows from a matrix continued fraction whose asymptotic closure is a linear matrix equation that we prove to be uniquely solvable throughout the dissipative regime \(A>0\), and the same construction in the coherence-one sector yields the emission spectrum. The method is validated against direct diagonalization, weak-pump perturbation theory, and closed-system spectra, reaches \(N=16\) in tens of seconds in the few-quanta regime, and has a quantified precision limit at large photon number. We use it to derive an exact two-atom photon-balance identity that isolates the cavity-induced pair coherence and relates it to a singlet–triplet population difference; to establish an exact pump-order hierarchy of connected correlations for a zero-temperature cavity and a parity property of the minimal collective-spin sector; and to benchmark the second-order cumulant closure used in few-emitter laser theory, which we find to be semi-quantitative for the photon number but to predict the wrong sign of the inter-emitter coherence above inversion. In a good-cavity regime the exact solution shows near-Poissonian statistics and strong line narrowing for two and three emitters.

We study the quasinormal-mode and quasibound-state spectra of a massless scalar field in weakly magnetized Ernst–Schwarzschild spacetime. In the separated $O(B_0^2)$ regime, the Klein–Gordon equation reduces to a radial confluent-Heun equation. We construct an endpoint-selected spectral Wronskian directly from the canonical confluent-Heun recurrence and its regular-to-irregular connection limit. Quasinormal modes and quasibound states are then obtained as zeros of the same analytic spectral function on the radiative and bound sheets, respectively, providing a unified treatment of the two spectral sectors within the separated weak-field problem. The resulting QNM and QBS frequencies agree with independent weak-field Ernst and massive-Schwarzschild benchmarks available in the literature. We further show, for representative cases, that the frequencies selected by the local Heun-series termination relation examined here do not satisfy the endpoint-selected quasibound-state condition. The construction therefore provides a direct horizon-to-infinity spectral condition for both radiative and bound states within the weak-field Ernst problem.

We investigate the dynamics of entanglement asymmetry in periodically driven two-dimensional conformal field theories with a global U$(1)$ symmetry, using a dynamical-system description based on iterated conformal maps, in particular Möbius maps. Starting from a symmetry-breaking excited state prepared by a local operator insertion, we show that a broad range of nonequilibrium phenomena, including local symmetry restoration, the quantum Mpemba effect, and its inverse, admit a simple geometric description in terms of the invariant data of the conformal map. We explicitly demonstrate this using Möbius maps, for which the invariant structure is described by the conjugacy classes. In particular, the dynamics of entanglement asymmetry is determined by the relative positions of the state-preparing operator insertion, the subsystem, and the fixed points, yielding distinct patterns of growth, decay, oscillation, and saturation. We further argue that this geometric picture extends to general holomorphic maps, establishing the conformal-map dynamics as a natural framework for organizing the phenomenology of entanglement asymmetry in periodically driven two-dimensional conformal field theories.

T-state cultivation is a resource-efficient protocol producing logical T states but recent benchmarks show that its logical error rate is considerably higher than intended i.e. than S-state cultivation, which is the analogous protocol for producing logical S states. In this paper, we explain this T-S discrepancy by analytically showing, under circuit-level depolarising noise, that distance-3 (-5) T-state cultivation has fault distance 2 (3) due to Pauli hook errors that propagate to coherent Clifford errors after its final double-check circuit; such errors remain Pauli in S-state cultivation, which consequently retains fault distance 3 (5). As part of our analysis we derive a general formula, and an $\mathcal O(n^3)$-time algorithm for fixed logical-qubit count, for the acceptance probability of a logical mixed state afflicted with a Clifford error, where $n$ is the physical qubit count. We then design flags that detect the malignant hook errors in cultivation, improving the pre-escape logical error rate from $\Theta(p^3)$ to $\Theta(p^5)$. At noise level $p =10^{-3}$, this is a 4.9$\times$ improvement, costing a 1.36$\times$ increase in attempts per accepted shot.

The recently introduced concept of quantum-state texture (QST) has found applications ranging from the identification of unknown quantum gates to the study of quantum phase transitions and criticality, and has already been experimentally investigated. Here, we advance its resource-theoretic formulation in several directions. Our approach centers on the experimentally accessible grand sum–the sum of all matrix elements of a density operator in a given basis. We clarify several points raised in the recent literature, including the relation between texture distillation and a simple grand-sum-based QST monotone. We completely characterize free operations for a single qubit and study the resulting state-conversion order; classify relevant families of free operations in arbitrary dimensions; derive bounds relating the texture of composite systems to that of their subsystems; and introduce the basis-independent concept of set texture. Together, these results strengthen and broaden the resource theory of QST, providing a foundation for its further development and applications.

Detection efficiency in gated-mode single-photon avalanche detectors recovers gradually after each gate edge, limiting attainable count rates, yet quantitative recovery models exist only for free-running operation. We extract the gated recovery time constant of a free-running InGaAs/InP detector at 1550 nm by sweeping the gate frequency from 100 kHz to 1 MHz and globally fitting count rates across four dead times, requiring neither a pulsed laser nor a time-to-digital converter. The recovery time decreases linearly with detection efficiency, from 301 to 161 ns between 10 % and 25 %, at 9.3 ns per percentage point. We further resolve a periodic count-rate modulation consistent with bias-dependent capacitive gate feedthrough.

We study the complexity of quantum decomposable randomized encodings (QDRE). We establish a bi-directional connection between the QDRE model and the communication complexity model of quantum private simultaneous message protocols (QPSM), where classical communication is free, and quantum communication is the primary complexity measure. We show the following upper and lower bounds. (1) For every quantum channel mapping $n$ to $m$ qubits, we give a QPSM protocol with quantum communication $m$, using exponential pre-shared entanglement. In particular, constant-output channels have $O(1)$ quantum communication, and classical-output channels require no quantum communication. (2) With $O(n)$ pre-shared entanglement, every one-qubit-output channel has an $O(n)$-quantum-communication QPSM protocol. Conversely, there exists a channel and a constant $c>0$ for which any protocol with at most $cn$ pre-shared entanglement requires $\Omega(n)$ quantum communication. (3) In contrast, we identify a structured class of quantum channels, Clifford-induced channels, for which there exist QPSM protocols with $O(n)$ pre-shared entangled qubits and only $O(1)$ quantum communication complexity. Through our connection, we obtain analogous upper and lower bounds on the quantum encoding size of QDRE. Our results show that the amount of pre-shared entanglement plays a central role in quantum encoding size and quantum communication complexity.

The impact of projective measurements on a many-body quantum state is tightly linked to its underlying entanglement structure. Critical states are particularly sensitive, as long-range entanglement allows local measurements to have global consequences. This has been extensively studied in the context of critical states described by a conformal field theory (CFT), where measurements can alter critical properties in post-measurement quantities ('measurement-altered criticality') and induce long-range entanglement with universal features ('measurement-induced entanglement'). By contrast, little is known about the role of measurements on critical states with quenched disorder, which admit no CFT description. Here, we develop a theory of measurements on one-dimensional critical states governed by infinite-randomness fixed points (IRFPs), focusing on two closely related examples: the random XXZ chain and the random transverse-field Ising model. We show that the measurement-induced entanglement decays as a power-law with universal exponent $(3-\sqrt{5})/2$ in both models, and that the minimum number of measurements required to establish this entanglement obeys a universal scaling form. When only a finite density of measurements is made, we show that the critical properties of the state are remarkably robust: `measurement-altered criticality' is absent, with measurements either preserving the critical exponents, or destroying the criticality entirely. These results establish IRFPs as an analytically tractable arena for measurements on critical states, complementary to the CFT case. The outcome randomness that necessitates replica methods in clean systems becomes trivial at infinite randomness, with the universal response governed by the statistics induced by the quenched disorder.

Using thermal analyticity, we derive directional large-frequency bounds on the smooth functions entering full eigenstate thermalization in continuum quantum field theory. The strongest directions reproduce the scales previously identified for lattice systems, while the complete analyticity domain reveals a broader asymmetric multifrequency structure. In thermal two-dimensional conformal field theory, exact two- and three-point functions saturate the corresponding bounds. At fourth order, where genuine dynamical information first appears, we show that the holographic CFTs studied here saturate the strongest full-ETH bounds. These results establish a direct connection between full ETH, free cumulants, and gravitational scrambling, and are consistent with the emergence of asymptotic freeness realized by the gravitational scrambling algebra.

Detector observables pose a fundamental challenge for nonperturbative lattice methods due to their intrinsically real-time and asymptotic nature. We propose quantum simulation platforms as an ideal setting for studying these observables. Using quantum spin systems as a demonstration, we construct lattice detector operators and establish their connection to continuum energy-flow observables. We demonstrate this framework in the $1+1$-dimensional quantum Ising model, where finite lattice calculations show quantitative agreement with conformal field theory expectations at criticality. These results support the interpretation of the lattice flow operators as regulated counterparts of continuum detectors in the scaling and asymptotic limits, providing a concrete route toward realizing high-energy collider physics on table-top quantum platforms.

Using thermal analyticity, we derive directional large-frequency bounds on the smooth functions entering full eigenstate thermalization in continuum quantum field theory. The strongest directions reproduce the scales previously identified for lattice systems, while the complete analyticity domain reveals an asymmetric multifrequency structure. Thermal conformal correlators saturate the second- and third-order bounds, and the leading gravitational Regge contribution saturates the strongest fourth-order direction.

Starting from a general Hamiltonian describing the quantum dynamics of probe particles interacting with a set of environment degrees of freedom, we derive the quantum master equation with which the reduced density matrix of a probe particle evolves, the general equilibration condition that they satisfy when the environment is prepared in a thermal state – encoded in a KMS property for line operators extended in real time – and the Langevin description that emerges. The novelty of our results resides in their generality: We do not assume a specific form of the environment self-coupling, of the environment operator that couples the particle to it, of the statistics of its correlation functions, whether the statistics of the momentum transfer is Gaussian or not, or whether the probe particles move relativistically. Our results only require that spacetime translations, parity and time reversal be symmetries of the Hamiltonian, and that there exists a separation of scales between those characterizing the dispersion relation of the probe particle and those of the environment. We also discuss the limiting case in which Gaussian Brownian motion emerges. Overall, our results constitute a first-principles derivation of what properties of the underlying quantum field theory govern the energy loss and momentum fluctuations of probe particles.

Barycentric Rényi divergences were introduced in [Mosonyi, Bunth, Vrana, Linear Algebra and its Applications, 2024] as an alternative to standard Kubo-Ando constructions to define multivariate quantum Rényi divergences. They are defined via a variational expression and depend on a finite collection of quantum relative entropies $D^{q_x}$. When all the relative entropies are monotone under CPTP maps then so are the corresponding barycentric Rényi divergences, and when all the relative entropies are additive then the corresponding barycentric Rényi divergences are subadditive under tensor product. Additivity has only been established before for the case where all $D^{q_x}$ are chosen to be the Umegaki relative entropy, which is also the only case where the barycentric Rényi divergence (called the minimal one) was known to admit an explicit expression. Here we settle the problem of additivity by showing that for any choice of monotone quantum relative entropies, the regularized barycentric Rényi divergence coincides with the minimal barycentric Rényi divergence on invertible inputs. This in turn implies that if at least two of the $D^{q_x}$ are strictly larger than the Umegaki relative entropy (in a precise sense), then the resulting barycentric Rényi divergence is not even weakly additive.

Hardware noise has been shown to significantly impact the accuracy of ADAPT-VQE, a ground state preparation algorithm. While previous work has studied the impact of noise on its parameter optimization step, its impact on the critical operator selection step remains comparatively unexplored. In this work, we examine the impact of a variety of noise channels on this step, using a linear H$_3$ molecule as a test case. We show that, despite the selection criterion's natural resilience to some noise, both coherent and incoherent noise can prevent convergence for sufficiently high noise rates. We employ quantum error mitigation techniques–dynamical decoupling, zero noise extrapolation, and Pauli twirling–and show that when combined appropriately, these techniques are capable of restoring a successful convergence profile. Our results highlight how error mitigation can improve the performance of ADAPT-VQE and enable convergence in the presence of hardware noise, offering valuable insights into the implementation of the algorithm on near-term quantum hardware.

We investigate antidistinguishability of states within the framework of general probabilistic theories (GPTs). We formulate antidistinguishability, strong and equal antidistinguishability as refined notions that imposed additional constraint on the measurement effects. We establish general results relating these notions of antidistinguishability and derive an upper bound on the cardinality of equally antidistinguishable sets in terms of the affine dimension of the state space. We then study antidistinguishability in polygonal theories, obtaining conditions for antidistinguishability of a set of states. In consequence, we show that the set of all pure states in a polygon model is antidistinguishable. Additionally, we identify broad families of strongly and equally antidistinguishable states. Finally, using Random Exclusion Codes, whose success probability is governed by the antidistinguishability of different sets of encoding states, we probe the nonclassicality of polygon theories. We find that certain polygon models can outperform the optimal quantum value, while their optimal performance converges to the quantum limit in the large-polygon limit.

Recent advances in quantum computing have been driven primarily by improvements in hardware. Here we show that substantial gains can instead arise from how finite computational resources are allocated throughout a quantum computation. We introduce Adaptive Algorithmic Control (A2C), a software paradigm founded on a State-Proxy Equalization theorem, which proves that the optimal allocation for a state-derived proxy-error functional equalizes cumulative computational hardness rather than physical time. The required computational hardness is inferred directly from the evolving quantum state, avoiding explicit reconstruction of the exponentially large many-body spectrum. Across quantum optimization problems containing up to 156 qubits, combining exact simulations, large-scale supercomputer computations and IBM quantum hardware experiments, A2C improves the low-energy sampling probabilities by $22\%$ to over $100,000\%$ under matched circuit depths and measurement budgets. These results demonstrate that quantum computational performance depends not only on hardware capabilities, but also on how finite computational resources are organized, establishing adaptive algorithmic control as a complementary software pathway for advancing quantum computation.

For the problem of simulating Lindblad evolution for time $t$ to precision $\epsilon$, Hamiltonian simulation provides an additive query lower bound, informally, $\Omega(t + \mathrm{polylog}(1/\epsilon))$. However, the best previously known algorithms for general Lindblad simulation achieve a multiplicative upper bound, informally, $\mathcal{O}(t\,\mathrm{polylog}(1/\epsilon))$, in query complexity. It has remained open whether this multiplicative dependence is necessary. In this paper, we close the gap in query complexity by giving an algorithm with optimal additive dependence on evolution time and precision in the block-encoding model. Our approach uses the transducer framework to reduce the query cost of composing first-order approximations to the evolution channel, together with linear combinations of reuse circuits of different lengths to suppress catalyst-removal error. We further achieve nearly optimal gate complexity in evolution time and precision through history compression and an efficient implementation of the query-free part of the transducer using operation reordering and linear combinations of unitaries, while preserving the optimal query complexity.

Rare outputs of random quantum circuits are usually treated as terminal statistics. We ask whether they reveal intermediate organization that remains useful beyond the selecting future. Comparing unconditioned random-normal (RN) and peak-selected random-peaked (RP) circuits from the same local generator, we find stronger pairwise correlations and probability redistribution but reduced bipartite and output spreading in RP across n=8-16. Exact full-suffix decomposition reveals stronger peak-directed interference. The structural separation and fresh-future advantage persist across four nominal depths at n=8-14, with 2.01-7.15 fold RP enrichment in the depth extensions at fixed, independently calibrated thresholds. Within the unconditioned ensemble, a structural prefix score predicts fresh-event probability without using the evaluated circuits' terminal outcomes. Population-preserving phase scrambling identifies a functional contribution from relative-phase organization across the tested settings, including primary-depth held-out confirmation. RP trajectory-guided initialization improves high-peak yield over Haar initialization under common local refinement. Intermediate multivariate guidance also improves the fresh-continuation susceptibility of constructed states beyond peak-only guidance across the same size-depth grid. Rare outputs thus reveal intermediate physical organization that remains useful under new dynamics and can guide circuit construction.

Scalable quantum computation is expected to rely on fault-tolerant quantum computation (FTQC), in which quantum error correction (QEC) suppresses physical errors sufficiently to support reliable logical operations. This requires quantum compilation to move beyond general-purpose circuit optimization toward encoding-aware and protocol-structured compilation across the full stack of fault-tolerant quantum computers. Beyond circuit synthesis and hardware mapping, an FTQC compiler must lower algorithm-level operations into the logical gate set supported by the chosen code, coordinate encoded data and ancilla resources, realize logical operations together with repeated syndrome extraction under hardware constraints, and provide the resulting measurement stream to real-time decoding. This survey presents a full-stack view of compiler design for QEC-protected quantum computation. We organize existing work into three interacting layers: logical-level QEC compilation, physical-level QEC realization, and decoder runtime integration. At the logical level, we review surface-code lattice-surgery compilers, beyond-surface-code code-surgery frameworks including emerging qLDPC approaches, and compilation support for non-Clifford operations such as magic-state distillation and code switching. At the physical level, we survey hardware-aware QEC realization on superconducting, trapped-ion, and neutral-atom platforms. We further examine decoder models, real-time decoding systems, and frame-management mechanisms that close the feedback loop during fault-tolerant execution. Finally, we identify open challenges in cross-layer optimization, qLDPC compilation, compiler-decoder co-design, runtime adaptivity, and the development of integrated and benchmarkable FTQC compilation stacks. An actively maintained paper list is available at: github.com/chenghongz/QEC-compiler-design.

A random unitary quantum circuit is expected to be incompressible for exponentially long times. We show that the constant-error circuit complexity of a random unitary circuit grows almost linearly with time as $\Omega(T/\log T)$. The bound holds for all $2\leq T\leq 4^n$ where $n$ is the system size, and involves no other $n$-dependence. This improves previous lower bounds derived from spectral gaps and unitary designs by a factor of $\mathrm{poly}(n)$. Drawing on insights from stochastic calculus, geometric functional analysis, and randomized linear algebra, our approach exploits the circuit's response to variations of individual gates and requires no control over convergence to high-order unitary designs.

We investigate the relaxation of an approximately conserved charge in interacting quantum systems close to local equilibrium. To this end, we provide a pedagogical review of Zubarev's non-equilibrium statistical operator approach in the minimal setting of a single non-conserved charge and apply it to the problem at hand. We explicitly highlight the physical assumptions that lead to a local relaxation law: weak charge violation, a separation between the short timescale of microscopic correlations and the much longer timescale of charge relaxation, and the resulting loss of microscopic memory. Under these conditions, the leading relaxation rate is determined by an equilibrium correlation function of the charge-violating operator. We show that the same result follows from a simpler local-equilibrium construction based on the system's evolution over an intermediate timescale, providing a direct alternative for practical calculations and making the common physical ingredients of the two approaches explicit. Beyond the decay law itself, we relate the relaxation rate to the equilibrium diffusion of the same charge. We then allow the charge density to vary in space, which leads to a diffusion-relaxation equation. Finally, we illustrate the formalism through electroweak $\mathrm{B+L}$ washout and a perturbative scalar model, where agreement with the linearized Boltzmann equation establishes a direct connection between equilibrium-correlator and kinetic descriptions.

Reliable quantum engineering is essential for turning quantum phenomena into practical technologies. As quantum platforms grow in scale and complexity, their characterization and operation require increasing human effort and coordination. Scientific artificial intelligence agents, which can plan experiments, operate instruments, and analyze observations, offer a promising route towards autonomous quantum engineering. Yet whether current agents can perform reliably in this setting has not been systematically established. To fill this gap, we developed Quantum-Harbor, a virtual laboratory that provides a controlled execution environment for agents to interact with quantum systems. This design enables direct verification of both the actions taken and the conclusions drawn. Building on this framework, we introduce QIQCBench, a benchmark of $49$ expert-authored tasks spanning multiple layers including calibration and control, error correction and compilation, sensing and networking. Across $17$ frontier agentic systems, QIQCBench reveals wide variation in verified performance. These results expose a substantial gap between demonstrating capability and achieving reliable operation, and establish Quantum-Harbor as a foundation for measuring progress towards verified autonomy in quantum engineering.

Electron-phonon interactions underpin a variety of phenomena, ranging from transport and superconductivity to polarons and ultrafast carrier dynamics. Despite being one of the most intensely studied subjects in condensed matter physics, research on electron-phonon physics mostly focused on linear, first-order couplings. Second- and higher-order nonlinear couplings are commonly ignored because their calculations are too demanding and we lack computational frameworks that can provide both diagonal and off-diagonal coupling matrix elements. In this work, we report a theory and computational method for computing nonlinear electron-phonon interactions of any order in real materials. Our approach combines the advantages of unit-cell calculations of electron wavefunctions and supercell calculations of phonon perturbations, is systematically improvable, can be used with either semilocal or nonlocal exchange-correlation functionals, and is amenable to Wannier-Fourier interpolation. As a first proof of concept, we illustrate this method by computing second-order electron-phonon coupling matrix elements in diamond, lithium fluoride, and graphite as representative nonpolar semiconductors, polar semiconductors, and metals, respectively. Furthermore, we generalize the ab initio polaron equations to second-order electron-phonon couplings, and we show that second-order couplings are essential to achieve quantitative accuracy in polaron formation energies and hopping barriers. The present methodology will find application in the study of all properties and phenomena that are currently being investigated within the linear electron-phonon coupling approximation, from phonon-mediated superconductivity to excited-states dynamics, both in harmonic and anharmonic systems.

A multiset of pure quantum states is said to be k-learnable if there is a measurement strategy that always narrows an unknown sample drawn from the list down to one of at most k candidates. The parameter k interpolates between distinguishability and antidistinguishability, and provides a unified framework for partial state identification. We prove two universal, and optimal, Gram-matrix criteria for k-learnability: a Frobenius-norm sufficient condition and an entrywise-$\ell_1$ necessary condition. We apply them to derive explicit learnability and copy-complexity guarantees for several well-known sets of states including SIC-POVMs, mutually unbiased bases, and stabilizer states. We further apply our results to zero-error mutation detection problems such as anomaly detection and changepoint detection.

$\mathsf{QAC}^0$ is the class of constant-depth $\mathrm{poly}(n)$-ancilla circuits obtained by extending $\mathsf{QNC}^0$, the class of local circuits, to include nonlocal interactions via arbitrary width Toffoli gates. It is believed to be weaker than its counterpart, $\mathsf{QNC}^0_f$, obtained by including arbitrary-width FANOUT gates instead ($\mathsf{QAC}^0 \subseteq \mathsf{QNC}^0_f$ [Moo99]). In this note, we show that every $O(\log n)$-qubit state can be exactly and cleanly prepared by a $\mathrm{poly}(n)$-ancilla $\mathsf{QAC}^0$ circuit. Previous known $\mathrm{poly}(n)$-ancilla circuits for arbitrary such states are only known via additional access to either FANOUT or QRAM (indexing) gates [Ros21b, GGJ26b], neither of which are known to be in $\mathsf{QAC}^0$. Equivalently, prior constructions of arbitrary $n$-qubit states in $\mathsf{QAC}^0$ require doubly exponential size and we obtain an exponential factor improvement.