Papers

Quantum states generated by generic time evolution are locally featureless: local measurements return random outcomes that are identical for all states. However, global snapshots in the computational basis are surprisingly effective at distinguishing between quantum states. We explore the ability of Bayesian classifiers to discriminate between many random quantum states using a small number of measurement outcomes. We identify a phase transition in the ability of the classifier to distinguish between $k$ candidate states with $m$ shots controlled by the variable $x = m / \ln k$, and derive the threshold value $x_c$. We extend our results to low-depth circuits near the onset of anti-concentration, as well as to noisy circuits and phase-random states.

We propose Bell tests for collider decays using independently sampled analysis axes as settings and detector regions to assign binary or null outcomes. We show that a Bell violation requires postselection, opening a loophole. However, under measurement independence and operational equivalence of acceptance events across settings, any local model exploiting the loophole must be nonclassical in the sense of measurement contextuality. We derive a Bell inequality violated by singlet correlations when the effective spin-analyzing powers are sufficiently high. Its violation then witnesses Bell nonlocality or measurement contextuality.

Quantum reservoir computing (QRC) is a machine learning approach which employs the internal dynamics of a physical system (the reservoir) to encode and process information. In this work, we explore the use of dual-unitary circuits in a brickwork architecture as a platform for QRC, well suited to current noisy intermediate-scale quantum devices. Dual-unitary circuits present both practical and conceptual advantages. Our results indicate that, under appropriate conditions, dual-unitarity can lead to an enhanced regime of operation: we numerically verify that it improves memory effects and nonlinear processing, and shields against finite-shot noise, mitigating exponential concentration. Moreover, dual unitarity offers an intuitive picture of how operator dynamics gives rise to memory and nonlinear processing in circuit-based reservoirs.

Preparing a quantum Gibbs state requires reproducing both its thermal distribution and the associated many-body eigenspaces. In this work, we formalize the spectral core-tail architecture (SCTA) as a framework comprising a structured thermal core, a geometrically characterized unitary tail, and an exact residual measuring the remaining core-frame Hamiltonian mismatch. We derive a local Gibbs-state error bound separating core-preparation, tail-implementation, and modeling errors. The modeling contribution is volume uniform when its Kubo-Mori response meets the shell summability condition and the relevant local data remain uniform. We then highlight three anchor Hamiltonian classes which admit exact core-tail constructions with zero residuals. For small deformations of an exact anchor, we employ a Schrieffer-Wolff reduction procedure to construct a corrected core-tail pair that formally removes the deformation order by order. Under uniform locality and solvability assumptions, we show that the first-order reduction yields a residual that remains bounded and is quadratic in the deformation strength. Furthermore, we numerically test the first-order reduction on deformed graph-stabilizer Hamiltonians. The numerical results show approximately quadratic suppression of both the Hamiltonian-level mismatch and the local Gibbs-state error in the perturbative regime. We also find that the constructed correction circuit structure remains useful as a variational ansatz beyond perturbative control, often improving on both the bare and prescribed first-order states.

In modern density functional theory, effective Hamiltonians are constructed to reproduce densities and forces of electrons at equilibrium. However, their nonlocal potentials leave systematic errors in spectral properties and real-time dynamics. Access to local optimized or inverted effective potentials would remove this limitation, but the numerical fragility in finite orbital bases has long prevented their wide adoption. Here, we introduce multipole splats, a class of trial potentials that carry the correct asymptotic decay required to support the unoccupied spectrum. By connecting the computation of effective potentials to variational and supervised variants of Hamiltonian learning, we recast both problems as stable nonlinear optimization formulated directly in standard orbital basis sets and applicable to any hybrid functional approximation. The resulting solver allows us to resolve spatial profiles of exchange-correlation potential errors during molecular dissociation and accurately reconstruct key excited states without empirical asymptotic corrections. We also show the deviation from the ionization potential theorem for different exchange-correlation approximations on a dataset of molecular systems. Multipole splats extract insights from established approximations and provide capacity for robust dataset generation for downstream processing and learning.

The entangling power of a unitary operator acting on a bipartite Hilbert space measures the entanglement it generates from product states, averaged over the inputs. A finite-dimensional unitary has a spectral decomposition $U=\sum_{a=1}^{n}e^{i\theta_a}P_a$, where $e^{i\theta_a}$ are the eigenvalues, $P_a$ the corresponding eigen-projectors, and $n$ is the number of distinct eigenvalues. After removing an overall phase, the entangling power is a function on the $(n-1)$-torus of relative eigenphases at fixed spectral projectors. We prove that this function is stationary at all $2^{n-1}$ points on the torus where every relative phase is $0$ or $\pi$, which we define as corners. Up to an overall phase, $U$ at each corner is a generalized reflection $R=\mathbb{I}-2Q$ satisfying $R^2=\mathbb{I}$, where $Q$ is the sum of spectral projectors whose relative phase is $\pi$. At the corner the entangling power is expressed in terms of seven local-unitary invariants of $Q$. A unitary gate $U$ can be realized as a corner of some projector family if and only if $U^2\propto\mathbb{I}$, a condition satisfied by many Clifford and non-Clifford gates. We illustrate the theorem with two-qubit gates, $SU(N)$ channel decompositions, and two-site spin chains, obtaining examples of minima, maxima, and saddle points. In addition, a corner that is a saddle point on the full phase torus can appear as a local maximum or minimum along different time-evolution trajectories.

Moving from quantum research and development to production-grade, fault-tolerant quantum workload execution remains one of the most significant challenges facing quantum platform builders. While Python frameworks have enabled an easy entry point for quantum algorithm design, the low-latency requirements for real-time quantum error correction (QEC) demand performance that traditional interpreted environments cannot provide. FPGAs and ASICs play a central role at these layers, but their specialized programming models make development rigid and time-consuming. CPUs, GPUs, and other accelerators introduce a different challenge: as infrastructure becomes increasingly heterogeneous, programming across different devices and their associated abstractions becomes more complex. Allowing researchers to write workloads in high-level languages that map to low-latency execution across diverse distributed target platforms will enable the development of key infrastructure for utility-scale quantum systems. For this, we introduce $\textit{Backline}$, a heterogeneous compilation and runtime framework built within PennyLane and Catalyst. Backline allows us to design and build quantum-classical workloads for high-performance and low-latency devices, with compilation directly from a Python interface through MLIR. We demonstrate the compilation and execution of several quantum workloads with low-latency data movement across a mix of CPUs, GPUs, and FPGAs, for both local and distributed remote hardware targets, all from a vendor-agnostic Python frontend. With an AMD VPK120 FPGA board as the controller, issuing each round from its hardware-handshake engine, we measured median steady-state round-trip latencies over RoCE v2 of $2.305~\mu$s to an AMD Ryzen Threadripper PRO CPU and $4.5~\mu$s to an AMD Instinct MI210 GPU across $10^6-1$ rounds per path, demonstrating microsecond-scale synchronous co-processing.

We study Parrondo's paradox – the phenomenon where combining losing strategies yields a winning one – in a minimal discrete-time quantum walk. We introduce the transport vector, encoded in the coin's steady state, whose inner product with the initial coin state gives the walker's asymptotic velocity. More generally, the paradox emerges exactly when the transport vector of the combined strategy falls outside the cone spanned by the individual ones – a geometric criterion valid for any combination of strategies. It explains, for instance, why composing two coin operators within a single step can produce the paradox while simple alternation between them cannot, since alternation keeps the combined vector confined to the cone. The paradoxical set has nonzero measure, and we compute its probability explicitly in representative cases. This casts the paradox as one instance of designing reachable transport in quantum walks.

Reconstructing fields governed by nonlinear partial differential equations (PDEs) from sparse measurements is a challenging task because the governing equations are strongly nonlinear and observations are available at only a few locations. Fluid velocity fields are a representative case. In this paper, we propose a variational quantum algorithm that reconstructs the solution over the entire spacetime domain at once. Rather than marching in time, the method encodes the full discrete spacetime solution in a single variational quantum state, so that all time points are optimized jointly. The cost function combines a sparse-measurement mismatch term with a physics-informed PDE violation term, letting data and the governing equation constrain the solution simultaneously. We demonstrate the method on the one-dimensional Burgers and Kuramoto–Sivashinsky equations using numerical simulations. The results suggest that variational quantum algorithms with a spacetime encoding scheme offer a compact framework for reconstructing nonlinear PDE dynamics.

We present a method for recovering the moral graph of a causal DAG from a probability distribution over discrete variables, using fully connected tensor networks (FCTNs) with nuclear-norm-regularized bond corrections. Each bond matrix is parameterized as a baseline all-ones matrix plus a low-rank correction $C_{ij} = U_{ij}V_{ij}^\top$, and the nuclear norm of the correction implemented via the variational Frobenius norm penalty on the factors drives unnecessary bonds to zero. We prove that under faithfulness, positivity, and a no-implicit-rerouting assumption on the local tensor architecture, every optimal FCTN with zero reconstruction error $\varepsilon = 0$ has effective graph exactly equal to the moral graph. For the approximate regime ($\varepsilon > 0$), we provide explicit recovery bounds using the Fannes-Audenaert continuity of conditional mutual information, and derive a sufficient condition on the regularization parameter $\beta$. The effective graph is read directly from the optimized bond matrices.

We generalize the sample-based Krylov quantum diagonalization (SKQD) method from ground-state calculations to the evaluation of single-particle Green's functions. By constructing and sampling unitary Krylov subspaces in the N +/- 1 particle-number sectors and evaluating all sector-connecting overlaps classically, the approach reconstructs the Green's function via a Lanczos continued fraction while retaining the shallow-circuit, ancilla-free character of SKQD. The quantum device is required only to prepare and sample short-time evolutions. Applied to the particle-hole-symmetric single-impurity Anderson model in chain geometry, with the discrete bath representation used in dynamical mean-field theory (DMFT), the method recovers the spectral function using a relatively small fraction of the full Hilbert space. Across a range of interaction strengths that spans the metal-insulator transition, the main spectral features are reproduced. These results suggest that SKQD-based Green's-function calculations may allow DMFT impurity solvers with a larger number of bath sites on near-term quantum hardware than is currently practical.

The Ballistic Macroscopic Fluctuation Theory (BMFT) is a path-integral based approach to treat large-scale correlations in interacting integrable systems which, so far, has only been applied to quasi-equilibrium settings. In this paper we extend this approach to integrable quench problems and, to illustrate it, we compute the time evolution of the full-counting-statistics (FCS) of a conserved charge. We identify the relevant path integral, solve it via saddle-point, and obtain a set of partial differential equations describing the dynamics of the FCS. We solve these equations explicitly for free fermionic systems and for the interacting cellular automaton Rule 54. In both cases, we recover the known exact results. For Rule 54, our construction moreover completes the solution across the entire ballistic window.

Non-Gaussian gates remain a key bottleneck for universal continuous-variable (CV) quantum computation because the nonlinearities they require are difficult to engineer. To address this challenge, we develop an efficient qubit-oscillator Rabi synthesis scheme for polynomial phase gates, with a total interaction time that scales polylogarithmically with the inverse target error \(\varepsilon\). Specifically, for a class of readily preparable initial states, we show that a degree-\(R\) phase gate can be approximated by an analytically constructed Rabi sequence with total time \(O(\log^{(R-1)/2+o(1)}(1/\varepsilon))\). This construction requires no numerical optimization and therefore extends naturally to arbitrarily large multimode systems. We further establish a total-time lower bound of \(\Omega(\log^{(R-1)/2}(1/\varepsilon))\), showing that the synthesis is near optimal. As applications, we use this scheme to simulate representative CV quantum dynamics and implement a CV quantum algorithm for solving linear partial differential equations. These results establish qubit-oscillator Rabi control as an efficient, analytically compilable, and near-optimal primitive for CV quantum information processing.

The Anderson orthogonality catastrophe (AOC) is a paradigmatic many-body phenomenon in which a local perturbation induces a macroscopic response of a Fermi sea. We probe signatures of the AOC by coherently driving heavy Fermi polarons in an ultracold $^6$Li-$^{133}$Cs mixture. We observe a power-law dependence of the measured Rabi frequency on the drive strength, with exponents consistent with AOC predictions. Finite-temperature simulations quantitatively reproduce the observed scaling, indicating that AOC signatures persist beyond the idealized zero-temperature, infinite-mass limit. The damping of the Rabi oscillations provides access to polaron dephasing and reveals a nonmonotonic drive dependence, qualitatively consistent with current theories. Our results establish coherently driven impurities as a versatile probe of quantum many-body dynamics through local coherent control.

Quantum statistics in low-dimensional systems predicts anyonic particles with fractional exchange statistics which are neither that of bosons nor fermions. While anyons are typically found in two dimensions as excitations of topologically-ordered states of matter, anyon-like exchange statistics has also been discussed in one dimension, for instance, in the context of the anyon-Hubbard model (AHM), the physics of which has recently been observed in experiment [Kwan et al., arXiv:2306.01737; Dhar et al., arXiv:2412.21131; and Bakkali-Hassani et al., arXiv:2602.20421]. The AHM can be formulated in terms of bosons featuring density-dependent Peierls phases, described by a statistical phase angle $\theta$, which controls asymmetric transport and the formation of dynamically bound pairs at finite momentum. Here, we show theoretically that the AHM also hosts exact two-body bound states in the continuum (BICs) for arbitrary $\theta\neq 0$, and genuine three- and four-body bound states. Unlike conventional bound states stabilized by attractive (or repulsive) interactions, which are energetically localized with a large effective mass, these clusters here are bound by a purely kinematic mechanism endowing them with fast chiral transport properties. We provide a simple variational approximation to the three-body bound states and explain their binding mechanism. Moreover, we show that the signatures of three-body bound states in the AHM can be directly probed experimentally from the expansion dynamics starting from three localized particles.

We show that one-way one-round quantum-LOCAL algorithms cannot $4$-color directed cycles with high probability. This is the first lower bound in the high-probability quantum LOCAL setting that goes beyond the non-signaling and bounded-dependence models, exploiting the structure of distributed quantum algorithms. Our proof establishes a bidirectional connection between distributed quantum computing and extremal combinatorics. We obtain our lower bound by proving a Mantel-type stability theorem for weighted matrix spaces.

We study one-dimensional spinless bosons with semirelativistic spinless-Salpeter dispersion and attractive pairwise contact interactions. Because the dispersion becomes linear at large momentum, the contact interaction is marginal by power counting and produces a logarithmic ultraviolet divergence. We construct the renormalized many-body theory using an enlarged Fock space and a Schur-complement representation of the resolvent, eliminating the bare coupling in favor of the physical zero-total-momentum two-body bound-state energy. The resulting cutoff-independent resolvent defines a self-adjoint Hamiltonian in each fixed particle-number sector. We treat the two-body problem explicitly and show, in the norm-resolvent sense, that the nonrelativistic limit reproduces the attractive Lieb–Liniger Hamiltonian. We also formulate a mean-field approximation directly within the renormalized theory. In the massless and deeply bound large-particle-number regimes, it predicts an exponentially increasing binding scale whose exponent is determined by a one-dimensional variational problem.

We establish a linear quantum query lower bound for high-accuracy convex optimization over an explicit family of $n$-dimensional ellipsoids. We focus on linear optimization with an explicitly given objective, where the feasible set is accessed through a membership oracle. We show that any algorithm that, for every unit linear objective, returns an exactly feasible point with additive objective error $\Theta(n^{-1/2})$ requires $\Omega(n)$ membership queries, where the ellipsoids are contained in the unit ball. The same lower bound can be shown to hold if the returned point is only required to be approximately feasible, within $\Theta(n^{-3/2})$ distance from the feasible set. This resolves an open question posed by Chakrabarti, Childs, Li, and Wu~(Quantum, 2020) and by van Apeldoorn, Gilyén, Gribling, and de Wolf~(Quantum, 2020). Coupled with the upper bounds in these papers, the query complexity of high-accuracy convex optimization is characterized tightly up to logarithmic factors. The proof is built around a lower bound for determinant computation that is derived via a novel polynomial method based on Fourier-rank. In the continuous matrix phase-query model, computing the determinant of a real $n\times n$ matrix requires at least $n/2$ matrix-vector product queries. The construction also yields an $\Omega(n)$ phase-query lower bound for estimating the minimum eigenvalue of a real symmetric $n\times n$ matrix to additive accuracy $\Theta(n^{-2})$. These results extend the determinant and minimum-eigenvalue lower bounds of Childs, Hung, and Li~(ICALP 2021) from finite fields to the real-valued setting. Based on the same constructions, we also prove an $\Omega(\min\{\sqrt\kappa,n\})$ gradient-query lower bound for constant-accuracy optimization of $1$-strongly convex and $\kappa$-smooth functions, which is optimal up to a logarithmic factor.

We prove quantitative lower bounds on the semidefinite extension complexity of the set of separable quantum states on $\mathbb{C}^d\otimes\mathbb{C}^d$. We consider semidefinite programs (SDPs) that approximate the maximum acceptance probability of a measurement over separable states, the optimization problem underlying QMA(2). In the extended-formulation model of Harrow, Natarajan, and Wu (HNW), all measurements share a common feasible region and an objective-independent embedding of product states that exactly reproduces their acceptance probabilities. For every $0<\theta<2/7$, there are constants $c_\theta,a_\theta>0$ such that, for sufficiently large $d$, any such SDP with uniform additive error $0<a\le a_\theta$ has size at least $d^{c_\theta\min\{a^{-1/3},d^\theta\}}$. The bound applies at sufficiently small constant error, is superpolynomial in $d$ whenever $a=o(1)$, and becomes $d^{\Omega(d^\theta)}$ when $a\le d^{-3\theta}$, improving HNW's quasipolynomial bound at inverse- square error. The same bound holds for any SDP-representable convex set of states that contains all separable states and lies within trace distance $a$ of them, giving a quantitative counterpart to Fawzi's theorem that the separable set has no exact semidefinite representation. Our proof combines the quantitative pseudo-density theorem of Lee, Raghavendra, and Steurer with explicit block-positive operators and Chebyshev amplification. Our main results are supported by Lean proofs.

The modular commutator provides a bulk, local, single-wave-function probe of the chiral central charge $c_-$ for gapped ground states. Its invariance under deformations was previously established under a local quantum Markov condition—namely, the conditional mutual information $I(A:C|B)$ is zero for all tripartitions of a disk into three consecutive strips A, B, and C \cite{Modular-commutator-Gapped}. However, the local quantum Markov condition also forces the probe to vanish, leaving open whether modular commutator remains robust in physically relevant states where the Markov property holds only approximately. In this paper, we resolve this tension for finite-dimensional Hilbert spaces: the approximate local quantum Markov property implies the change of the modular commutator under topology-preserving deformations vanishes asymptotically. We next prove trace-norm continuity of the modular commutator. Combining deformation invariance with trace-norm continuity, we establish that the modular commutator remains asymptotically invariant within gapped quantum phases connected by quasi-local unitary paths that preserve the approximate local quantum Markov condition. Conversely, by analyzing finite-time dynamics generated by modular Hamiltonians, we derive a quantitative lower bound on the conditional mutual information required for a non-zero modular commutator: $I(A:C|B)$ across such strip tripartitions cannot decay faster than exponentially with the width of B given that the state satisfies entanglement area law, extending the exact no-go theorem of \cite{strict-J-2024} to a quantitative finite bound . Finally, we demonstrate that those conclusions apply equally to the Hall conductance estimator \cite{FanSahayVishwanath2023}.

Various exotic many-body phenomena such as quantum scars and fractons have been linked to Hilbert space fragmentation. In this work, we find that in non-Hermitian settings, Hilbert space connectivity has an even more universal and fundamental influence, tightly controlling the nature of spectral amplification and state localization. Far more complicated than real-space lattices, non-Hermitian many-body Hilbert space graphs not only possess intricate competing amplification channels, but also global feedback loops connecting remote Fock states related by particle symmetry. These features lead to amplification behavior with unconventional scaling and localization properties. Particle occupation constraints can furthermore remove selected Hilbert space pathways, leading to robust unipolar and asymmetric bipolar skin localization in otherwise reciprocal processes. These results extend beyond simple interacting bosonic models and establish Hilbert space connectivity as a versatile control knob for many-body non-Hermitian critical transitions.

We propose a protocol for preparing the singlet Bell state in an analogue device implementing the transverse-field Ising model with ZZ interactions and local X and Z fields, which can be engineered within the superconducting platform, among others. This protocol is performed by direct control of the terms of the Hamiltonian alone. The method exploits the fact that the singlet state is the first excited state of a symmetric Hamiltonian family, and comprises two steps: an adiabatic interpolation preparing the ground state of said symmetric Hamiltonian, followed by the resonant population transfer between its two lowest energy levels. For realistic parameters, the protocol achieves fidelities comparable to standard gate-based preparation within similar time scales ($\sim$100 ns), and can reach infidelities on the order of $10^{-4}$ with a moderately increased duration. We further analyse robustness against systematic control errors and show that high fidelities are maintained under implementation imperfections.

We show that the capacity of a quantum channel demarcates a phase transition: while reliable transmission below capacity is always possible, any attempt to transmit information above it fails catastrophically. Specifically, we prove exponential strong converse theorems for unassisted quantum and classical communication over arbitrary finite-dimensional memoryless quantum channels. At rates beyond the respective capacity, the entanglement-generation fidelity and the success probability for classical communication decay exponentially with the number of channel uses. This rules out transmission above capacity even when one tolerates arbitrarily large errors. Our proof follows the classical Arimoto strategy, augmented by a crucial new ingredient: integral representations of Rényi information measures that lead to asymptotic continuity bounds for Rényi capacities.

We study stochastic and sharp restart in a one-dimensional lackadaisical discrete-time quantum walk with self-loop weight $\ell$. In the absence of restart, the dynamics has a flat band responsible for intrinsic localization and two dispersive bands supporting ballistic propagation. We compare two initially localized benchmark states: a flat-band-active state with finite flat-band overlap and a flat-band-dark state with zero flat-band overlap. For geometric stochastic restart with per-step restart probability $q$, the stationary mean-squared displacement scales as $q^{-2}$ as $q\to0$. In the same limit, the restart-site occupation probability approaches the restart-free intrinsic localized value for the flat-band-active state, whereas for the flat-band-dark state it vanishes as $q\ln(1/q)$. For power-law restart, where $p_m\propto m^{-s}$ is the probability that the waiting time to the next restart is $m$ steps, a normalized stationary site-occupation distribution exists only for $s>2$, while the stationary absolute spatial moment of order $p$ is finite only for $s>p+2$. In the regime $1<s\leq2$, at every fixed lattice site, the flat-band-active occupation converges to the intrinsic flat-band profile, while the flat-band-dark occupation tends to zero. We also consider monitored first detection with sharp restart, in which the walk is reinitialized after a fixed number $r$ of consecutive unsuccessful measurements. For fixed $r$, the mean first-detected-passage time of the flat-band-active state exhibits a minimum at an intermediate self-loop weight, whereas the flat-band-dark state approaches a ballistic detection limit as $\ell\to\infty$.

The Generalized Superfast Encoding (GSE) is a fermion-to-qubit mapping that has error-correcting/detecting properties. To this point, all demonstrations have been relegated to error-detection only, as no fault-tolerance under circuit-level noise has been observed. Here, we introduce an even-distance $d$ constant stabilizer-weight GSE where each of $N$ modes is assigned a $d$-qubit block arranged on a ring. The resulting stabilizer generators have constant weight 4 or 6 for any even distance $d$. Furthermore, the full stabilizer set of this construction can always be partitioned into four qubit-wise commuting groups, which enables compact syndrome-extraction scheduling. We simulate quantum memory experiments under circuit-level depolarizing noise for two instances of this code, $[[48,8,6]]$ and $[[64,8,8]]$ and the threshold is observed to be $\approx 4\times10^{-3}$. This is, to our knowledge, the first fault-tolerant quantum-memory characterization of a fermion-mapping with threshold-like scaling.

Dynamic circuits, which augment unitary operations with mid-circuit measurements and classical feedforward, can generate long-range entanglement in constant depth, enabling low-depth primitives ranging from nontrivial state preparation to many-qubit entangling gates. Escaping the light-cone constraints of unitary circuits, however, comes at a cost: these primitives typically require a number of mid-circuit measurements that scales with system size and that, together with feedforward latency, can introduce errors that degrade the long-range entanglement they rely on. Here, we alleviate this tension by showing that many such primitives, when cast into a common framework, admit an error-detection scheme that trades infidelity for postselection overhead with no additional ancillas. Our framework thus unifies and upgrades a broad class of primitives including fan-out gates, multi-qubit Pauli rotations, the preparation of W and higher-weight Dicke states, and certain non-normal matrix product states. We also introduce a reduced-depth, error-detected implementation of the Hadamard test, extending the use cases of dynamic circuits to a key algorithmic primitive. Finally, we establish the practical utility of our scheme through experiments on a superconducting quantum processor. We demonstrate the error-detected preparation of a long-range entangled Bell pair spanning a 100-qubit chain with fidelity $F=0.59\pm0.02$, surpassing the entanglement-certification threshold $F>0.5$ that the baseline dynamic-circuit implementation fails to reach ($0.39\pm0.01$). Separately, we demonstrate constant-depth preparation of W states of up to 20 qubits by consuming GHZ states of up to 40 qubits, finding absolute fidelity improvements of $\Delta F\approx 0.2$ across the largest sizes studied. Altogether, these results bring low-depth dynamic-circuit primitives within practical reach on present-day hardware.

Molar heat capacity at constant pressure, C_p (T), is a central thermodynamic quantity in materials science, but it remains difficult to calculate accurately from first principles when anharmonic vibrational effects become important. In this work, rocksalt ZrC is used as a high-temperature benchmark for the Beyond Quasi-Harmonic (BQH) method, a prepared-supercell first-principles approach that extracts anharmonic vibrational energy directly from density-functional-theory energy evaluations. The calculated BQH molar heat capacity is compared with CALPHAD reference values, a fully anharmonic thermodynamic-integration calculation, a calculated C_v (T) curve from the present work, and a quasi-harmonic calculation. The BQH curve gives a substantial improvement beyond C_v (T) and beyond the quasi-harmonic approximation. Because ZrC is electronically conductive, an electronic heat-capacity correction was also estimated from the density of states at the Fermi level and added to the vibrational BQH result. This correction brings the calculated molar heat capacity into close agreement with the fully anharmonic theoretical benchmark through approximately 1200 K. These results show that the BQH method fully captures important anharmonic phonon contributions missing from ordinary quasi-harmonic calculations.

We study the dynamics of a many-body quantum system strongly interacting with a bosonic reservoir. The coupling is given by a potential operator for the system and it is linear in the field. We show that in the limit of infinite coupling strength the system undergoes instantaneous spatial decoherence. To resolve the decoherence process in time we consider large coupling strengths $\lambda$ and short times scaling as $t\propto \lambda^{-\alpha}$, with $\alpha\ge0$, in the limit $\lambda\rightarrow\infty$. On short time scales $\alpha>1$ the dynamics is trivial while on longer ones $0\le\alpha<1$ the decoherence is instantaneous. We show that the decoherence process is resolved exactly for $\alpha=1$, defining the fine-grained time scale $\tau=\lambda t$. We construct an approximate effective evolution map of the many-body system with controlled error estimates. Generically, the effective dynamics is markovian, but not given by a dynamical semigroup. As a physical application we give a rigorous description of the phenomenon of localization of macroscopic quantum objects in position space.

The compilation of an algorithm can vary significantly with the choice of physical hardware platform and error correction model. Yet, current compilation frameworks typically commit to a single architecture-hardware configuration, making it difficult to assess resource estimates across platforms. We present a platform-aware compilation framework that re-compiles a quantum circuit into a hardware-compatible instruction set as well as fault-tolerant operations and provides end-to-end resource estimates in terms of physical-qubit count, time-to-solution, and classical processing time. We benchmark the framework by obtaining end-to-end resource estimates for different compilers, each tailored to the functionalities of specific hardware modalities: connectivity, clock speed, and noise model. As part of this framework, we introduce a transversal active volume (t-AV) compilation architecture designed for the efficient execution of fault-tolerant operations in platforms supporting long-range logical connectivity. We benchmark the framework for Hamiltonian simulation of the 2D Fermi Hubbard model as well as for eigenenergy estimation of a small molecule (trimethylenemethane) as a candidate for early fault-tolerant demonstration of quantum chemistry. For the latter, we show that end-to-end quantum simulations can be achieved with $\sim10^4$ physical qubits and runtimes ranging from $10^2$ ms (photonics, superconducting) to $10^5$ ms (neutral atoms).

We introduce a sparse Walsh-Pauli correlation encoding for MaxCut, in which graph variables are represented by diagonal Pauli-string expectation values computed classically as normalized XOR autocorrelations of Walsh coefficients. The complete Walsh basis can reproduce the diagonal correlators of arbitrary quantum states, while a structured sparse support reduces the number of trainable coefficients to $m+1$ for $m$ graph variables. We evaluate the method on $1{,}400$ held-out random graphs with up to $7{,}000$ vertices, obtaining empirical approximation ratios near $0.98$ relative to MQLib heuristic references. On Gset instances G14, G23, G60, and G64, the sparse model achieves mean refined approximation ratios of $0.9828$, $0.9926$, $0.9781$, and $0.9369$, respectively, with $80.4\%$-$89.3\%$ fewer parameters than the complete Walsh representation. The trained coefficients are transferred without retraining to quantum circuits. Statevector simulations of the four Gset instances achieve fidelities above $0.99994$ and preserve all correlator signs. Separately, a seven-qubit experiment on a $15$-vertex graph executed on IBM quantum hardware achieves a correlator-sign agreement of $0.927\pm0.049$ relative to the corresponding noiseless circuit. These results demonstrate the potential of sparse Walsh-PCE for large-instance quantum-inspired MaxCut optimization while validating the transfer of classically trained parameters to quantum hardware.