Papers

Qudits provide a larger local Hilbert space than qubits and have recently attracted interest as building blocks for efficient fault-tolerant quantum computation (FTQC). In this work, we extend many-hypercube (MHC) codes, high-rate concatenated quantum codes, from qubits to qudits of prime dimension $q$. We construct the level-2 and level-3 MHC codes with parameters $\left[\!\left[6^2,4^2,2^2\right]\!\right]_q$ and $\left[\!\left[6^3,4^3,2^3\right]\!\right]_q$, respectively, and generalize the level-by-level minimum-distance (LLMD) decoder originally proposed for the qubit MHC codes. In a qudit $X$-error model, we evaluate the code-capacity performance of the qudit MHC codes for dimensions up to $q=13$. We find that the error threshold increases monotonically with the local dimension $q$, reaching $10.0\%$ for $q=13$, nearly double the value of $5.1\%$ for qubits. Furthermore, for sufficiently large local dimensions, we observe a pronounced waterfall regime in which the logical error rate decreases substantially faster than expected from conventional distance-based estimates. To understand the origin of the observed qudit advantage, we analyze the decoding performance in terms of the entropy of the underlying $q$-ary noise channel. This analysis reveals a competition between the increased syndrome information available at larger $q$ and the simultaneous growth of the typical physical error weight at fixed entropy. These results demonstrate that higher-dimensional quantum systems can substantially improve the performance of high-rate concatenated quantum codes and motivate further development of qudit-based FTQC architectures.

Quantum compilers play a critical role in transforming high-level quantum programs into optimized, hardware-compatible circuits. However, verifying the correctness of compiler passes remains challenging, as determining the expected output of large, deeply entangled quantum circuits is computationally intractable. This challenge is further amplified when compiler passes modify already complex circuit structures, making manual validation of transformed circuits impractical. In this work, we perform a systematic analysis of unit tests for quantum compiler passes in four quantum programming frameworks (PennyLane, Qiskit, Cirq, and pytket). Our findings indicate validation is dominated by program-content and program-metric assertions, and test circuits are generally small and shallow. Motivated by these observations, we introduce a testing methodology for automated validation of quantum compiler passes based on retromorphic testing and principles from the Hadamard test. This methodology analyzes a compiler pass, test circuit, and expected pass behavior to verify semantic preservation and intended structural modifications. We implement our methods in a framework, RetroQ, and apply it to compiler passes in PennyLane and Qiskit. Experimental evaluation reproduced several existing bugs as well as uncovered previously undetected defects, such as flawed symbolic parameter handling, incorrect commutation logic, failure to recognize self-adjointness of gates, and runtime crashes. These findings highlight the need for compiler-pass-specific testing methodologies to improve the reliability of the evolving quantum software stack.

An outstanding challenge in superconducting quantum circuits is mitigating loss from two-level system (TLS) defects. SWAP spectroscopy with flux-tunable qubits can detect individual TLSs, but the Rabi chevrons that signal coherent exchange have been observed only for the most strongly coupled defects. Here, we introduce a sequence with fast flux pulses only at state preparation and readout, switched off during the energy-relaxation delay for finer frequency resolution and longer interaction times. We detect Rabi chevrons at swap rates as low as 0.1 MHz, an order of magnitude lower than previously reported. In the dressed-state picture, we fit the coherent swap oscillations to extract the TLS energy-relaxation time. These Rabi chevrons reveal coherent TLSs with a median energy-relaxation time of 10 microseconds, at coupling strengths previously associated with incoherent TLSs. The swap coherence times exceed the qubit T2* limited by flux noise, indicating that the dressed gap protects them from low-frequency 1/f noise.

The three gauge couplings of the Standard Model (SM) can be parameterized as the fine structure constant $\alpha$, the weak mixing angle $\sin^2\theta_w$, and the strong coupling $\alpha_s$. They are fundamental constants whose values remain unexplained. Previously we showed that minimizing magic production in charged-lepton scattering reproduces $\sin^2\theta_w$ with great precision. Here we study magic production in the six flavor-diagonal color-singlet channels $q\bar q\to q\bar q$ at tree level, including photon, gluon, $W/Z$, and Higgs exchange. Varying only $\alpha_s$, with all other inputs fixed at each center-of-mass energy, we find that the finite-$\alpha_s$ magic minimum in the top channel reproduces the $\overline{\mathrm{MS}}$ value of $\alpha_s$ to within $5\%$ from $1~$TeV to $10^9~$GeV. Higgs exchange involving the large top Yukawa coupling is essential for this agreement. All six channels produce near-minimal magic at the SM couplings, and reducing $\alpha_s$ toward $\alpha$ increases their magic production, potentially explaining why the strong interaction is “strong.” To understand why minimizing magic reproduces both $\sin^2\theta_w$ and $\alpha_s$, we conjecture that the parameters of fundamental interactions among color singlets reflect a principle of quantum computational efficiency, with the physical universe emerging from a quantum simulation subject to constrained resources.

We show that, for stabilisers codes, there always exists a logical subspace requiring $\tilde{\Omega}(k^2)$ ancillary qubits to be measured with a sparse surgery ancilla. For CSS codes the hard subspace can be taken to be generated by all-X, or all-Z operators. As a result, for codes with large $k$, constant overhead ancillas can only realise a small fraction of possible measurements.

While conventional quantum resource theories quantify utility relative to an idealized set of free states, practical implementations are confined to a specific supply environment—a framework encompassing all states realizable or preparable via current experimental apparatus and design choices, not limited to free states. This work proposes a novel framework for evaluating the relative utility of arbitrary quantum states against the resource set made accessible by these current selections. We specifically focus our investigation on two canonical representations: the set of states reachable via free operations as the attainable boundary imposed by current experimental constraints, and the set defined through numerical optimization as the criterion for operational equivalence. Our framework establishes two core evaluation methodologies. First, we provide a strategy-dependent benchmark by assessing a state's performance relative to the reference set under its individually optimized strategy, thereby quantifying achievable performance. Second, we derive a computable lower bound on this superiority by considering optimal strategies for each state individually, enabling the quantification of strategy-independent relative performance independent of specific experimental setups. Beyond relative efficiency metrics, we demonstrate the practical utility of this approach for resource management scenarios, including the selective extraction of states advantageous for storage and distribution, and the concentration of residual resources. Using quantum entanglement as a paradigmatic example, we prove that distillable entanglement can be fully recovered via extraction and concentration when the reference set is restricted to pure states, thereby demonstrating the practical relevance of our framework.

Hyperbolic geometry hosts a plethora of exotic quantum phenomena ranging from holographic duality to novel topological phases. However, investigating these effects experimentally remains challenging due to the Euclidean constraints of natural crystalline materials. While recent synthetic lattices have achieved static realizations, they often lack the dynamical tunability required to explore the full geometric landscape. Here, we overcome these limitations by implementing a quantum simulation of hyperbolic geometry within the parameter space of a superconducting quantum circuit. We construct a Hyperbolically Driven Quantum System (HDQS) by mapping the hyperbolic properties onto the dynamically controllable Hamiltonian parameters. By probing the systems' response under geometric quantum driving, we elucidate how the intrinsic geometry of the parameter space dictates observable physical quantities. Furthermore, we extend the theoretical framework to realize ensemble simulation. This generalization enables us to harness the fast coherent control of superconducting qubits to capture essential geometric characteristics, establishing a versatile platform for exploring quantum dynamics on hyperbolic manifolds.

We show that the fast surgery framework of Baspin-Berent-Cohen can be instantiated using at most $\tilde{O}(n(k + d))$ ancilla qubits, improving on the previously achievable $O(n\cdot k \cdot d)$ overhead. This result also establishes that fast surgery can be performed at a cost comparable to the $\tilde{O}(nk)$ overhead required for regular surgery. We build the surgery ancilla by first starting with a dense, but expanding system; and then applying expansion-preserving sparsification methods from gauging and code embeddings.

Understanding the dynamics of interacting quantum fields remains a fundamental challenge. We propose a superconducting transmission line for analog quantum simulation of $(1+1)$-dimensional $\phi^4$ field theory. The transmission line comprises fluxonium-like circuit elements whose continuous and unbounded phase variables encode a scalar field without Hilbert-space truncation. Their anharmonic potentials provide strong interactions. Tuning the circuit parameters provides access to two distinct regimes. In the first, the transmission line emulates $\phi^4$ field theory with a single-well potential. We confirm this correspondence through lattice Monte Carlo calculations of the low-energy spectra of both the circuit and lattice $\phi^4$ theory. This regime enables scattering experiments between counter-propagating particle wave packets. The second parameter set yields a double-well potential that emulates $\phi^4$ theory in the symmetry-broken phase and hosts degenerate vacua. Interfaces between the two vacua form topological kinks, and the transmission line can simulate kink-antikink collisions. We present state preparation and measurement protocols for both collision experiments, enabling spatially resolved, real-time studies of particle and soliton scattering in an interacting quantum field theory.

Accurate excited state energies are essential for interpreting fluorescence and photochemical processes, yet variational quantum eigensolvers (VQEs) on noisy intermediate-scale quantum (NISQ) hardware have largely been confined to ground states. Subspace-search VQE (SSVQE) offers a NISQ-friendly route to excited states without ancilla-based overlap measurements, however it has lacked an experimental demonstration since it requires the coherent preparation and manipulation of multiple orthogonal basis states under a shared variational unitary. Here we realize SSVQE on a photonic platform by encoding orthogonal qudit states in the orbital angular momentum of single photons and optimizing a shared variational circuit. We estimate excited state energies for a four-dimensional $\rm{HeH^+}$ molecule and an eight-dimensional Heisenberg chain, thereby demonstrating scalable excited state eigensolving in a high-dimensional Hilbert space. Our results establish photonic qudits as a resource-efficient pathway to excited state quantum simulation.

Hybrid quantum neural networks (QNNs) pair a classical feature extractor with a variational quantum circuit, and the effective dimension of the circuit's quantum Fisher information matrix (QFIM) is widely used to assess such models. This scalar is often interpreted as an indicator of trainability or accuracy, although these readings are rarely tested under controlled conditions. We therefore investigate what it actually measures. We define the effective dimension as the participation ratio of the QFIM diagonal, which lies between one and the parameter count, and we evaluate it across two image datasets, four frozen backbones including a random-projection control, four circuit depths on eight qubits, and three seeds. During training, the effective dimension remains well below the parameter count, and its correlation with test accuracy ranges from -0.72 to +0.87, changing sign across seeds in half of the configurations. Increasing depth activates a larger share of the circuit directions, from 0.38 to 0.91 of the parameter count, while the initialization gradient variance remains between 1e-5 and 1e-4, so no barren plateau (BP) appears at eight qubits. At a fixed circuit, the four backbones share an initial effective dimension of 6 to 9, even though CIFAR-10 accuracy ranges from 23.14% to 86.44%. These results show that the effective dimension characterizes circuit geometry rather than model quality. We conclude with a practical protocol that assigns each diagnostic to the question it can answer.

The Travelling Salesman Problem (TSP) is a classic combinatorial optimisation problem which is NP-hard in optimisation form and NP-complete as a decision problem. The standard question asks for the shortest tour that visits every city exactly once and returns to the origin. This paper studies a threshold-fraction variant, which we call the robust TSP, formulated as a promise problem: given a distance threshold $K$ and a promised fraction $p$, decide whether at least a fraction $p$ of all tours have total length at most $K$, or whether no such tour exists. We show that Grover's quantum search algorithm decides this problem using $O(1/\sqrt{p})$ oracle queries, independent of the number of cities $N$, with each query implemented by a quantum circuit of polynomial size in $N$. For any fixed robustness level $p$, the total runtime is therefore polynomial in $N$. Measured in oracle queries, the quantum algorithm offers a quadratic improvement in the dependence on $1/p$ over classical random sampling, which needs $\Theta(1/p)$ samples; because each quantum query is costly, however, it is faster in total running time only when $p$ is very small (roughly below $N^{-4}$), where the number of queries is no longer constant. We describe the problem formulation, detail the oracle construction (edge-length loading, sequential quantum addition, and threshold comparison), and analyse the query complexity to achieve the required result.

Many-body entanglement in atomic ensembles offers the potential for enhanced sensing devices. Entanglement can be generated by interfacing atoms with a cavity. Traditional methods use effective two-level systems isolated from more complex atomic level structures. However, alternative strategies allow entanglement to be generated in atoms confined to a single hyperfine manifold. These strategies enable entanglement in ways fundamentally not available to two-level systems but feature extremely slow dynamics due to requiring strongly off-resonant laser fields. Here, I show that equivalent squeezing dynamics can be achieved much closer to resonance, offering entanglement generation over a hundred times faster than typical experiments. Furthermore, the Hamiltonian can be used to speed up the creation of maximally entangled states via adiabatic passage.

Orbital angular momentum (OAM) modes have emerged as an important platform for high-dimensional quantum communication but remain vulnerable to environmental noise and channel imperfections. Here we introduce a logical-qubit representation of OAM propagation in which modes evolve as qubits through noisy quantum channels. In this representation, turbulence manifests as leakage from the logical OAM subspace into turbulence-induced leakage components, providing a unified description of degradation in both single-photon and coherent-beam regimes. We show that turbulence-induced leakage exhibits systematic dependence on turbulence strength and OAM order, revealing structured signatures of information redistribution beyond the logical subspace. Leveraging this insight, we develop a distributed quantum feature-extraction scheme that encodes high-dimensional OAM states into quantum representations and employs quantum convolutional operations to extract turbulence-robust features. Simulations and experimental measurements demonstrate robust extraction of these features across a broad range of turbulence strengths, OAM orders, and propagation conditions. Our results establish a direct link between OAM-channel dynamics, structured leakage, and quantum learning, providing a physics-informed framework for characterizing turbulence-degraded high-dimensional optical states and extracting robust signatures of turbulence-induced information redistribution.

Spontaneous collapse models provide a possible, testable solution to the quantum measurement problem, but constructing a relativistic version applicable to quantum field theory remains an important open challenge. Challenges in constructing relativistic collapse models include avoiding superluminal signaling and foliation dependence, controlling energy production, and ensuring vacuum stability. Here, we present a relativistic collapse framework that addresses these problems at the cost of introducing a new space of physical states, whose complete characterization is left open. A modified, history-dependent Aharonov–Albert prescription describes instantaneous nonlocal state updates on arbitrary spacelike foliations while preserving foliation independence. To ensure vacuum stability, we modify the standard unitary evolution through a prescription that we name dynamical vacuum subtraction. The resulting dynamical map is linear and trace-preserving but not positive on the full set of standard density operators. We establish no-signaling by proving microscopic parameter independence, and identify conditions under which standard nonrelativistic collapse dynamics are recovered. Finally, we apply our framework to a free massive scalar field, obtaining finite particle-number and energy-increase rates at leading order in the long-time regime, together with further promising evidence for the consistency of the framework.

Quantum fault tolerance is a prerequisite to harness the full potential of quantum computers. However, achieving fault tolerance remains a major challenge since it requires optimizing tradeoffs between several intertwined theoretical and experimental parameters, including the encoding rate, code distance, parity-check weights, code planarity, and routing. Surface codes remain strong candidates for fault tolerance due to their simple geometric structure, established decoding methods, locality, and experimental attainability. In this work, we present finite families of hyperbolic surface codes that leverage the optimal efficiency scaling $kd^2/n = C (\log{k})^2$ attainable by surface codes with bounded local geometry. We show that optimizing the periodic identifications can double the code distance and thereby increase the code's efficiency by a factor of four, at fixed qubit count, encoding rate, and parity-check weight. We also address the routing problem of hyperbolic surface codes by introducing a topology-aware algorithm that partitions a hyperbolic code into bounded planar modules while reducing long-range communications demand. Circuit-level Monte Carlo simulations yield finite-size threshold estimates for both modular and monolithic layouts, showing that tripling the long-range gate error probability mildly lowers, but does not eliminate, the estimated error-correction thresholds. Together, these results strengthen the case for hyperbolic surface codes as structured and highly efficient large-scale quantum error correction codes for future fault-tolerant architectures.

Polaritons and quantum vacuum dressing are usually regarded as intertwined consequences of ultrastrong light-matter coupling. Here we show that they can be controlled independently through helicity. We consider cyclotron resonance coupled to a chiral cavity supporting a single circular mode. When the helicity of the cavity field matches the cyclotron motion, energy is exchanged resonantly between light and matter, producing a large Rabi splitting and conventional polaritons, while the ground state remains the bare vacuum. Reversing the magnetic field reverses the cyclotron motion without changing the cavity. The same mode then couples through anomalous processes that create and annihilate light and matter excitations in pairs: the conventional polaritonic anticrossing disappears, while the ground state acquires squeezing and virtual excitations. These two regimes show that spectral hybridization and quantum vacuum dressing are distinct manifestations of ultrastrong coupling, and that a large Rabi splitting alone does not imply a dressed quantum vacuum. Helicity therefore provides a route to controlling polariton formation and quantum correlations as distinct resources in cavity quantum materials.

In quantum mechanics of genus-1 potentials, perturbation theory around the topologically trivial saddle and non-perturbative instanton saddle are constructively related via the P/NP relation. Whether such a relation persists for higher-genus potentials has remained an open problem. In this work, we resolve it using tools from complex algebraic geometry combined with exact WKB. The classical energy conservation relation $p^2 = 2(E-V(q))$ defines a genus-g Riemann surface $X$, whose periods are naturally organized by its Jacobian variety $J(X) = \mathbb{C}^{\text{g}}/\Lambda$ via the Abel-Jacobi map, and independently by the solution basis of the associated Picard-Fuchs equations. We show that the physically relevant, WKB-active cycles are generally related to the Picard-Fuchs basis by a linear transformation that lies in $\text{SL}(2\text{g},\mathbb{Z})$ but not in the symplectic group $\text{Sp}(2\text{g},\mathbb{Z})$ once $\text{g}\geq2$, in contrast to the genus-1 case, where the two groups coincide. This mismatch is the obstruction that has made an explicit higher-genus P/NP relation elusive. We show that it can be resolved by passing to a modified Riemann bilinear identity, built from a suitably transformed intersection matrix, which the WKB-active periods do satisfy exactly. The result is an all-orders quantum P/NP relation valid for potentials of arbitrary genus, which we derive explicitly for genus-2 (quintic and sextic) and genus-3 (septic and octic) anharmonic oscillators.

Quantum fidelity estimation is a fundamental task in quantum information and computing to benchmark the quality of quantum states, and hence of quantum processes, on noisy quantum hardware. Point estimates of fidelity by existing methods generally lack the rigorous uncertainty quantification required for reliable preparation and verification of these tasks. While Bayesian and bootstrap frameworks are widely used for uncertainty quantification, they are sensitive to model misspecification or lack formal coverage guarantees in non-asymptotic regimes. This paper introduces a hybrid "Bayesian-informed" conformal prediction-based framework to provide distribution-free, rigorous prediction intervals for quantum state fidelity estimation which can be used, with care, to approximate confidence intervals with respect to the quantum randomness of Born's rule. The framework requires a point estimator, and we consider both classical point estimators as well as data-driven neural net estimators. We evaluate the robustness of the methodology across a diverse range of experimental challenges, including finite-sample noise, tomographic incompleteness, physical model error, and out-of-distribution data. Our results demonstrate that conformalized estimators maintain statistical validity where traditional methods fail, offering a scalable and reliable approach for the verification of modern quantum systems. The best performing variant of our methodology is based on a class-conditional conformal prediction, as this most closely approximates the conditional coverage desired for a true confidence interval.

We formulate diffractive ring focusing of paraxial beams carrying orbital angular momentum (OAM) through a finite circular aperture as a variational optimization problem. For a fixed topological charge, we determine the real-valued radial pupil that maximizes the intensity at a prescribed ring radius and propagation distance under a normalization constraint on the input field. The resulting problem admits an exact analytical solution: the optimal pupil combines the familiar Fresnel phase structure with an OAM-dependent Bessel radial modulation, and the associated eigenvalue yields a rigorous upper bound on the achievable ring intensity. We further analyze the lens-assisted configuration and derive a simple bound that allows direct comparison between diffractive and refractive vortex focusing. The theory also provides a quantitative framework for evaluating the performance of practical mask designs, including binary Fresnel-Bessel zone plates and amplitude-weighted pupils. We have experimentally tested our predictions in the optical domain by implementing the corresponding vortex beam pupils and comparing their propagation and focusing performance with the optimal solution. Our results establish the vortex-beam analogue of optimal amplitude-only focusing and identify the fundamental limits governing diffractive concentration of structured waves

One aspect of complexity for quantum many-body systems resides in their ability to exhibit entanglement, uniquely quantum correlations central to quantum computation. To quantitatively explore the diminishing effect that quantum noise has on entanglement resources, we focus on the negativity witness, an entanglement measure based on local time reversal transformations that provides a perfect witness in simple physical contexts. Beyond calculation of the negativity, we analyze the associated eigenvalue spectra of partially transposed density matrices for qudit-qudit bipartitions, finding that higher negativity rank provides greater(reduced) robustness to targeted(depolarizing) noise. In particular, we extend the maximum number of separable states that can be arbitrarily mixed into an entangled pure ensemble while retaining negativity to be exactly equal to the original negativity rank. Furthermore, we report how understanding the role of the negativity rank with respect to the completely depolarizing channel allows direct calculation of (1) certain noise boundaries for the Absolutely Positive Partial Transpose (APPT) subspace beyond which no unitary operator is capable of generating negativity and (2) the maximum qutrit-qutrit APPT purity. Beyond proving tight bounds and contributing to the ongoing search for APPT entanglement, these results expand our understanding of the nuanced relationship between computation with entanglement and practical environments for operating quantum devices.

We investigate the relaxation dynamics and steady state of a qubit interacting with a coherent environment through an energy-conserving flip-flop interaction within the Markovian repeated-interaction framework. We derive an exact analytical solution for the evolving and stationary state, nonperturbative in the environmental coherence. We show that environmental coherence provides a resource for dissipative state preparation by expanding the set of accessible steady states. In particular, coherent ancillas can increase the system ground- state population beyond that of the bath, corresponding to an effective temperature below the bath temperature, and enhance its steady-state purity, with these effects controlled by the interplay between the system energy scale and the system-ancilla coupling. Nevertheless, we prove that the purity of the system can never exceed the purity of the ancilla. We further analyze the thermodynamics of the protocol and show that environmental coherence can modify and even reverse the natural direction of heat transfer, giving rise to anomalous heat flow. Remarkably, for fixed interaction parameters, the direction of the coherence-induced heat transfer is governed by the relative phase between the system and ancilla coherence, whereas their magnitudes determine the amount of heat exchanged. Our results establish environmental coherence as a resource for controlling steady-state preparation and energy transfer in repeated-interaction dynamics.

The Minimum Birkhoff Decomposition (MBD) seeks a sparse weighted sum of matchings and is a challenging optimization problem with applications in network scheduling and energy trading. We scale a quantum-assisted decomposition method by combining single-layer QAOA sampling with Extended Fully-Corrective Frank-Wolfe (E-FCFW) optimization, spectral graph partitioning, and greedy feasibility repair. We demonstrate the pipeline on the 1,354-node PEGASE bus test case (representing a 1,354-bus transmission grid with 1,710 transmission lines), whose 1,710 edges define a native 1,710-variable matching optimization problem requiring 1,710 qubits in the unpartitioned encoding. Partitioning enables distributed execution on IBM superconducting quantum processors. The best reported hardware result uses a 50-qubit partition bound, while reducing partitions to 20 qubits degrades convergence in the partition-size comparison. Larger partitions are more demanding for matrix product state (MPS) simulation, and bond-dimension tests show that truncating quantum correlations reduces candidate quality. The results therefore motivate retaining a substantive quantum sampling task within each partition as the overall problem scales. On the PEGASE-1354 benchmark, repaired QAOA samples achieve lower residual decomposition error than both simulated annealing and uniform random sampling baselines, while spatial circuit packing reduces hardware execution time by approximately a factor of three. These results demonstrate that combining spectral partitioning, spatial circuit packing, and classical feasibility repair provides an executable path for deploying gate-based quantum sampling on thousand-variable constrained optimization problems on current hardware.

The island proposal guarantees a unitary Page curve for evaporating black holes, implying that operators deep behind the horizon must be fully reconstructable from asymptotic Hawking radiation. However, because the interior is causally disconnected and highly dynamical, standard entanglement wedge reconstruction methods, relying on global isometries or continuous modular flow, fail to provide this mapping. We resolve this by constructing a protocol for island reconstruction using the algebraic Petz map. By using modular theory, we reflect island operators into the accessible complement, transport them to the boundary, and map them into the radiation algebra. Furthermore, we demonstrate that this purely algebraic derivation naturally yields the structure of Papadodimas-Raju mirror operators. This framework provides a rigorous operational dictionary for the island formula, proving that information trapped inside a black hole can be decoded.

Effective models make complex quantum dynamics tractable by retaining only the states, processes, and timescales relevant to a given physical question. Their predictive power, however, depends on treating the retained manifold, initial state, observables, micromotion, dissipative channels, and eliminated degrees of freedom consistently. We develop a unified framework for constructing and validating effective descriptions using projection methods, Schrieffer–Wolff transformations, Magnus expansions, adiabatic elimination, small rotations, time coarse graining, and Floquet theory. The quantum Rabi model and its dispersive limits serve as recurring benchmarks for identifying control parameters, virtual processes, spectral corrections, observable dressing, and breakdown. Higher-order resonances and applications to collective light–matter coupling, Raman processes, spin-chain buses, lossy mediators, and driven lattices illustrate how effective interactions can be interpreted and designed. A physical prediction is organized into three order-consistent steps: encoding into the retained description, evolution under the effective dynamics, and reconstruction of the physical observable. This viewpoint exposes failures caused by leakage, small denominators, neglected micromotion, inconsistent observables, memory effects, or incorrectly transformed dissipation, while linking derivation, physical interpretation, and mechanism-guided discovery. Companion notebooks provide QuTiP implementations, convergence tests, and microscopic-to-effective comparisons.

Many potential future events have devastating consequences, from the onset of earthquakes to financial black swan events. Accurate predictions of their probability of occurrence are vital. Yet as the stochastic systems underlying such events become increasingly complex, these probabilities can depend on ever-growing amounts of past data, which require ever more memory to track. The accuracy of our estimates is ultimately limited by both computational and memory constraints; the former to reduce sampling error, the latter to avoid sampling bias. Traditional quantum algorithms – such as amplitude estimation – address only the former, and become untenable especially in near-future quantum devices where quantum memory is a premium. Here, we offer quantum-algorithmic means to reduce systematic bias while maintaining a quadratic speed-up. Our results thus advance the timeline for the practical deployment of quantum technologies, and illustrate their additional benefits when simulating processes of growing complexity.

Quantum low-density parity-check (qLDPC) codes can substantially reduce the qubit overhead of fault-tolerant quantum computation, but any useful architecture based on such codes also requires an efficient mechanism to implement non-Clifford gates in a fault-tolerant manner. We introduce a space-time-efficient magic state factory for high-rate qLDPC codes by combining the transversal non-Clifford gates of recently developed tricycle codes with single-shot four-dimensional balanced product quadcycle codes. The key ingredient is an efficient "escape" mechanism that teleports postselected logical magic states from tricycle codes to larger distance quadcycle codes. Under a standard circuit-level noise model at physical error rate $10^{-3}$, our factories produce $\mathrm{CCZ}$ states at logical error rates as low as $10^{-9}$ with 10-40 times lower space-time cost than state-of-the-art magic state generation methods. The resulting states are directly encoded in high-rate blocks suitable for computation. We identify the quadcycle codes by an AI-assisted search and show that they can serve as excellent memories capable of single-shot error correction. Finally, we present a concrete implementation of the entire factory with highly efficient atom transport on reconfigurable neutral-atom quantum computers. Together, these results provide an end-to-end, practical protocol for producing and utilizing high-fidelity magic states within a high-rate qLDPC architecture, with the lowest space-time cost to date.

Optimizing Josephson-based nonlinear microwave devices is computationally demanding because the straightforward approach requires exploring broad circuit parameter spaces through expensive nonlinear simulations. Josephson Circuits Optimizer addresses this problem by using harmonic balance simulations in two stages: fast linear simulations to select promising circuit configurations according to properties such as impedance and phase matching, followed by nonlinear simulations to optimize their operating conditions. However, pump-induced effects such as impedance renormalization and Kerr-induced modifications of phase matching are not captured during the initial linear stage. We therefore introduce a nonlinear feedback extension that transfers information from the pumped response back to the linear optimization. The approach is investigated using a Josephson traveling-wave parametric amplifier with a reversed-Kerr architecture, whose model is validated against experimental gain measurements. We then evaluate the difference between the linear and pumped response values of a metric based on the input reflection coefficient, while excluding configurations with insufficient third-harmonic suppression. This discrepancy is considered a candidate feedback observable, as it exhibits features similar to the gain landscape, supporting its use in subsequent optimization cycles.

Quantum mechanics predicts that a vibrating object's energy comes in discrete packets, yet no measurement of its position reveals this discreteness. Resolving individual energy levels requires a qualitatively different measurement, one coupling to the resonator's energy rather than its displacement. We use a superconducting qubit dispersively coupled to a nanomechanical resonator to perform repeated quantum nondemolition measurements of the phonon number. An aligned transfer-print technique integrating the qubit and resonator yields a mechanical lifetime of $T_1 = 2.1$ milliseconds and a dispersive shift of $2\chi/2\pi = 328$ kilohertz per phonon. We heralded single-phonon states with 85% fidelity and observed quantum jumps between the resonator's first excited state and ground state. These discontinuous transitions are a striking manifestation of quantum mechanics in a massive, vibrating object.

A long-term goal of quantum simulation is to faithfully reproduce the low-energy Hamiltonians of correlated quantum materials, establishing a direct connection between solid-state experiment, electronic-structure theory, and programmable many-body systems. Here, we introduce an integrated quantum-simulation architecture based on fermionic alkaline-earth atoms that enables programmable control over the key ingredients of multi-orbital material Hamiltonians. Long-lived clock states encode synthetic orbitals, their differential polarizabilities generate orbital-selective tunneling, and contact interactions provide multi-orbital Hubbard and Hund couplings. Spatially structured coherent driving on the ultra-narrow clock transition further realizes symmetry-selective inter-orbital hybridization, while the clock detuning independently controls orbital energy offsets. In this way, the spatial symmetries of solid-state orbitals can be encoded directly into the effective Hamiltonian, even though the atoms themselves remain in conventional $s$-wave Wannier orbitals of the lowest optical-lattice bands. We demonstrate the resulting integrated control using the four-band low-energy Hamiltonian of the bilayer nickelate La$_3$Ni$_2$O$_7$ as a demanding benchmark. Self-consistent calculations show that the microscopic parameters obtained from first-principles modeling can be reproduced within a single experimentally accessible lattice configuration and independently programmed over substantial parameter ranges. Our results establish a general route for translating material-derived multi-orbital Hamiltonians into programmable ultracold-atom quantum simulators.