Papers

Rotation-symmetric cat (RS-cat) codes are a bosonic-code platform for quantum information processing, combining finite-energy realizability with robustness against photon loss through their discrete rotational symmetry. For applications in long-distance quantum communication and fusion-based quantum computation (FBQC), efficient Bell state measurement (BSM) is a key primitive. In this work, we consider a BSM protocol for RS-cat codes using only a half beam splitter (HBS) and photon-number-resolving detectors (PNRDs). By exploiting the characteristic photon-number structure induced by the discrete rotational symmetry of RS-cat codes, our protocol extracts both photon-number modulo and phase information for Bell-state discrimination. We show that, under ideal loss-free conditions, the proposed BSM protocol becomes deterministic for arbitrary symmetry order $N$ for sufficiently large amplitudes $\alpha$. We further numerically evaluate the success probability under photon loss and identify the loss regime in which higher-order RS-cat codes provide an advantage. Finally, we show that post-selection can enhance the success probability.

We introduce a gauge-propagation approach for approximately converting generic tensor-network states into an isometric tensor-network form with a prescribed orthogonality center. In one dimension, this propagation is exact because the non-isometric factor produced by a QR or singular-value decomposition is supported on a single virtual bond. In higher-dimensional networks, however, a local step can have several outgoing directions, and the residual factor is generally not separable into independent single-bond contributions. We address this local obstruction by approximating a local tensor, or a contracted local cluster, by structured terms consisting of an isometric factor multiplied by a tensor product of output-leg factors. The isometric factor is retained at the current site or cluster, while the output-leg factors are absorbed into neighboring tensors along the propagation directions. This construction applies to general local input-output partitions for which the input-side dimension is no smaller than the output-side dimension and provides a local truncation criterion for gauge propagation. Benchmarks on random tensors show that the proposed decomposition is effective in the low-term regime and that the residual decreases for larger local clusters. For the loop-gas tensor representation of the Kitaev spin liquid, two structured terms reduce the local residual to numerical precision, and the same cluster refinement further lowers the leading-term truncation error and reduces error accumulation during gauge propagation on a finite honeycomb network. These results identify a propagation-compatible local decomposition as a useful building block for approximate isometrization and as a potential initializer or preconditioner for variational isoTNS algorithms.

We show that incoherently pumped qubits can realize a cascaded dissipative mechanism for stabilizing Wigner-negative magnon steady states. The mechanism combines qubit pumping with dispersive magnon-number selectivity to direct the steady-state population toward selected magnon Fock states. In the single-qubit case, the single-magnon population can approach unity, accompanied by strong antibunching and pronounced Wigner negativity. Extending the same principle to multiple qubits yields Wigner-negative steady states dominated by higher magnon Fock components. We further derive an analytical birth–death model that captures the mechanism and agrees with numerical results. These results establish incoherent qubit pumping as a controllable dissipative resource for generating nonclassical magnon states in hybrid quantum systems.

Measurement-based continuous-variable optical quantum computing inherently offers high-speed, large-scale operations, yet its practical performance remains constrained by the processing latencies and throughput bottlenecks imposed by classical electronic feedforward circuits. To overcome these limitations, we propose a loss-tolerant, all-optical feedforward (AOFF) architecture for generalized quantum teleportation capable of executing arbitrary linear operations. Quantitative noise analysis under realistic device parameters demonstrates that the architecture successfully suppresses hardware-induced noise floor, confirming its compatibility with fault-tolerant quantum computing requirements. By eliminating optoelectronic conversions, this scheme enables continuous high-throughput operations that drastically reduce circuit runtime. Ultimately, this approach delivers a noise-resilient platform that reconciles operational versatility with the intrinsic speed and bandwidth of optical quantum information processing.

We investigate the thermodynamic performance of a quantum Otto machine whose working substance is a single electron confined in a double quantum dot under an external magnetic field and Rashba spin-orbit interaction. The Hamiltonian is controlled by the Zeeman splitting, the interdot tunneling amplitude, and the Rashba coupling, which induces spin-flip tunneling between localized orbital states. Within a quasistatic Otto cycle, we analyze the heat exchanged with the reservoirs, the extracted work, and the efficiency as functions of the Hamiltonian parameters and reservoir temperatures. We show that the Rashba interaction acts as an effective control parameter for switching among heat-engine, refrigerator, heater, and accelerator regimes. A global numerical analysis over the Hamiltonian parameters and reservoir temperatures identifies the optimal operating points for efficiency and work output in the heat-engine regime. The highest efficiencies occur near the maximum temperature gradient explored and approach the Carnot bound, whereas the largest work output appears in a different region of parameter space. The results reveal a clear trade-off between maximum efficiency and maximum extracted work, governed by the spectral deformation induced by the Zeeman splitting, tunneling amplitude, and Rashba coupling.

Reading out a qubit often requires coupling it to a resonator, but that same resonator can also give the qubit an extra path to decay. Here, we study a way to reduce this loss using a built-in permanent electric dipole. The dipole shifts the cavity field in different directions for the qubit ground and excited states. This shift makes the relevant wave functions overlap less, which weakens the transverse qubit–cavity exchange that causes Purcell decay. In a simplified displaced rotating-wave model, this exchange vanishes at $\eta=\sqrt{2}$. In the full transverse model, this exact zero is lifted, but strong suppression remains at a larger dipole-induced displacement. Using dressed open-system decay rates, we find an operating point where the cavity-mediated decay is strongly reduced while the longitudinal readout signal remains finite. For the benchmark studied here, at fixed pointer separation, the normalized lifetime increases from $\kappa T_1=11.1$ to $47.3$, and the estimated single-shot readout error drops from $0.21$ to $0.07$. These results show that permanent electric dipoles can provide an internal, channel-selective form of Purcell protection.

We study the broken-symmetry phase of the Lipkin-Meshkov-Glick (LMG) model, whose two lowest states form a near-degenerate parity doublet split by tunnelling. We show that the same instanton action S_inst that sets the doublet splitting also controls how much parity information a static J_z magnetisation readout can extract. Although J_z measures magnetisation rather than parity - and so distinguishes the two wells easily while remaining almost blind to their relative sign - WKB barrier arguments together with exact diagonalisation show that the spectral gap, the total-variation distance, and the nonlinear distinguishability measures (Jensen-Shannon divergence and Chernoff information) share a single instanton exponent, rather than the doubled exponent a naive small-deviation expansion in the lobes would suggest. Exact diagonalisation up to N = 4500 supports a common leading exponent for all four quantities, with fitted values within a few percent of the WKB instanton value in the largest reliable windows. The same coupling acts strongly inside the doublet: its off-diagonal element grows as |J_01| -> N m_*/2, so the bath can disturb the parity label far more strongly than it can read it from a frozen histogram. We call this separation the static parity horizon - a benchmark for the idealised static J_z channel, not a universal bound on time-resolved monitoring. Restoring the full monitored dynamics, continuous-monitoring simulations (1.48 million full-LMG trajectories with matched QND controls across 77 independent settings) show that a time-resolved homodyne record extracts parity information hidden from the single-shot histogram, over a finite window of system sizes organised by the ratio xi = omega_01/Gamma_01 of coherent doublet rotation to measurement-induced dephasing, and closing again under strong measurement.

High harmonic generation (HHG) is a highly nonlinear optical process in which radiation from a strong driving field is up-converted into its high-order harmonics. In atomic systems, this nonlinearity manifests itself through the intensity scaling of the emitted harmonics with the driving field strength. Despite the highly nonlinear nature of HHG, when the driving field is prepared in a classical Gaussian state and atomic depletion remains negligible, the quantum statistical properties of the generated harmonics retains classical Gaussian quantum statistics. Driving HHG with bright squeezed vacuum (BSV) light challenges this paradigm, as its enhanced field fluctuations can modify the statistical properties of the generated harmonics. In this work, we investigate the conditions under which BSV-driven HHG gives rise to non-classical Gaussian states, and identify the regimes where this Gaussian description breaks down. For bichromatic driving by a strong coherent field at frequency $\omega$ and a perturbative BSV field at $2\omega$, the even-harmonic response is approximately linear in the BSV quadrature, leading to non-classical multimode Gaussian entanglement in the harmonic field. We show that this state can be described as a distributed collective squeezed mode over the even-harmonic manifold, and characterize its covariance matrix, entanglement structure, and quantum teleportation fidelity as an operational benchmark. Our results highlight the potential of non-classically driven HHG as a platform for engineering Gaussian and non-Gaussian states of light in the extreme ultraviolet regime.

The empirical bitstring distribution is the most accessible observable on Rydberg-atom arrays, but the bipartite von~Neumann entropy it constrains is far costlier to obtain. We present a six-term linear closed form for the entropy, built on bitstring-derivable physics scalars, and characterize its accuracy, portability, scaling behaviour, and calibration cost. The feature set is selected with guidance from a trained graph neural network: probing the network localizes its entropy prediction to the two-point correlators on the bipartition boundary, and an exhaustive ground-truth search restricted to those boundary correlators isolates the form. It reaches $0.024$~nats mean absolute error in distribution: $6.4$ times the network's error, but in a form a human can read and apply without retraining. Fit once and applied unchanged, it has lower error than the base network on five of six out-of-distribution pools and ties the sixth. An independent density-matrix renormalization-group study to one hundred atoms – five times the reach of exact diagonalization – settles the size-extrapolation question: coefficients frozen at small size fail at scale, but the failure is structured. Refit per size the form holds to $25$–$50$~mnat (cross-validated); two of its six slopes follow clean inverse-size laws, one a downward curving growth, and the others are trendless; the fitted laws deploy the form label-free at roughly $40$–$80$~mnat. The result fixes a label-budget rule: at large sizes, a few dozen labels recalibrate the closed form to match a fine-tuned in-distribution ensemble on the same features, while nonlinear ML models pull ahead only given large labelled datasets.

We construct an explicit Lewis-Ermakov-type dynamical invariant for time-dependent two-level systems by exploiting their algebraic correspondence with the time-dependent harmonic oscillator through the $su(2)$ and $su(1,1)$ algebras, which share the common complexification $sl(2,\mathbb{C})$. This invariant provides a closed-form evolution operator and an exact propagator for arbitrary time-dependent coupling $a(t)$ and detuning $b(t)$. We illustrate the method on representative scenarios, including Landau-Zener transitions, non-Hermitian dissipative processes, and adiabatic rapid passage, and we obtain inverse-engineered shortcuts to adiabaticity with fully explicit control fields when the auxiliary scaling function is taken to be real.

We propose a direct, model-independent search for irreversible coherence loss during a reversible measurement. A mesoscopic apparatus measures a microscopic two-state system by storing which-state information and is then returned to its pre-measurement state; unitary quantum mechanics predicts recovered coherence, while collapse leaves residual endpoint loss. In one representative device, a coherently controlled molecular force source displaces a charged nanoparticle that serves as the apparatus; during one $4.19\,{\rm ms}$ measurement-and-reversal cycle, its two states become almost fully distinguishable. Such a device would give a first direct bound in a measurement-and-reversal setting. Repeating this cycle $5\times10^5$ times would bound the corresponding irreversible coherence-loss rate beyond ordinary decoherence at $5.51\,{\rm s}^{-1}$. Continuous Spontaneous Localization is included as a secondary benchmark on the same apparatus history.

We extend the nullifier-based certification framework of catability from parity-defined coherent cat states to parity-less Kerr cat states. Since Kerr cats cannot be distinguished by parity alone, we replace the parity component of the original nullifier with a displaced-parity operator that captures their characteristic interference structure. The resulting generalized catability remains directly observable and can be evaluated from a finite number of photon-number measurements without full state tomography. Numerical benchmarks show that the method faithfully certifies Kerr-cat features, produces accurate approximations of ideal Kerr cat states, and is more resilient to optical loss than fidelity-based certification. We also identify an exact anti-linear nullifier based on complex conjugation, providing an ideal algebraic description of Kerr cat states. Our results broaden the scope of catability and provide an experimentally practical approach to the characterization of Kerr cat states.

A holographic code assigns a state-dependent entropy remainder to every boundary region, but such remainders need not be the extremal lengths of any one bulk metric. We study this common-source question for the proto-area of a calibrated recovery, the entropy of a boundary region minus that of the matter recovered from it. At zeroth order the reference values must match the lengths of one reference geometry in a fixed renormalization scheme, and this matching also determines the entropy-to-length factor. On a graph with a fixed minimum-cut chamber the data derivatives must lie in the image of the cut-incidence matrix, whose left null vectors are witnesses. On the hyperbolic disk the first variation of renormalized length is the rank-two geodesic X-ray transform, with closed range in an adapted data space, and the geodesic displacement, fixed by a forced Jacobi equation, enters at second order. The resulting normal Hessian gives a gauge-invariant criterion, necessary and sufficient, for a regular pair of response coefficients to come from one metric two-jet. For the constant-curvature family generated by a boundary reparametrization the Hessian has a nonzero rank-four mode, so the image of the length map is curved. For a fixed recovery the proto-area Hessian is minus the Bogoliubov-Kubo-Mori information lost in recovery, which the Petz map decomposes orthogonally at a product reference, and which, on a finite-dimensional space of logical directions with positive minimum retained fraction, is at most a sharp multiple of the retained information. Geometric realization requires this loss to reproduce the normal length Hessian on every interval. Two codes show that exact regional area operators can fail to sew into one graph geometry, and that a matched reference with vanishing first response can fail at second order. All criteria refer to one recovery branch and one extremal-surface branch.

High qubit overhead is a key bottleneck for fault-tolerant quantum computation. Quantum low-density parity-check (qLDPC) codes offer high encoding efficiency but typically require non-local connectivity in every syndrome extraction cycle, incurring additional physical errors and implementation complexity. We introduce a hierarchical logical processor (HLP) architecture that implements a high-rate quantum CSS code with distance-$d_{0}$ rotated surface codes (RSC), allowing long-range connectivity to be used only once every $\Theta(d_{0})$ rounds of surface-code syndrome extraction. HLPs introduce elongated RSC patches called shuttle buses. Using transversal hybrid-unit CNOT gates, a single shuttle bus can simultaneously couple to multiple standard RSC patches. This capability enables efficient level-1 syndrome extraction with suppressed level-1 error correlations and supports highly parallel logical Pauli measurements. We perform circuit-level simulations of several concrete HLP constructions and benchmark both logical memory and logical Pauli measurement performance. At a physical error rate of $10^{-3}$, a hierarchical logical processor can achieve 3-4 times higher qubit efficiency than the rotated surface code and 20-30 times shorter logical error-correction cycle times than the yoked surface code.

The quantum Hamming bound arises from a direct dimension estimate for exact quantum error-correcting codes. For nondegenerate codes, distinct correctable errors map the code space into orthogonal subspaces, so dimension counting directly gives the bound; degeneracy allows these subspaces to overlap and invalidates the argument. Although linear-programming, asymptotic, and structural approaches have advanced the problem from several directions, the general local-dimension case has remained open. Here we prove the quantum Hamming bound for every local dimension $q\ge3$. Building on the exact two-center Fourier reduction, we develop new overlap estimates for nonbinary Hamming spaces. For $q\ge4$, Jacobi estimates and monotonicity give a uniform gap; qutrits form the boundary case where the gap vanishes and are handled by a filtered correction. This completes the finite-length nonbinary case; together with the existing qubit result, it establishes the quantum Hamming bound for arbitrary local dimension.

Liouville pathways provide the conceptual foundation for interpreting multidimensional spectroscopies and are commonly represented as independent contributions to the nonlinear response. In open quantum systems, however, the effective reduced Liouvillian need not preserve this observational pathway decomposition. Environmental interactions can transport amplitude between pathway sectors during the free-evolution intervals, generating measurable signatures in the nonlinear spectroscopic response.} We develop a geometric framework in which pathway transport is governed by a Liouvillian connection, its associated curvature, and the resulting observational holonomy. The framework applies to open quantum systems in which the environment selects a pointer basis distinct from the observational basis used to construct the spectroscopic response. This basis incompatibility induces transport among Liouville pathways, generating characteristic spectral distortions and a nontrivial Liouvillian curvature. Using a Duhamel expansion of the Liouvillian propagator, we derive a reconstruction procedure that identifies the transport operators responsible for the observed redistribution of pathway weight, accurate throughout the full range of basis misalignment. This perspective reframes spectral features as determined not only by which pathways exist but by how amplitude is transported among them. Spectral distortions, peak shifts, and otherwise-forbidden pathway contributions become geometric signatures of a curved Liouville-space manifold rather than phenomenological broadening corrections, identifying pathway geometry as a complementary layer of organization in nonlinear spectroscopy.

We develop a response-geometric framework for open quantum systems by decomposing the stationary-state response tensor into symmetric and antisymmetric sectors. The symmetric sector defines a metric-like response tensor governing local susceptibility, while the antisymmetric sector defines a curvature two-form associated with nonreciprocal response and geometric work. We show that the work curvature is precisely the antisymmetric component of the response tensor, establishing a fluctuation–response relation that extends the geometric structure of equilibrium thermodynamics to nonequilibrium steady states, and reveals a response geometry with both metric and symplectic sectors. In equilibrium, the antisymmetric sector vanishes by reciprocity, recovering the familiar metric geometry of thermodynamic response. Open quantum systems admit a broader structure in which reciprocal and nonreciprocal responses coexist on the same control manifold. We illustrate this with a driven dissipative qubit under pure dephasing, where finite curvature emerges from the misalignment between the Hamiltonian eigenbasis and the pointer basis selected by the environment, without requiring strong driving or engineered reservoirs. Comparison with the Bures metric shows that response geometry and information geometry characterize distinct properties of the stationary-state manifold: the former governs susceptibility and geometric work, the latter quantifies state distinguishability. Geometric work thus emerges as a measurable signature of nonreciprocal response in open quantum systems.

We study the effect of subsystem decoherence to an extended cluster state which is a symmetry protected topological (SPT) phase. The model includes many subsystem $Z_2$ symmetries. We report that subsystem decoherence induces local charge fluctuations, leading to a mixed SPT state in the unaffected subsystems. If we start from the extended cluster state, hierarchical mixed-state SPT phases emerge in response to step-by-step subsystem decoherences. These mixed-state SPT phases keep strong symmetries the symmetry of which is protecting symmetries for the initial cluster SPT. Moreover, these SPTs can be characterized by Rényi-2 string orders. Then, as the subsystems are progressively decohered, the hierarchy of mixed-state SPT phases terminates in a $Z_2$ strong-to-weak spontaneous symmetry breaking (SWSSB) state on the final remaining subsystem, where a long-range entangled state appears, namely a glassy Greenberger-Horne-Zeilinger (GHZ) state. Our work demonstrates that decoherence is not merely a destructive process, but can induce and organize series of nontrivial mixed-states. This reveals a systematic route from mixed-state SPT order to SWSSB with the glassy GHZ-type long-range entanglement.

The spatial confinement of defect-induced bound states is conventionally governed by the effective mass in dispersive bands. More recently, Compact Localized States (CLSs) arising from exact destructive interference have been utilized to achieve confinement in flat bands. However, CLSs rely on pristine lattice symmetries and fine-tuned defect profiles. The introduction of a generic local impurity inevitably breaks these strict phase-matching conditions, resulting in extensive bound states whose fundamental length scale has remained an open question. Here, we establish a third regime of confinement: the quantum metric bound state. We provide a rigorous mathematical proof demonstrating that in the absence of kinetic energy and CLS protection, the exponential decay length of these states is lower-bounded by the quantum metric of the unperturbed flat band. We demonstrate the tightness of this geometric limit by constructing a family of highly tunable flat-band generators, and we verify its universality across diverse realistic architectures. Ultimately, this classification establishes the independently measurable quantum metric as a predictive design principle for engineering confined modes in synthetic wave platforms.

Fault tolerance is an indispensable prerequisite for constructing large-scale universal quantum computers. Drawing philosophies from classical computer architecture, this paper presents a hardware-agnostic three-layer high-level architectural framework for generic fault-tolerant quantum computation. Guided by the real execution workflows of fault-tolerant quantum algorithms, the proposed model is decoupled from specific physical qubit hardware platforms and quantum error correction codes, serving as a universal abstract standard rather than a platform-specific implementation scheme. Special attention is devoted to the intermediate Fault-Tolerance Layer, which serves as the architectural bridge between application-level logical programs and hardware-level execution. We systematically characterize its five internal components, the interfaces and data exchanged among them, and the execution, correction, and adaptation paths that together enable logical synthesis, fault-tolerant resources management, decoding, and runtime fault-tolerant control. An end-to-end example is further provided to illustrate the full-stack operating pipeline of fault-tolerant quantum algorithms under this framework. Given the increasing emphasis on modular, heterogeneous, and cross-layer fault-tolerant quantum systems, our architecture provides a unified foundational model for organizing such designs.

Experimental progress in quantum simulators highlights the role of long-range (LR) interactions in reshaping quantum criticality and stabilizing exotic phases beyond the short-range (SR) paradigm. We study ferromagnetic long-range quantum $O(n)$ models with interactions decaying as $1/r^{d+\sigma}$ and develop a perturbative renormalization-group expansion around the LR–SR boundary by setting $d=3-\epsilon$ and $\sigma=2-\delta$. In this parametrization, the full interacting LR window $2d/3<\sigma<2$ becomes $0<\delta<2\epsilon/3$, and is therefore perturbatively controlled. A two-loop calculation yields explicit expressions, in terms of $\epsilon$, $\delta$, and $n$, for the correlation-length exponent $\nu$ and for the frequency and momentum anomalous dimensions $\eta_\omega$ and $\eta_k$. The resulting exponents reduce to long-range Gaussian scaling at $\sigma=2d/3$ and to SR quantum Wilson-Fisher scaling in the $\sigma \to 2$ limit, thereby identifying $\sigma_*=2$ as the LR–SR boundary within the controlled $3-\epsilon$ expansion. Combining the RG results with scaling boundaries and classical LR analogies, we propose a $(d,\sigma)$ universality diagram for ferromagnetic long-range quantum $O(n)$ criticality and use it as an organizing framework for the phase diagram of long-range quantum spin chains.

We propose a microscopic realization of the idle-level quantum heat engine architecture based on a two-qubit non-Hermitian XY model with a staggered imaginary magnetic field. The energy spectrum naturally separates into two working levels coupled to the external field and two field-decoupled idle levels entirely independent of it. Tuning the non-Hermitian parameter drives the system from a dissipative accelerator regime into a genuine heat engine regime, while simultaneously enhancing both the net work output and the cycle efficiency. The efficiency enhancement originates from the compression of the idle-level gap, which redistributes level occupations and progressively suppresses the idle-level heat current, signalling the approach to the reverse heat-flow regime that underlies the idle-level engine principle. We map the full thermodynamic phase diagram identifying engine, refrigerator, accelerator, and heater regimes, and decompose the heat current into working-level and idle-level contributions to clarify the microscopic origin of the performance gain. The model is implementable in trapped-ion and NMR quantum simulators. These results establish non-Hermiticity as a versatile control knob for idle-level quantum thermal machines.

Superconducting quantum computing is one of the most mature solid-state platforms for quantum computation, with processors exceeding one hundred qubits. Yet further scaling toward fault-tolerant quantum computing is increasingly constrained by calibration complexity. Conventional scripts are brittle to anomalous signals, and expert judgment is bounded by cognitive bandwidth and serial operation time, failing to keep pace with system scale. Here we report Vibe Calibration, an autonomous calibration system orchestrated by large language model agents, which distills expert tacit knowledge into reusable Skills. Each Skill is organized as a decision tree that packages parameterized measurement commands, quantitative acceptance criteria, and audit records, enabling autonomous execution and self-healing. We capture this knowledge through a three-phase human-in-the-loop distillation process and fine-tune a large language model on validated trajectories. On a 112-qubit processor with frequency-tunable transmons, the system autonomously completes calibration of 108 out of 112 qubits in 4.7 hours, achieving a 4–5$\times$ speedup over manual calibration of the full 112 qubits. A cross-validated comparison with expert manual calibration on a 16-qubit subset shows agreement on 14 out of 16 qubits. More importantly, the model demonstrates transferable calibration workflows across devices. While low-level control scripts require minor interface adaptation for different hardware platforms, the core decision logic and task orchestration generalize to new processors, demonstrating a reusable laboratory interface rather than a memorized script.This work demonstrates, for the first time, fully autonomous calibration of a hundred-qubit superconducting processor through reusable and auditable Skills, removing a critical barrier to scalable quantum hardware operation.

Storing an unknown quantum computation in a quantum state and retrieving it at a desired later time is a challenging task, hindered by the no-programming theorem of quantum computations. In the previous studies on the task of probabilistic storage-and-retrieval (pSAR) of quantum channels, the maximum probability of exactly retrieving a single unknown unitary channel from a quantum state in which the unknown unitary has been encoded via multiple calls to the unknown unitary channel is derived. In this work, we consider a higher-order version of pSAR, the probabilistic storage-and-retrieval of definite-causal unitary superchannels, which are physically modeled by sequences of unitary channels with open slots where arbitrary channels can be inserted between the unitary channels for intervention. This task requires activating the "retrospective” intervention functionality on the superchannel, beyond its normal intervention functionality. We propose two protocols: partial teleportation, which is supported by our numerical results for the small queries, and staircase backstitch, which achieves unit success probability asymptotically as the number of queries increases. We also derive a universal inversion protocol for unitary superchannels.

Monte Carlo integration is fundamentally limited by the M^(-1/2) rate that the Cramer-Rao bound imposes on any sample-mean estimator of an expectation value, regardless of how the samples are drawn. Coined discrete-time quantum walks (DTQWs) are known to spread ballistically - their position variance scales as T^2 against the diffusive T of classical random walks - yet this faster spreading has not been exploited for numerical integration. We show that coupling the ballistic scaling of a 2D DTQW to the Hardy-Huxley asymptotic for Gauss circle lattice counts produces estimators whose dominant error is a deterministic number-theoretic residual controlled by walk depth T, not a statistical fluctuation controlled by sample count M. The construction replaces the empirical mean of a sample-mean estimator with the ratio N(R-hat)/R-hat^2 of a lattice count to the square of a radial position quantile, a structural change that sidesteps the Cramer-Rao barrier. A single batch of measurements then propagates through classically precomputed multipliers to cover an entire family of integrals simultaneously. We develop the framework for convex smooth domains via Kraetzel's lattice asymptotic and for smooth integrals with convex or annular super-level sets via Cavalieri's principle, and provide a parameter-free identity for the bias floor (validated to within 1.5x across all tested depths). Every experiment is benchmarked against the classical random walk with the identical estimator to isolate the quantum contribution; the framework is oracle-free in the QAE sense (no controlled unitary encoding the integrand is required) and structurally distinct from quantum amplitude estimation and Szegedy-walk approaches. These ratios compare measurement counts at fixed precision and do not include quantum circuit execution cost.

Quantum machine learning is often motivated by the exponentially large state space of quantum systems, but this promise leaves a basic generalization problem unresolved: how can a learner assign different meanings to unseen quantum directions when the training data provide no preferred basis, measurement frame, or other orienting structure? We address this identifiability problem by formulating supervised learning without an external quantum reference frame, so that predictions cannot depend on an arbitrary choice of Hilbert-space coordinates. This requirement forces the learned classifier to preserve every unitary symmetry left unbroken by the training data. We prove that whenever the training states fail to span the full Hilbert space, all pure states orthogonal to their span must receive the same prediction – even when those states are mutually orthogonal and perfectly distinguishable once an appropriate measurement is supplied. The limitation is therefore not caused by state discrimination, optimization, or computational power, but by missing reference information. We further establish a robust version under weak symmetry breaking and show that learning generic unstructured concepts on multiqubit systems requires exponentially many independently oriented training directions. Numerical illustrations visualize the resulting prediction collapse and its controlled relaxation. Our results identify feature maps, measurement bases, Hamiltonians, locality, symmetry priors, architectures, and sufficiently diverse training states as operational resources for generalization. The central implication is that Hilbert-space dimension alone is not a learnable feature space: successful QML must specify the physical structure that gives unseen quantum directions semantic meaning.

The quantum internet enables distribution of quantum states across distant nodes, supporting secure communication, distributed computing, and quantum sensing. Unlike classical networks, it is constrained by the no cloning theorem, probabilistic entanglement generation, decoherence, and hardware drift, making classical abstractions inadequate. Scalable quantum networking therefore requires new architectures, protocols, and optimisation methods that explicitly account for these limitations. This thesis studies the architecture, routing, and operation of quantum networks under realistic constraints, focusing on bipartite entanglement distribution over quantum repeater networks. Key metrics include end to end fidelity, throughput, scalability, and fairness. At the network layer, routing strategies are developed beyond assumptions of homogeneous nodes and full network knowledge. Routing under heterogeneous repeater efficiencies shows how partial knowledge of node quality improves fidelity and reduces path blocking. A grey box routing approach is then introduced, where path selection relies only on topology and end to end estimates, achieving robustness and fairness without detailed link information. At the link layer, calibration and hardware drift are addressed through a calibration aware model separating activation and calibration phases. For linear repeater chains, an optimal calibration schedule is derived to balance operation time and calibration overhead. This is extended to general topologies with shared links, where a greedy orchestration heuristic is proposed. Finally, the thesis connects network protocols with hardware via an instruction set architecture for programmable quantum repeater nodes based on NV centers, enabling coherent programmability and linking physical operations to higher layer protocols.

It is often asserted that quantum states for same-type particles must be symmetrized due to “label redundancy,” i.e. the assumption that the permutations of labels in direct-product states do not reflect any real physical distinction and thus their permutations constitute an “exchange degeneracy”. This assumption is directly challenged by the case of scattering of same-type particles such as electrons, which involves two physically distinct scattering channels effectively corresponding to permutation of the labels. I discuss this counterexample with critical attention to an extant portrayal in the literature that omits pertinent physical content. I further note ways in which the assumption that symmetrization must be universally imposed is not supported by actual calculations of particle interactions, nor by seemingly viable particle states based on preparations and outcomes.

Distinguishing transverse coherence length from single-particle wavepacket extent is fundamentally challenging, as both manifest through spatial broadening of observed intensity profiles in conventional experiments. Here we introduce a method based on helical neutron wavefronts that enables this separation. Helical neutron states produce annular intensity profiles whose peak radius depends on the transverse wavepacket extent, while coherence length only contributes to profile broadening. In our experimental geometry we measure a beam divergence of ~1.1 mrad, corresponding to a transverse coherence length of ~180 nm. In contrast, the same measurement places a lower bound of >= 2 um on the spatial extent of the individual neutron wavepackets, more than an order of magnitude larger than the coherence length. These results provide direct experimental evidence that transverse coherence length and single-particle wavepacket extent are distinct physical quantities, resolving a longstanding source of confusion in the neutron literature.

Quantum optimization offers a route to searching the large defect-configuration spaces that arise in materials design. We develop an end-to-end, constraint-aware quantum optimization workflow for composition-defect search in a doped ZrO2 thermal-barrier-coating (TBC) material system, using a MACE-MPA-0 energy dataset to fit a 24-variable QUBO over 8 cation-occupation and 16 oxygen-vacancy variables with exactly two rare-earth substitutions and one oxygen vacancy, yielding 448 feasible configurations. The QUBO surrogate reproduces the MACE energies with held-out R2 = 0.997 (full-data R2 = 0.999, RMSE = 17 meV). We validate two complementary quantum pathways against exact enumeration: a constraint-preserving XY-mixer QAOA that confines sampling to the feasible subspace and places 86% of probability mass within 1 meV of the MACE optimum at depth p = 3, and a fault-tolerant constrained Grover Adaptive Search oracle with explicit fixed-point arithmetic, branch-safe comparison, feasibility checking, and phase kickback. Across threshold cases, the validated oracle uses 324 high-level logical qubits, or 352 to 358 with conservative clean-ancilla v-chain accounting, and requires 3.6 to 4.3 x 104 Toffoli gates per Grover (GAS) iteration. An idealized feasible-space amplification estimate suggests up to a 240x reduction in total Toffoli cost relative to the full 224 occupation space, providing a resource-estimation bridge between materials-informed QUBO modeling, constraint-aware QAOA, and fault-tolerant threshold search.