Papers

The emergence of randomness from unitary quantum dynamics is a central problem across diverse disciplines, ranging from the foundations of statistical mechanics to quantum algorithms and quantum computation. Physical systems are invariably subject to constraints – from simple scalar symmetries to more complex non-Abelian ones – that restrict the accessible regions of Hilbert space and obstruct the generation of pure random states. In this work, we show that for systems with noncommuting symmetries such as SU(2), the degree of Haar-like randomization achievable under unitary dynamics is strongly constrained by experimental limitations on state initialization, in particular low-entanglement initial states, rather than by the symmetry-constrained dynamics themselves. Specifically, we show that time-evolved states can, in principle, reproduce Haar-like behavior at the level of finite statistical moments (i.e., those accessible under realistic experimental conditions with a finite number of state copies) provided that the initial state matches the corresponding moments of the conserved operators in the Haar ensemble. However, for the unentangled initial states commonly used in programmable quantum systems, this condition cannot be satisfied. Consequently, even at asymptotically long times in strongly quantum-chaotic regimes, late-time states remain distinguishable from Haar-random states in probes such as entanglement entropy, with deviations from Haar behavior that remain finite with increasing system size. We quantify the maximal entanglement entropy achievable and identify the unentangled initial conditions that yield the most entropic late-time states. Our results show that the combination of non-Abelian symmetry structure and experimental constraints on state preparation can strongly limit the degree of Haar-like randomization achievable at late times.

Out-of-time-order correlators (OTOCs) are the main tool for probing quantum chaos and scrambling, and have become crucial probes in many areas of quantum computing. However, the measurement of OTOCs is difficult to implement on analog quantum computers due to the requirement of backward time evolution. In this paper, we develop and implement a randomized measurement protocol to compute OTOCs on Aquila by QuEra Computing. Unlike traditional methods that require backward time evolution, our approach utilizes a sequence of global randomized quenches that approximates the unitary 2-design properties necessary for extracting infinite-temperature OTOCs from statistical correlations. We demonstrate the protocol's success by explicitly observing the lightcone of information propagation in 1D Rydberg chains, and compare hardware results to both state-vector simulations and matrix product state (MPS) tensor network calculations. This work establishes the first demonstration of fully analog randomized OTOC measurements in neutral-atom simulators, providing a scalable pathway to probe quantum chaos in complex many-body systems.

Spin-boson systems have attracted increasing attention as accessible experimental platforms and for their potential applications in designing quantum technologies. One characteristic of these systems is the transition from regular to completely chaotic behavior when certain control parameters are varied. However, the characterization of their mixed phase space has not been thoroughly explored. In this work, we investigate the properties of mixed eigenstates in spin-boson systems, comparing one-photon interactions with two-photon interactions. We propose a generalized definition of the phase-space overlap index to identify genuine mixed eigenstates. Our study highlights the fundamental differences that arise when two-photon processes are considered compared to one-photon processes and provides complementary evidence supporting the validity of the principle of uniform semiclassical condensation of quasiprobability functions in spin-boson systems.

Efficient classical simulation of noisy intermediate-scale quantum (NISQ) circuits has been a topic of intense study over the past few years. The majority of results on efficient simulation assume that the circuits undergo some variant of unital noise or involve sufficient randomness. However, there are limited results for circuits undergoing non-unital noise in the absence of randomness. In this work, we present a polynomial-time classical algorithm to sample from the output distributions of amplitude-damped instantaneous quantum polynomial (IQP) circuits. Our algorithm works for circuits generated by arbitrary $l$-local diagonal gates with depth $d = \Omega(\log(n))$, undergoing constant amplitude-damping noise.

Exponential complexity of many-body wave functions limits accurate numerical simulations of real-time dynamics, especially beyond 1D, where rapid entanglement growth poses severe challenges. Neural Quantum States (NQS) have emerged as a powerful approach for real-time dynamics in 2D, but their scalability and accuracy in 3D have remained an open challenge. Here, we establish NQS as a scalable framework for 3D quantum dynamics by introducing a residual-based convolutional architecture tailored to cubic spin lattices. Focusing on the 3D transverse-field Ising model, we demonstrate that NQS reliably capture distinct quench regimes, including collapse-and-revival dynamics and, most challengingly, the dynamics following a sudden quench to the quantum critical point. We perform finite-rate quenches to the critical point on lattices containing up to $1000$ qubits, an unprecedented system size for numerical simulations of real-time dynamics beyond 1D. This enables the first large-scale numerical demonstration of the 3D quantum Kibble–Zurek mechanism. The QKZM in 3D is particularly intriguing because it lies at the upper critical dimension of the Ising universality class, where the standard power laws are modified by logarithmic factors together with prominent sub-leading logarithmic corrections. By deriving these corrections from renormalization-group flow equations up to two-loop order, we obtain a robust data collapse across all simulated system sizes for the correlation function, the excess energy, and the quantum Fisher information, the latter revealing universal multipartite-entanglement dynamics. In all cases, we find compelling agreement with the expected scaling dimensions. Our findings establish NQS as a scalable and reliable tool for exploring nonequilibrium phenomena in 3D quantum matter and for providing numerical benchmarks for 3D quantum simulators.

Understanding the structure of operators that commute with $k$ identical replicas of unitary ensembles, also known as their $k$-commutants, is an important problem in quantum many-body physics with deep implications for the late-time behavior of physical quantities such as correlation functions and entanglement entropies under unitary evolution. In this work, we study the $k$-commutants of free-fermion unitary systems, which are heuristically known to contain $SO(k)$ and $SU(k)$ groups without and with particle number conservation respectively, with formal derivations of projectors onto these commutants appearing only very recently. We establish a complementary perspective by highlighting a larger $O(2k)$ replica symmetry (or $SU(2k)$ respectively) that the $k$-commutant transforms irreducibly under, which leads to a simple geometric understanding of the commutant in terms of coherent states parametrized by a Grassmannian manifold. We derive this structure by mapping the $k$-commutant to the ground state of effective ferromagnetic Heisenberg models, analogous to the ones that appear in the noisy circuit literature, which we solve exactly using standard representation theory methods. Further, we show that the Grassmannian manifold of the $k$-commutant is exactly the manifold of fermionic Gaussian states on $2k$ sites, which reveals a duality between real space and replica space in free-fermion systems. This geometric understanding also provides a compact projection formula onto the $k$-commutant, based on the resolution of identity for coherent states, which can prove advantageous in analytical calculations of averaged non-linear functionals of Gaussian states, as we demonstrate using some examples for the entanglement entropies. In all, this work provides a geometric perspective on the $k$-commutant of free-fermions that naturally connects to problems in quantum many-body physics.

Contextuality and measurement incompatibility are two fundamental aspects of nonclassicality, and their manifestations in observed quantum correlations are often deeply interconnected. Recently, measurement incompatibility has been studied in connection with nonlocality, particularly in terms of their robustness under various quantum channels. This line of investigation helps establish a connection between the channels that break nonlocality and those that break incompatibility. In this study, we focus on an asymmetric bipartite Bell scenario involving three and four inputs on Alice and Bob sides, respectively, with each of these inputs having dichotomous outcomes. Under the assumption of locality, the observed statistics in this asymmetric scenario obeys the Elegant Bell inequality (EBI). Here, we use a different version of the EBI that relies on the assumption of the preparation noncontextuality. By taking the violation of this noncontextual version of EBI as a witness of preparation contextuality we establish a connection between the channels that break contextuality and the channels that break triple-wise measurement incompatibility. Our results suggest that any channel which breaks EBI contextuality will also break Clauser-Horne-Shimony-Holt (CHSH) nonlocality; however, the reverse does not hold. We also show that a depolarising channel that breaks N-wise incompatibility can also break a certain form of contextuality, witnessed by a generalised inequality involving N measurements on one wing of a bipartite Bell scenario.

Recently, Yamaguchi and Kempf [Phys. Rev. Lett. 136:010801, arXiv:2501.02757] proved that encrypted qubits can be cloned. In this work, we generalize the encrypted cloning protocol and prove that it also applies to higher-order quantum systems. Given that a straightforward generalization of the protocol using the exponential of the shift and phase operators fails to satisfy the unitary requirement for a quantum gate, we propose a different approach. We introduce a new operator to be used in the encryption process and show that it is unitary. We adapt the decryption operator from the reference paper to fit in the framework of multi-level quantum systems. We analyze the circuit implementation of the proposed operators and show that the overhead imposed by larger dimensions scales linearly with qudit dimension.

The Boltzmann-Loschmidt dispute of 1876 questioned the possibility of a statistical irreversible description by time reversible classical equations of motion of atoms. Here we show analytically and numerically that the quantum chaos diffusion of cold atoms, or ions, in a harmonic trap and pulsed optical lattice can be inverted back in time with up to 100% efficiency. This is in sharp contrast to classical evolution where exponentially small errors break time reversibility. We argue that the existing experimental skills allow highlighting the Boltzmann-Loschmidt dispute from a quantum perspective.

Quantum coherence provides a controllable thermodynamic resource that can raise or lower the effective temperature of a cavity mode, enabling efficiency tuning in quantum heat engines. Here, we derive analytic expressions for the effective engine temperature, demonstrating the enhanced temperature tunability achievable via $N$-level ground-state coherence. We further unify ground- and excited-state coherence within a single analytic framework, revealing their interplay as a mechanism for thermodynamic control. Such quantum resources serve as tunable parameters that enable switching between heating, cooling, and cancellation regimes, driving the effective temperature from near-zero to divergence. Ultimately, our framework connects and generalizes previous models of quantum heat engines, and we identify rubidium atoms as a promising candidate for experimentally realizing these coherence-assisted effects.

We propose a representative, globally-admissible phenomenological spectral density of the bath for the non-Markovian Brownian motion of an optomechanical resonator, motivated by the near-resonance experimental observation of a non-Ohmic spectrum in [Nat. Commun. 6, 7606 (2015)]. To avoid divergences arising from a naive global extrapolation, we propose a globally-admissible, phenomenological bath spectrum that extends the experimentally-observed, near-resonance non-Ohmic behavior beyond the measurement window while ensuring finite bath-induced renormalizations and quadrature fluctuations of the resonator. The corresponding model of the structured environment produces a nonlocal mechanical response whose analytic pole structure encodes the observed linewidth. The resulting dissipation kernel exhibits a power-law-modulated exponential decay with transient negativity, signaling memory effects. In the weak-coupling regime, the optical readout based on homodyne detection enables near-resonance spectroscopy and, with a calibrated drive on the resonator, permits, in principle, the reconstruction of the full mechanical susceptibility, thereby providing access to both the dissipative and dispersive bath contributions. Our results provide a consistent route from locally-inferred spectral properties to globally-admissible open-system descriptions and establish a framework for probing structured environments in cavity optomechanics.

Simulating lattice gauge theories on quantum computers presents unique challenges that drive the development of novel theoretical frameworks. The orbifold lattice approach offers a scalable method for simulating SU($N$) gauge theories in arbitrary dimensions. In this work, we present three improvements: (i) two new simplified Hamiltonians, (ii) an encoding of the SU(2) theory with smaller number of qubits, and (iii) a reduction in the requirement for large scalar masses to reach the Kogut-Susskind limit, achieved via the inclusion of an additional term in the Hamiltonian. These advancements significantly reduce circuit depth and qubit requirements for quantum simulations. We benchmarked these improvements using Monte Carlo simulations of SU(2) in (2+1) dimensions. Preliminary results demonstrate the effectiveness of these developments and further validate the use of noncompact variables as a promising framework for scalable quantum simulations of gauge theories.

Data-driven surrogates can replace expensive multiphysics solvers for parametric PDEs, yet building compact, accurate neural operators for three-dimensional problems remains challenging: in Fourier Neural Operators, dense mode-wise spectral channel mixing scales linearly with the number of retained Fourier modes, inflating parameter counts and limiting real-time deployability. We introduce HQ-LP-FNO, a hybrid quantum-classical FNO that replaces a configurable fraction of these dense spectral blocks with a compact, mode-shared variational quantum circuit mixer whose parameter count is independent of the Fourier mode budget. A parameter-matched classical bottleneck control is co-designed to provide a rigorous evaluation framework. Evaluated on three-dimensional surrogate modeling of high-energy laser processing, coupling heat transfer, melt-pool convection, free-surface deformation, and phase change, HQ-LP-FNO reduces trainable parameters by 15.6% relative to a classical baseline while lowering phase-fraction mean absolute error by 26% and relative temperature MAE from 2.89% to 2.56%. A sweep over the quantum-channel budget reveals that a moderate VQC allocation yields the best temperature metrics across all tested configurations, including the fully classical baseline, pointing toward an optimal classical-quantum partitioning. The ablation confirms that mode-shared mixing, naturally implemented by the VQC through its compact circuit structure, is the dominant contributor to these improvements. A noisy-simulator study under backend-calibrated noise from ibm-torino confirms numerical stability of the quantum mixer across the tested shot range. These results demonstrate that VQC-based parameter-efficient spectral mixing can improve neural operator surrogates for complex multiphysics problems and establish a controlled evaluation protocol for hybrid quantum operator learning in practice.

Contextuality and nonlocality are distinct manifestations at the foundation of quantum mechanics, yet their coexistence within a single quantum state remains subtle. In a hybrid CHSH–KCBS scenario involving the entanglment of a qubit and a qutrit, the qutrit supports the KCBS contextuality test, and the CHSH nonlocality arises from correlations between the qubit and qutrit. Here, we derive the analytical closed-form expressions for both inequalities and also simulate this physics on a quantum circuit. We show that contextuality is governed solely by a population parameter $p_2$, associated with the occupation of the qutrit subsystem in the $|2\rangle$ level, which plays a distinguished role in the KCBS structure. In contrast, nonlocality depends irreducibly on coherence, involving both amplitudes and phases encoded in parameters $(X_i, Y_i)$. This separation of physical resources reveals parameter regimes that optimize KCBS violation while suppress CHSH violation, and vice versa. As a result, the optimal regions do not overlap, and coexistence is restricted to a narrow intermediate regime in parameter space.

PulsePol is an elegantly designed pulse-sequence-based quantum control scheme that enables polarization transfer between electron and nuclear spins, for example, in nitrogen-vacancy (NV) centers. However, previous analyses of PulsePol assumed very strong, near-ideal, instantaneous microwave pulses, which is rarely achievable at higher magnetic fields. We revisit the PulsePol scheme under finite-pulse constraints and show that its performance significantly degrades due to finite-pulse effects. Using bimodal Floquet theory, we identify the symmetry-breaking mechanism responsible for this deterioration in fidelity. By phase adjustment, we reestablish the proper symmetry of the interaction-frame spin Hamiltonian, leading to a sequence called Q-PulsePol, where "Q" reflects the restored quadrature symmetry. Our results demonstrate robustness to finite-pulse effects and improved polarization transfer efficiency, establishing Q-PulsePol as a practical and reliable scheme for bulk hyperpolarization of nuclear spins in solids using a single-mode (zero-quantum or double-quantum) transfer. This work bridges idealized quantum control with realistic pulse engineering, establishing design rules for spin-based quantum control protocols.

This paper presents a quantum search approach to combinatorial constraint satisfaction problems, demonstrated through the generation of magic squares. We reformulate magic square construction as a quantum search problem in which a reversible, constraint-sensitive oracle marks valid configurations for amplitude amplification via Grover's algorithm. Classical pre-processing using the Siamese construction and partial constraint checks generates a compact candidate domain before quantum encoding. Rather than integrating classical and quantum solvers in an iterative loop, this work uses the classical component for structured initialisation and the quantum component for search, and benchmarks the quantum approach against classical brute-force enumeration and backtracking. Our Qiskit implementation demonstrates the design of multi-register modular arithmetic circuits, oracle logic, and diffusion operators. Experiments are conducted on small grid instances, as larger grids are intractable on classical statevector simulators due to exponential memory growth. The results validate the correctness of the proposed quantum search pipeline and confirm the theoretical quadratic query advantage over classical search.

We establish fundamental uncertainty relations for the hydrodynamic variables arising from the Madelung representation of quantum fields in curved spacetime. Through canonical quantization of the density \(n\) and phase \(\theta\) variables and their conjugate momenta, we derive exact uncertainty principles that depend on spacetime geometry through the lapse function \(N\) and spatial metric \(\gamma_{ij}\). These relations reveal how gravitational fields modulate quantum fluctuations and provide first-principles constraints for Scalar Field Dark Matter (SFDM) models and stochastic quantum gravity. We present two groundbreaking applications. First, By coupling the density-velocity uncertainty to the Newtonian condition of hydrostatic equilibrium, we derive the exact scaling law for the minimum core radius of a self-gravitating scalar field halo. We naturally find the scale \(r_c \propto m^{-1/2}\) which is a testable prediction. Second, by evaluating the phase–momentum commutator in Rindler coordinates and relating the canonical momentum \(\Pi_\theta\) to the energy density via the Hamiltonian, we obtain the acceleration scale \(k_B T = C\hbar a/c\). The proportionality constant \(C=1/(2\pi)\) is fixed by the topological quantization of the Madelung phase circulation around the Euclidean horizon. This dual achievement demonstrates that quantum uncertainty on curved backgrounds is the unifying principle behind both galactic structure and black hole thermodynamics.

We present QCommute, a software tool implemented in C++ for symbolic computation of nested commutators between a Hamiltonian and local observables in quantum many-body spin-1/2 systems on one-, two-, and three-dimensional hypercubic lattices. The computation is performed algebraically directly in the thermodynamic limit, and the Hamiltonian parameters are kept symbolic. Importantly, this way the entire parameter space is covered in a single run. The implementation supports extensive parallelization to achieve high computational performance. QCommute can serve as a computational backend for Heisenberg-picture approaches to quantum dynamics in strongly correlated regimes, ranging from direct Taylor expansion in time to advanced techniques such as the recursion method.

The phrase “buy a quantum computer” hides several different procurement problems. An institution may be seeking cloud access for teaching, reserved capacity for research, a local instrument for hardware training, an optimization appliance, or a strategic installation that reshapes facilities, staffing, and budgets. Because these choices differ in purpose, operating burden, and useful lifetime, the decision should be framed as acquisition of quantum capability rather than selection of a presumed hardware winner. This manuscript develops a practical procurement framework that distinguishes five capability layers, separates peer-reviewed results from commercial offerings, pricing anchors, and public roadmaps, and compares the main commercial platform families – superconducting circuits, trapped ions, neutral atoms, quantum annealing, and photonics – through the lens of institutional fit, access model, and refresh pressure. The main conclusion is that most institutions should begin with the smallest layer of capability that produces repeatable near-term value, builds internal expertise, and preserves strategic flexibility. Large on-premises systems are justified only when mission requirements, site readiness, staffing, governance, and upgrade paths are already clear.

Theories of the measured homodyne current generated by a stochastic Schrödinger equation (SSE) can be tested in a simulation of the Einstein-Podolsky-Rosen (EPR) correlations for a two-mode squeezed state. We carry out such a simulation, and determine the correct stochastic term for the measured current in the broad-band limit. Stratonovich rather than Ito stochastic noise agrees with experiment. We show that this is relevant to measurement noise and errors in quantum technologies. By analyzing the SSE trajectories as measurement settings are changed, we propose a modern version of Schrodinger's gedanken experiment, where one measures position and momenta simultaneously, “one by direct, the other by indirect measurement”.

The phenomenon of interaction-free measurement (IFM) enables the probabilistic detection of an absorbing object with reduced photon absorption. We report the experimental implementation of a generalized IFM of multiple objects using a single quantum probe on the cloud-based Ascella photonic processor developed by Quandela. We demonstrate sequential IFM of up to 5 emulated absorbers using a single photon, significantly extending the original IFM scheme for a single object. The experimental error-mitigated results confirm the theoretical predictions for this sequential IFM setup, and demonstrate a practical approach to scaling IFM to more complex quantum interrogation tasks.

We propose a data-adaptive probabilistic intensity remapping framework for structure-preserving transformation of grayscale images. The suggested method formulates intensity transformation as a continuous, data-driven remapping process, in contrast to traditional histogram-based techniques that rely on hard thresholding and generate piecewise-constant mappings. The image statistics yield representative intensity values, and Gaussian-based weighting methods probabilistically allocate each pixel to several components. Smooth transitions while preserving structural features are achieved by computing the output intensity as an expectation over these components. A smooth transition from soft probabilistic remapping to hard assignment is made possible by the introduction of a nonlinear sharpening parameter $\gamma$ to regulate the degree of localization. This offers clear control over the trade-off between intensity discrimination and smoothing. Furthermore, the resolution of the remapping function is determined by the number of components $k$. When compared to thresholding-based methods, experimental results on standard benchmark images show that the suggested method achieves better structural fidelity and controlled information reduction as measured by PSNR, SSIM, and entropy. Overall, by allowing continuous, probabilistic intensity modifications, the framework provides a robust and efficient substitute for discrete thresholding.

Combinatorial optimization problems become computationally intractable as these NP-hard problems scale. We previously proposed extraction-type majority voting logic (E-MVL), a quantum-inspired algorithm using digital logic circuits. E-MVL mimics the thermal spin dynamics of simulated annealing (SA) through controlled sparsification of spin interactions for efficient ground-state search. This study investigates the performance potential of E-MVL through systematic optimization and comprehensive benchmarking against SA. The target problem is the Sherrington-Kirkpatrick (SK) model with bimodal and Gaussian coupling distributions. Through equilibrium state analysis, we demonstrate that the sparsity control mechanism provides a consistent search of the solution space regardless of the problem's coupling distribution (bimodal, Gaussian) or size. E-MVL not only achieves the best performance among all tested algorithms–solving exact solutions up to 1600 spins where the best SA baseline is limited to 400 spins–but also provides insights that significantly improve SA's own temperature scheduling. These results establish E-MVL's dual contribution as both an efficient optimizer and a practical methodology for enhancing SA performance. Moreover, FPGA implementation achieved an approximately 6-fold faster solution speed than SA.

Dynamic holographic optical tweezers provide a programmable route to array assembly and reconfiguration essential for scalable neutral-atom quantum computation. However, phase mismatch between successive holograms can cause destructive interference during finite spatial light modulator (SLM) refresh. In this work, we analyze finite SLM refresh to establish a phase-stability criterion for prescribed trap amplitudes and develop a weighted-projective Gerchberg-Saxton (WPGS) method that efficiently approximates the corresponding phase-only complex-field optimization. Enforcing this phase constraint also reduces the number of iterations required for each update, achieving convergence within five iterations and enabling hologram generation within a few milliseconds. Numerical simulations of 2D and 3D reconfiguration involving more than $10^3$ traps, together with nonuniform-intensity interlayer transport, show that WPGS preserves endpoint intensity quality while suppressing inter-frame phase mismatch, transient intensity degradation, trap splitting, and motional heating. Similar suppression of phase mismatch and transient-intensity degradation is maintained under Gaussian SLM-plane illumination. These results establish the phase-stability criterion as a practical design principle for dynamic holographic control and scalable neutral-atom array reconfiguration.

We present a systematic numerical investigation of the "entanglement geometry gravity" chain in random tensor networks (RTN) established by the ER EPR conjecture and Jacobson's thermodynamic derivation. First, we verify the kinematic foundation: the entanglement first law $\delta\langle K\rangle=\delta S$ (slope=1.000), the encoding of geometry by mutual information (correlation=0.92), and the locality of holographic perturbations (3.3x). We also confirm that gravitational dynamics (JT gravity) does not emerge, identifying a sharp kinematics-dynamics boundary. Second, and more importantly, we discover that many-body localization (MBL) is the mechanism that protects emergent holographic geometry from thermalization. Replacing Haar-random evolution (geometry lifetime $t\sim6$) with an XXZ Hamiltonian plus on-site disorder, we observe a finite-size crossover at disorder strength $W_c\approx10-12$ above which mutual-information-lattice correlations persist indefinitely ($r>0.5$ for $t>50$). We map the full parameter space: the optimal regime is a near-Ising anisotropy $\Delta\approx50$ with $W=30$ yielding $r=0.779\pm0.002$ (confirmed by a fine scan over $\Delta\in[30,70]$); only holographic (RTN) initial states sustain geometry, while product, Néel, and Bell-pair states do not. MBL preserves the spatial structure of entanglement (adjacent/non-adjacent MI ratio ~2.6-4.2x vs. 1.0x in the thermal phase), rather than its total amount. A comparison with classical cellular automata reveals that MBL uniquely breaks the entanglement-structure trade-off imposed by quantum monogamy: classical systems achieve spatial structure only at the cost of negligible mutual information, while MBL sustains both.

We formulate a global-position colored-permutation encoding for the capacitated vehicle routing problem. Each of the $K$ vehicles selects a disjoint partial permutation, and the sum of these $K$ color layers forms a full $n\times n$ permutation matrix that assigns every customer to exactly one visit position. This representation uses $n^2K$ binary decision variables arranged as $K$ color layers over a common permutation structure, while vehicle capacities are enforced by weighted sums over the entries of each color class, requiring no explicit load register and hence no extra logical qubits beyond the routing variables. In contrast, many prior quantum encodings introduce an explicit capacity or load representation with additional qubits. Our construction is designed to exploit the Constraint-Enhanced QAOA framework together with its encoded-manifold analyses. Building on a requirements-based view of quantum utility in CVRP, we develop a routing optimization formulation that directly targets one of the main near-term bottlenecks, namely the additional logical-qubit cost of vehicle labels and explicit capacity constraints. Our proposal shows strong algorithmic performance in addition to qubit efficiency. On a standard benchmark suite, our end-to-end pipeline recovers the independently verified optima. The feasibility oracle may also be of independent interest as a reusable polynomial-time decoding and certification primitive for quantum and quantum-inspired routing pipelines.

This thesis develops a decision-theoretic framework for extracting thermodynamic work from temporal correlations in quantum systems. We model a classical agent – lacking quantum memory – performing adaptive work extraction through continuous inference and decision-making under uncertainty. By introducing $\rho^*$-ideal protocols, we demonstrate that exploiting memory effects allows adaptive strategies to surpass non-adaptive bounds. We formalize this via the Time-Ordered Free Energy (TOFE), a novel upper bound for causal, adaptive operations that reveals a thermodynamic gap linked to adaptive ordered discord. Additionally, we tackle work extraction from unknown sources using reinforcement learning. By adapting multi-armed bandit algorithms, we show an agent can simultaneously learn an unknown i.i.d. quantum state and extract work, achieving polylogarithmic cumulative dissipation that significantly outperforms standard tomography. Overall, this work lays the foundation for predictive and learning-based quantum thermodynamics.

Characterizing quantum states is essential for validating quantum devices, yet conventional quantum state tomography becomes prohibitively expensive as system size grows. Direct tomography offers a distinct route by enabling selective access to individual complex density-matrix elements, with a particular advantage for sparse target states and some verification tasks. Here we introduce a direct quantum state tomography scheme combining strong-measurement estimation with a fan-out coupling architecture. It enables mutually commuting interactions between system qubits and a single meter qubit, thereby achieving constant circuit depth, independent of system size. Notably, the involutory fan-out coupling reduces to the identity under repetition, enabling straightforward noise scaling for quantum error mitigation. We experimentally validate the scheme on a superconducting quantum processor via the IBM Quantum Platform, demonstrating four-qubit state reconstruction and single-circuit GHZ-state fidelity estimation up to 20 qubits with error mitigation. Consistent results with standard tomography and improved efficiency establish our scheme as a promising approach to reconstructing full quantum states and scalable verification tasks.

Quantum simulation and computing traditionally has been based on two main paradigms, namely, digital and analog. In the digital paradigm, usually single and two-qubit gates (where qubit is an acronym for quantum bit) are employed as building blocks for scalable, universal quantum computing, although errors add up fast and error correction will be ultimately needed for scaling up. In the analog paradigm, large analog blocks are normally employed for a unitary dynamics that carries out the computation, enabling quantum operations on many qubits with reduced errors, but with the drawback of a limited choice of evolutions and lack of universality. In the past decade, a new paradigm has emerged, showing interesting possibilities for quantum simulation and computing in the near and mid term. This is the paradigm of digital-analog quantum technologies, which proposes to combine the best of both paradigms: large analog blocks, provided by native interactions of the employed quantum platform, enabling scalability, combined with digital gates, allowing for more versatility and, ultimately, universality. In this Perspective, I give an overview of the evolution of the field along the past decade, and an outlook for its future possibilities.

Quantum clock synchronization (QCS) aims to establish a shared temporal reference between distant nodes by exploiting uniquely quantum phenomena such as entanglement, single-photon interference, and quantum correlations. In contrast to classical synchronization and time-transfer techniques, which are limited by signal propagation delays, atmospheric disturbances, and oscillator drift, QCS protocols offer the potential to surpass classical precision bounds and enhance resilience against adversarial manipulations. As precise and secure time synchronization underpins distributed quantum networks, navigation systems, and emerging quantum Internet infrastructures, understanding QCS principles, capabilities, and implementation challenges has become increasingly important. This survey provides a unified and critical overview of the rapidly growing QCS research landscape, highlighting fundamentals, protocol types, enabling resources, performance constraints, security considerations, and practical implementations of QCS. We first introduce the theoretical underpinnings of QCS, including entanglement-assisted time transfer, Hong-Ou-Mandel interference-based synchronization, and quantum slow-clock transport. We then categorize the main QCS protocols, ranging from ticking-qubit and entanglement-based schemes to time-of-arrival correlation methods, conveyor-belt synchronization, and quantum-enhanced two-way time transfer. This organization clarifies the relationships between protocol families and their achievable precision advantages over classical methods. Key quantum resources such as spontaneous parametric down-conversion-based entangled photon pairs, Greenberger-Horne-Zeilinger and W multipartite states, squeezed and frequency-entangled light, quantum frequency combs, and quantum memories are reviewed in the context of scalability and robustness.