Papers

Noisy intermediate-scale quantum (NISQ) devices impose dual challenges on quantum circuit execution: limited qubit connectivity requires extensive SWAP-gate routing, while time-dependent decoherence progressively degrades quantum information. Existing qubit mapping algorithms optimize for hardware topology and static calibration metrics but systematically neglect transverse relaxation dynamics (T2), creating a fundamental gap between compiler decisions and evolving noise characteristics. We present TRAM (Transverse Relaxation Time-Aware Qubit Mapping), a coherence-guided compilation framework that elevates decoherence mitigation to a primary optimization objective. TRAM integrates calibration-informed community detection to construct noise-resilient qubit partitions, generates time-weighted initial mappings that anticipate coherence decay, and dynamically schedules SWAP operations to minimize cumulative error accumulation. Evaluated on Qiskit-based simulators with realistic noise models, TRAM outperforms SABRE by 3.59% in fidelity, reduces gate count by 11.49%, and shortens circuit depth by 12.28%, establishing coherence-aware optimization as essential for practical quantum compilation in the NISQ era.

Low-frequency Raman peaks, below 250 cm-1, are observed in hydrogen between 2-174 GPa and 13-300 K. The origin of these features is attributed to reorientational transitions (DeltaJ = 0; Q0-branch), which shift from the Rayleigh line as anisotropic intermolecular interactions lift the mJ degeneracy. This family of excitations closely follows the behavior of the S0-branches, sharing their dependence on pressure, temperature, and ortho-H2 concentration. Above 65 K, spectra corrected by the Bose-Einstein population factor reveal a broad continuum arising from populated higher J-states and increased ortho-para disorder. Upon entering phase III, where molecular rotation is inhibited, this continuum is quenched, giving way to well-established optical phonons. Below 25 K, equilibrated samples demonstrate a fine structure from isolated and pair excitations from impurity ortho-H2 molecules in a parahydrogen lattice, the latter a sensitive probe to anisotropic intermolecular interactions relevant to the quantum modeling of solid H2.

An important proof technique in the random oracle model involves reprogramming it on hard to predict inputs and arguing that an attacker cannot detect that this occurred. In the quantum setting, a particularly challenging version of this considers adaptive reprogramming wherein the points to be reprogrammed (or the output values they should be programmed to) are dependent on choices made by the adversary. Some quantum frameworks for analyzing adaptive reprogramming were given by Unruh (CRYPTO 2014, EUROCRYPT 2015), Grilo-Hövelmanns-Hülsing-Majenz (ASIACRYPT 2021), and Pan-Zeng (PKC 2024). We show, counterintuitively, that these adaptive results follow from the nonadaptive one-way to hiding theorem of Ambainis-Hamburg-Unruh (CRYPTO 2019). These implications contradict beliefs (whether stated explicitly or implicitly) that some properties of the adaptive frameworks cannot be provided by the Ambainis-Hamburg-Unruh result.

Quantum low-density parity check (QLDPC) codes can significantly reduce the overhead of quantum computing, provided the methods for performing logical operations do not require substantial space and time resources. A popular method for performing logical operations is by measuring logical Pauli operators. We present a simple, explicit construction for fixed gadgets that can measure arbitrary logical Pauli operators on QLDPC codes when dynamically connected to the code block. We apply this construction to a family of generalised bicycle codes with distances relevant to utility-scale quantum computation ($10\leq d \leq 24$) and show that it reduces the space overhead by at least an order of magnitude compared to corresponding surface code architectures, without increasing the time overhead.

Recent advancements in quantum algorithms have reached a state where we can consider how to capitalize on quantum and classical computational resources to accelerate molecular resonance state identification. Here we identify molecular resonances with a method that combines quantum computing with classical high-throughput computing (HTC). This algorithm, which we term qDRIVE (the quantum deflation resonance identification variational eigensolver) exploits the complex absorbing potential formalism to distill the problem of molecular resonance identification into a network of hybrid quantum-classical variational quantum eigensolver tasks, and harnesses HTC resources to execute these interconnected but independent tasks both asynchronously and in parallel, a strategy that minimizes wall time to completion. We show qDRIVE successfully identifies resonance energies and wavefunctions in simulated quantum processors with current and planned specifications, which bodes well for qDRIVE's ultimate application in disciplines ranging from photocatalysis to quantum control and places a spotlight on the potential offered by integrated heterogenous quantum computing/HTC approaches in computational chemistry.

We study the universality of work statistics performed during a quench in gapless quantum systems. We show that the cumulants of work scale separately in the fast and slow quench regimes, following a power law analogous to the universal scaling in the Kibble-Zurek mechanism for topological defect formation in phase transition. As an example, we analyze the nonequilibrium dynamics of a quenched Heisenberg XXZ chain at its critical gapless state using the bosonization picture, resulting in a Tomonaga-Luttinger liquid. The analytical scaling is in agreement with the exact numerical calculation for the fast and slow quench regimes. In finite systems, the characteristic function display an oscillatory pattern which disappears in the thermodynamic limit. This study is particularly useful for understanding the thermodynamics of adiabatic quantum computation.

Quantum machine learning (QML) is a computational paradigm that seeks to apply quantum-mechanical resources to solve learning problems. As such, the goal of this framework is to leverage quantum processors to tackle optimization, supervised, unsupervised and reinforcement learning, and generative modeling-among other tasks-more efficiently than classical models. Here we offer a high level overview of QML, focusing on settings where the quantum device is the primary learning or data generating unit. We outline the field's tensions between practicality and guarantees, access models and speedups, and classical baselines and claimed quantum advantages-flagging where evidence is strong, where it is conditional or still lacking, and where open questions remain. By shedding light on these nuances and debates, we aim to provide a friendly map of the QML landscape so that the reader can judge when-and under what assumptions-quantum approaches may offer real benefits.

Loop quantum gravity (LQG) attempts to unify general relativity with quantum physics to offer a complete description of the universe by quantising spacetime geometry, but the numerical calculations we encounter are extraordinarily difficult. Progress has been made in the covariant formulation of LQG, but the tools do not carry over to the canonical formulation. These tools are graphical by nature, describing space with spin networks to make calculations in LQG more intuitive to the human hand. Recently, a new notation for working with spin networks has been used by arXiv:2412.20272 to offer the first accurate numerical results in canonical LQG by allowing the underlying graphs to change throughout the calculation, though they are forced to concede visual intuitiveness. In this thesis, we offer a more radical rephrasing of spin network calculations by translating them into the finite-dimensional ZX-calculus, extending previous attempts to translate into the standard (qubit) ZX-calculus (arXiv:2111.03114). Specifically, we derive the mixed-dimensional ZX-diagrams representing the generating objects of spin networks and the rules for the Penrose Spin Calculus (arXiv:2511.06012), and use these to present the ZX-form and correctness of "loop removal". We also derive the forms for several fundamental LQG objects in the finite-dimensional ZX-calculus for the first time. This gives us a high-level, intuitive graphical language that retains a flexibility to handle changing graph structures, and thus we argue positions the PSC as the new definitive language for canonical LQG. Furthermore, we investigate the possibility for a matrix-like normal form for spin networks deriving from a novel perspective of the PSC in terms of W-nodes.

We propose high-fidelity single-qubit spin-dependent kicks (SDKs) for trapped ions using nanosecond Raman pulses via amplitude modulation of a continuous-wave laser with a tunable beat frequency. We develop a general method for maintaining SDK performance in the presence of micromotion by identifying optimal choices of the RF phase and frequency that suppress unwanted backward kicks. The proposed scheme enables SDK infidelities as low as $10^{-9}$ in the absence of micromotion, and below $10^{-5}$ with micromotion. This study lays the foundation for the realization of sub-trap-period and high-fidelity two-qubit gates based on SDKs.

Measurement incompatibility–the impossibility of jointly measuring certain quantum observables–is a fundamental resource for quantum information processing. We develop a graph-theoretic framework for quantifying this resource for large families of binary measurements, including Pauli observables on multi-qubit systems and $k$-body Majorana observables on $n$-mode fermionic systems. To each set of observables we associate an anti-commutativity graph, whose vertices represent observables and whose edges indicate pairs that anti-commute. In this representation, the incompatibility robustness–the minimal amount of classical noise required to render the set jointly measurable–becomes a graph invariant. We derive general bounds on this invariant in terms of the Lovász number, clique number, and fractional chromatic number, and show that the Lovász number yields the correct asymptotic scaling for $k$-body Majorana observables. For line graphs $L(G)$, which naturally arise in the characterisation of exactly solvable spin models, we obtain spectral bounds on the robustness expressed through the energy and skew-energy of the underlying graph $G$. These bounds become tight for highly symmetric graphs, leading to closed formulas for several graph families. Finally, we identify structural conditions under which the robustness is determined by a simple function of the graph's maximum degree and the number of vertices and edges, and show that such extremal cases occur only when combinatorial structures such as Hadamard, conference or weighing matrices exist.

We introduce a new renormalisation scheme to construct the Landau quasiparticles of Fermi fluids. The scheme introduces an energy cutoff $\Lambda$ to remove the resonant couplings, enabling the dressing of the particles into quasiparticles via a unitary transformation. The dynamics of the quasiparticles is then restricted to low-energy transitions and is fully determined by an effective Hamiltonian which unifies the Landau function $f$, the pair interaction $g$ responsible for superfluidity, and the collision amplitude $\mathcal{A}$ responsible for transport and equilibration. Studying the flow equation that results from infinitesimal variations of the cutoff, we recover the Bethe-Salpeter relation between $f$ and the forward limit of $\mathcal{A}$, and we demonstrate an analogue relation between $g$ and the frontal limit of $\mathcal{A}$. We show that our effective theory captures all the low-energy phenomena of Fermi liquids, from the equation of state to the transport properties, both in the normal and in the superfluid phase. We apply it to the calculation of non-Fermi liquid corrections to the quasiparticle lifetime. This publication is continued by arXiv:2607.07041 where we apply the effective theory to a Fermi fluid of ultracold atoms.

We consider stimulated Raman adiabatic passage (STIRAP) when the final state is a superposition of two non-degenerate states. The system consists of four states coupled by two light fields. We find the relative phase of the final superposition depends on relative amplitude, width and timing of the adiabatic transfer pulses. We discuss these results in the context of experiments measuring symmetry violation in atomic and molecular systems.

We use the Tomonaga-Schwinger (TS) formulation of quantum field theory to determine when state-dependent additions to the local Hamiltonian density (i.e., modifications to linear Schrodinger evolution) violate relativistic covariance. We derive new operator integrability conditions required for foliation independence, including the Frechet derivative terms that arise from state-dependence. Nonlinear modifications of quantum mechanics affect operator relations at spacelike separation, leading to violation of the integrability conditions.

Spins in solids and molecules are promising for applications of quantum sensing technology. The sensitivity of the quantum sensing depends on how precisely spin observables can be determined in the measurement, and is intrinsically limited by the uncertainties of the observables. The use of a spin-squeezed state in a quantum sensor can reduce the uncertainty below the standard quantum limit when combined with an appropriate measurement procedure. Here, we discuss the simulation study of the generation of a squeezed state in an interacting spin system. We show that a spin system coupled by the magnetic dipole interaction can create a squeezed state. Model systems to realize the spin squeezing experimentally are also discussed. In addition, we find that a squeezed state is a type of entangled state. The present work paves the way to realize a squeezed state using a spin system to build a quantum sensor network with improved sensitivity, and to use it for the detection of quantum entanglement.

The ensemble-averaged dynamics of open quantum systems are typically irreversible. We show that this irreversibility need not hold at the level of individually monitored quantum trajectories. Our main results are analytical stochastic Schrödinger equations for quantum reverse diffusion, along with corresponding stochastic master equations. These equations describe the exact and approximate stochastic reverse processes for continuously monitored Pauli channels, including time-dependent depolarizing noise. We show that the reverse processes generalize the forward dynamics by combining the noise effects of the forward processes with an additional stochastic drift that dynamically steers a quantum state back to its initial configuration. Consequently, the exact reverse stochastic Schrödinger equations admit closed-form solutions that can be implemented in real-time without the need for variational techniques. Our findings establish an analytical framework for quantum state recovery, noise-resilient quantum gates, quantum generative modelling, quantum tomography via forward-reverse cycles, and potential paradigms for quantum error correction based on reverse diffusion.

In this work, we present a novel method to express the stabilizer of a k-uniform complete hypergraph state as a linear combination of local operators. Quantum hypergraph states generalize graph states and exhibit properties that are not shared by their graph counterparts, most notably, their stabilizers are intrinsically nonlocal, as hyperedges can involve arbitrary subsets of vertices. Our formulation provides an explicit description of the stabilizers for k-uniform complete hypergraphs and may offer new insights for exploring these states within the stabilizer formalism. In particular, this approach could facilitate the construction of new Bell inequalities or find applications in quantum error correction.

Modular trapped-ion quantum computing hardware, known as QCCDs require shuttling operations in order to maintain effective all-to-all connectivity. Each module or trap can perform only one operation at a time, resulting in low intra-trap parallelism, but there is no restriction on operations happening on independent traps, enabling high inter-trap parallelism. Unlike their superconducting counterparts, the design space for QCCDs is relatively flexible and can be explored beyond current grid designs. In particular, current grid-based architectures significantly limit the performance of many promising, high-rate codes such as HGP codes and BB codes, suffering from numerous trap to trap “roadblocks", forcing serialization and destroying the inherent parallelism of these codes.. Many of these codes are highly parallelizable, meaning that with appropriate hardware layouts and matching software schedules, execution latency can be reduced. Faster execution, in turn, reduces error accumulation from decoherence and heating, ultimately improving code performance when mapped to realistic hardware. To address this, we propose Cyclone, a circular software-hardware codesign that departs from traditional 2D grids in favor of a flexible ring topology, where ancilla qubits move in lockstep. Cyclone eliminates roadblocks, bounds total movement, and enables high levels of parallelism, resulting in up to ~4$\times$ speedup in execution times. With HGP codes, Cyclone achieves up to a 2$\times$ order of magnitude improvement in logical error rate, and with BB codes, this improvement reaches up to a 3$\times$ in order of magnitude.Spatially, Cyclone reduces the number of required traps and ancilla qubits by $2\times$.The overall spacetime improvement over a standard grid is up to $\sim 20 \times$, demonstrating Cyclone as a scalable and efficient alternative to conventional 2D QCCD architectures.

To perform meaningful computations, Quantum Computers (QCs) must scale to macroscopic levels - i.e., to a large number of qubits - an objective pursued by most quantum companies. How to efficiently test their quantumness at these scales? We show that the violation of Macrorealism (MR), being the fact that classical systems possess definite properties that can be measured without disturbances, provide a fruitful avenue to this aim. The No Disturbance Condition (NDC) - the equality used here to test MR - can be violated by two consecutive parity measurements on $N$ qubits and found to be independent of $N$ under ideal conditions. However, realistic noisy QCs show a quantum-to-classical transition as $N$ increases, giving a foundationally-motivated scalable benchmarking metric. Two methods are formulated to implement this metric: one that involves a mid-circuit measurement, probing the irreversible collapse of the wavefunction, in contrast to the reversible entanglement generated in the other. Both methods are designed to be clumsiness-loophole free: the unwanted classical disturbances are negligible within statistical error. Violation of MR is detected on a IBM QC up to $N = 38$ qubits, increasing $N$ by one order of magnitude over best known results of MR. Two QCs are benchmarked using the proposed NDC metric, showing a three-fold improvement in their quantumness from one generation to the next.

We propose an experimental scheme to test the nonclassicality of a macroscopic ensemble of qubits, through the violation of the classical notion of macrorealism (MR) via the fundamental measurement-induced disturbance of quantum systems. An electromagnetic resonator is used to probe the parity of the qubit-ensemble. The action of sequential measurements allows the nonclassicality of whole ensemble to manifest itself, in the ideal case, irrespective of its size. This enables to probe the macroscopic limits of quantum mechanics as the qubit-ensemble is, effectively, a single large spin of many $\hbar$ units. Even as $\hbar \rightarrow 0$ in comparison to the total angular momentum of the ensemble, a constant amount of violation of MR is found in the noiseless case. However, environmental decoherence and inhomogeneity of qubit-electromagnetic field couplings precipitate the quantum-to-classical transition. This illustrates that Bohr's correspondence principle is not fundamental, but a consequence of practical limitations. We outline an implementation with a variety of qubits (superconducting qubits, spins in semiconductors, and Rydberg atoms) coupled to a coplanar waveguide resonator, and – via the corresponding noise analysis – find that violation of MR is detectable up to $100$ qubits via current technology.

A longstanding belief in quantum tomography is that estimating a mixed state is far harder than estimating a pure state. This is borne out in the mathematics, where mixed state algorithms have always required more sophisticated techniques to design and analyze than pure state algorithms. We present a new approach to tomography demonstrating that, contrary to this belief, state-of-the-art mixed state tomography follows easily and naturally from pure state algorithms. We analyze the following strategy: given $n$ copies of an unknown state $\rho$, convert them into copies of a purification $|\rho\rangle$; run a pure state tomography algorithm to produce an estimate of $|\rho\rangle$; and output the resulting estimate of $\rho$. The purification subroutine was recently discovered via the "acorn trick" of Tang, Wright, and Zhandry. With this strategy, we obtain the first tomography algorithm which is sample-optimal in all parameters. For a rank-$r$ $d$-dimensional state, it uses $n = O((rd + \log(1/\delta))/\varepsilon)$ samples to output an estimate which is $\varepsilon$-close in fidelity with probability at least $1-\delta$. This algorithm also uses poly$(n)$ gates, making it the first gate-efficient tomography algorithm which is sample-optimal even in terms of the dimension $d$ alone. Moreover, with this method we recover essentially all results on mixed state tomography, including its applications to tomography with limited entanglement, classical shadows, and quantum metrology. Our proofs are simple, closing the gap in conceptual difficulty between mixed and pure tomography. Our results also clarify the role of entangled measurement in mixed state tomography: the only step of the algorithm which requires entanglement across copies is the purification step, suggesting that, for tomography, the reason entanglement is useful is for consistent purification.

Bosonic systems, such as photons and ultracold atoms, have played a central role in demonstrating quantum-enhanced sensing. Quantum entanglement, through squeezed and GHZ states, enables sensing beyond classical limits. However, such a quantum advantage has so far been confined to two-mode bosonic systems, as analogous multi-mode squeezed states are non-trivial to prepare. Here, we develop a Monte-Carlo based optimization technique which can be used to efficiently engineer a Hamiltonian control-sequence for multi-mode bosonic systems to prepare multi-mode squeezed states. Specifically, we consider a Bose-Einstein condensate in an optical lattice, relevant for applications in gravimetry and gradiometry, and demonstrate that metrologically useful squeezed states can be generated using the Bose-Hubbard Hamiltonian which includes on-site atomic interactions, tunable via Feshbach resonances. By analyzing the distribution (density) of the quantum Fisher information (QFI) over the Hilbert space, we identify a characteristic intermediate scaling of the QFI: $\mathcal{O}(N^2 L+L^2 N)$, which lies between the standard quantum limit (SQL) and the Heisenberg limit (HL) for $N$ atoms in $L$ modes. We show that in general, within the Hilbert space there is a finite, $\mathcal{O}(1)$ measure subset of Hilbert space with an intermediate QFI scaling. Therefore, one can find a Hamiltonian control sequence using a Monte Carlo optimization over random control sequences, that produces a state with intermediate scaling of the QFI. We assume an experimentally accessible range of the control parameters in the Hamiltonian resources and show that the intermediate scaling can be readily achieved. Our results indicate that the HL can be approached in quantum gravimetry using realistic experimental parameters for systems with $L=\mathcal{O}(1)$ and $N\gg L$.

We propose a class of periodically driven (Hermitian) modified bosonic Kitaev chains that effectively hosts rich nonHermitian Floquet topological phenomena. Two particular models are investigated in details as case studies. The first of these represents a minimal topologically nontrivial model in which nonHermitian skin effect, topological zero modes, and topological $\pi$ modes coexist. The other displays a more sophisticated model that supports multiple topological zero modes and topological $\pi$ modes in a tunable manner. By subjecting both models to perturbations such as a finite onsite bosonic frequency and spatial disorder, these features exhibit distinct responses. In particular, while generally all topological edge modes are robust against such perturbations, the nonHermitian skin effect is easily suppressed and revived by, respectively, the onsite bosonic frequency and spatial disorder in the first model, but it could be insensitive to both perturbations in the second model. Our studies thus demonstrate the prospect of a periodically driven bosonic Kitaev chain as a starting point in exploring various nonHermitian Floquet topological phases through the lens of a Hermitian system.

We study quantum advantage in the 1-step graph domination game on cycle graphs numerically, analytically and through the use of Noisy intermediate scale quantum (NISQ) processors. We find explicit strategies that realise the recently found upper bounds for small graphs and generalise them to larger cycles. We demonstrate that NISQ computers realise the predicted quantum advantages with high accuracy.

We establish a direct correspondence between Krylov and Nielsen complexity by choosing the Krylov basis to be part of the elementary gate set of Nielsen geometry and selecting a Nielsen complexity metric compatible with the Krylov metric. Up to normalization, the Krylov complexity of a Hermitian operator then equals the length squared of a straight-line trajectory on the manifold of unitaries that connects the identity operator with a precursor operator. The corresponding length provides an upper bound on Nielsen complexity that saturates whenever the straight line is a minimal geodesic. While for general systems we can only establish saturation in the limit of small precursors, we provide evidence that in broad classes of models and for suitable initial operators there is a precise correspondence between Krylov complexity and (the square of) Nielsen complexity for a finite range of precursors.

Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge theories induced by automorphisms of the gauge group, when the gauge theories have nontrivial topological actions in different spacetime dimensions. We discover the automorphism symmetry can be extended, become a higher group symmetry, and/or become a non-invertible symmetry. We illustrate the discussion with various models in field theory and on the lattice. In particular, we use automorphism symmetry to construct new transversal non-Clifford logical gates in topological quantum codes. In particular, we show that 2+1d $\mathbb{Z}_N$ qudit Clifford stabilizer models can implement non-Clifford transversal logical gate in the 4th level $\mathbb{Z}_N$ qudit Clifford hierarchy for $N\geq 3$, extending the generalized Bravyi-König bound proposed in the companion paper [arXiv:2511.02900] for qubits.

We demonstrate that Dirac fermions in 2+1 dimensions, coupled to Abelian gauge fields in multiply-connected regions, exhibit a parity anomaly that directly manifests as Aharonov-Bohm (AB) type topological phases. Using the Fujikawa method, we show that this anomaly reproduces both the AB phase and the spin-dependent Aharonov-Casher (AC) phase. We explicitly calculate the induced topological currents, establishing that their characteristic divergence-free form provides a direct signature of this parity-anomalous topological phase.

We investigate the critical behavior and real-time scattering dynamics of the interacting $\phi^4$ quantum field theory in (1+1)-dimensions using uniform matrix product states (uMPS) and the time-dependent variational principle (TDVP). A finite-entanglement scaling analysis at $\lambda = 0.8$ bounds the critical mass-squared to $\mu_c^2 \in ]-0.2595,-0.2594[$ and provides a quantitative map of the symmetric, near-critical, and spontaneously broken regimes. Using these ground states as asymptotic vacua, we simulate two-particle collisions in a sandwich geometry and extract the elastic scattering probability $P_{11\to 11}(E)$ and Wigner time delay $\Delta t(E)$ using a sandwich geometry protocol. We find strongly inelastic scattering in the symmetric phase ($P_{11\to 11} \simeq 0.712$, $\Delta t \simeq -158$ for $\mu^2 = +0.2$) and almost perfectly elastic collisions in the spontaneously broken phase ($P_{11\to 11} \simeq 1$, $\Delta t \simeq -108$ for $\mu^2=-0.1$ and $P_{11\to 11} \simeq 1$, $\Delta t \simeq -177.781$ for $\mu^2=-0.5$). Crucially, the scattering protocol exhibits a distinctive divergence near the critical coupling; we show that this behavior serves as a dynamical signature of the quantum critical point, arising directly from the closing of the mass gap. These results demonstrate that TDVP-based uMPS can effectively probe nonperturbative scattering and critical dynamics in lattice field theories with controlled entanglement truncation.

Drawing inspiration from gradient-descent methods developed for data processing in quantum state tomography [\href{https://iopscience.iop.org/article/10.1088/2058-9565/ae0baa}{Quantum Sci.~Technol.~10 045055 (2025)}] and quantum process tomography [\href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.150402}{Phys.~Rev.~Lett.~130, 150402 (2023)}], we introduce stochastic gradient descent (SGD) algorithms for fast quantum measurement tomography (QMT), applicable to both discrete- and continuous-variable quantum systems – thus completing the tomography trio. A measurement device or detector in a quantum experiment is characterized by a set of positive operator-valued measure (POVM) elements; the goal of QMT is to estimate these operators from experimental data. To ensure physically valid (positive and complete) POVM reconstructions, we propose two distinct parameterization schemes within the SGD framework: one leveraging optimization on a Stiefel manifold and one based on Hermitian operator normalization via eigenvalue scaling. Within the SGD-QMT framework, we further investigate two loss functions: mean squared error, equivalent to L2 or Euclidean norm, and average negative log-likelihood, inspired by maximum likelihood estimation. We benchmark performance against state-of-the-art constrained convex optimization methods. Numerical simulations demonstrate that, compared to standard methods, our SGD-QMT algorithms offer significantly lower computational cost, superior reconstruction fidelity, and enhanced robustness to noise. We make a Python implementation of the SGD-QMT algorithms publicly available at \href{https://github.com/agtomo/SGD-QMT}{github.com/agtomo/SGD-QMT}.

For the preparation of high-dimensional functions on quantum computers, we introduce tensor network algorithms that are efficient with regard to dimensionality, optimize circuits composed of hardware-native gates and take gate errors into account during the optimization. To avoid the notorious barren plateau problem of vanishing gradients in the circuit optimization, we smoothly transform the circuit from an easy-to-prepare initial function into the desired target function. We show that paradigmatic multivariate functions can be accurately prepared such as, by numerical simulations, a 17-dimensional Gaussian encoded in the state of 102 qubits and, through experiments, a 9-dimensional Gaussian realized using 54 qubits on Quantinuum's H2 quantum processor.

We establish exact scalings for the maximal group velocity of translation-invariant quantum walks in periodic electric fields. Our main result shows that the maximal group velocity decays exponentially with the period of the field in the whole parameter range, thus affirming a conjecture of arXiv:2302.01869 and at the same time augmenting it to an exact equality. We further demonstrate explicit revival relations and characterize the absolutely continuous spectrum in these models. Our results apply directly also to generalized CMV matrices.