Papers

Magic State Distillation is considered to be one of the promising methods for supplying the non-Clifford resources required to achieve universal fault tolerance. Conventional MSD protocols implemented in surface codes often require multiple code blocks and lattice surgery rounds, resulting in substantial qubit overhead, especially at low target error rates. In this work, we present practical magic state distillation factories on Bivariate Bicycle (BB) codes that execute Pauli-measurement-based Clifford circuits inside a single BB code block. We formulate distillation circuit design as a joint optimization of logical qubit mapping, gate scheduling, measurement nativization, and protocol compression via qubit recycling. Based on detailed resource analysis and simulations, our BB factories have space-time volume comparable to that of leading distillation factories while delivering lower target error at a smaller qubit footprint, and are particularly compelling as second-round distillers following magic state cultivations.

The aging transition refers to the shift from an oscillatory state to a globally ceased state due to some forms of deterioration in classical physics. Similar behavior has also been observed in quantum oscillators. Although it has received extensive attention in coupled oscillator systems, it has not yet been studied in coupled qubits. In this manuscript, we explore the aging transition in a network of coupled qubits. Our model describes {numerous} qubits driven by a laser, with both dissipative and coherent qubit-qubit couplings. The ratio of inactive qubits to total qubits and the population in the excited state of the qubits are employed to characterize the aging transition. We find a transition where the population in the excited states suddenly drops when the ratio exceeds a threshold. This behavior is intriguing and contrasts with coupled oscillators, where no sudden drop is observed. Additionally, we demonstrate how the couplings and driving laser influence the threshold. The underlying physics of the sudden drop is elucidated. The region where the aging transition occurs is determined based on stability analysis theory.

Black holes permit matter to cross their event horizon in only one direction. We show that interacting bosons in optical lattices with asymmetric barrier exhibit an analogous phenomenon, creating unidirectional quantum transport without external driving or dissipation. This directionality emerges purely from many-body interactions, which cause asymmetric projection of the initial state onto transport-enabled or transport-forbidden sectors. The resulting dynamics create an effective one-way boundary in Hilbert space, forming a quantum analog of a black-hole event horizon. Our results establish interactions as a fundamentally new route to directional transport, enabling coherent rectification in atomtronic circuits by the use of intrinsic properties of the system only.

Quantum machine learning (QML) sits at the intersection of quantum computing and classical machine learning, offering the prospect of new computational paradigms and advantages for processing complex data. This chapter introduces the fundamentals of QML for readers from both communities, establishing a shared conceptual foundation. We connect the worst-case, adversarial perspective from theoretical computer science with the physical principles of quantum systems, highlighting how superposition, entanglement, and measurement collapse influence learning and robustness. Special attention is given to adversarial robustness, understood as the ability of QML models to resist inputs designed to cause failure. We motivate the study of QML in adversarial settings, outlining distinctions between classical and quantum data and computations when the adversary is a core element. This chapter serves as a starting point to adversarial and robust quantum machine learning in subsequent chapters.

Sidney Coleman has noted that superluminal particles or observers would be able to go back in time and have no definite trajectory according to subluminal observers, while not violating Lorentz invariance [1]. Recently, Dragan and Ekert have significantly developed similar ideas even further, which lead to formulation of “quantum principle of relativity” that intimately links the two theories [2]. However, field theory descriptions of an on-shell tachyon, described by scalar field $\phi$ with negative mass squared parameter, lead to violation of basic principles of relativity or quantum mechanics. In this work, we investigate whether purely virtual tachyons can be consistent within the fakeon framework–the only known viable formulation of purely virtual particles. We show that the supports of the real part of the tachyon Feynman propagator, which is also the principal-value propagator (PVP), and the Wheeler propagator intersect only on the light cone. We show that PVP cannot be time-ordered two-point function of a local Hermitian field, excluding the direct extension of the canonical formalism to free fakeon tachyon. Finally, with an imposed tachyonic PVP, interactions with electrons generate composition-dependent accelerations that violate the weak equivalence principle, and we provide a quantitative bound on this scenario. Our analysis identifies obstacles to formulating covariant quantum field theory of interacting virtual tachyon.

We present a universal fault-tolerant quantum computing architecture based on identical particle qubits (IPQs), where we find that the first-order IPQ - bath interaction fundamentally differs from the conventional first-order qubit-bath interaction. This key distinction necessitates a redesign of existing strategies to fight decoherence. We propose that the simplest quantum error correction code can be realized directly within the physical qubit, provided that conventional correction and restoration are generalized beyond unitary operations to employ physically implementable reversal operations – naturally placing logical and physical qubits on equal footing. We further demonstrate that dynamical decoupling (DD) remains effective within this unified framework, and that a decoherence-free subspace (DFS) – like structure emerges. Unlike previous approximate treatments, our analytically solvable IPQ-Bath model enables rigorous testing of these strategies, with numerical simulations validating their effectiveness.

We report progress toward a CMOS-integrated quantum diamond biosensing platform that combines nitrogen-vacancy (NV) centers in diamond with a custom 40 nm CMOS Single-Photon Avalanche Diode (SPAD) array. The system integrates on-chip active quenching and digital readout with external FPGA-based photon counting, compact microwave delivery, and practical optical excitation and collection schemes to support widefield optically detected magnetic resonance (ODMR). System-level design considerations spanning fluorescence collection efficiency, detector count-rate capability, and microwave homogeneity are analyzed with biological compatibility and scalability in mind. Using superparamagnetic iron oxide nanoparticle (SPION)-labeled HEK293T cells as a representative use case, simple dipole-field estimates indicate that sub-$\mu$T sensitivity is required to resolve ODMR shifts within typical ensemble linewidths. Based on the proposed architecture and efficiency analysis, a magnetic field sensitivity of approximately 90 nT/$\sqrt{\mathrm{Hz}}$ per pixel is estimated. These results outline a practical path from optics-heavy quantum diamond microscopes toward compact, CMOS-integrated NV-based biosensors for quantitative magnetic imaging in complex biological environments.

We introduce a data-driven framework for approximating the convex set of $N$-representable two-electron reduced density matrices (2-RDMs). Traditional approaches characterize this set through linear matrix inequalities that define its supporting hyperplanes. Here, we instead learn a vertex-based approximation to its boundary from molecular data and use this information to improve the set defined by low-order positivity constraints, without explicitly constructing higher-order conditions. The resulting semidefinite machine learning approach – combining an input convex neural network with semidefinite programming – drives a direct variational calculation of the 2-RDM with enhanced accuracy at computational cost comparable to two-positivity calculations. Applications to the potential energy curves of ${\rm C}_2^{2-}$, ${\rm N}_2$, and ${\rm O}_2^{2+}$ demonstrate these systematic improvements as well as close agreement with complete active space configuration interaction results. Overall, semidefinite machine learning interweaves data-driven boundary information with semidefinite positivity constraints to yield more accurate energies and 2-RDMs without explicit higher-order positivity conditions.

Fractional statistics give rise to quantum behaviors that differ fundamentally from those of bosons and fermions. While two-dimensional anyons play a major role in strongly correlated systems and topological quantum computing, the nature of their one-dimensional (1D) counterparts remains the subject of intense debate, with renewed interest fueled by recent experimental progress. Theoretically, 1D anyons are predicted to host exotic many-body phases and quantum phase transitions, yet experimental signatures have remained elusive. Using ultracold atoms in an optical lattice, we prepare two-body ground states of the 1D anyon-Hubbard model by combining Hamiltonian engineering via quasiperiodic drives and adiabatic state manipulation. We uncover the effects of statistical interactions that lead to pseudo-fermionization and to the formation of chiral bound states when particles remain close together. Our results establish a link between lattice and continuum realizations of anyon models, and mark important steps towards the precise control of 1D anyons in both equilibrium and out-of-equilibrium settings.

The zero-point energy of a trapped ultracold Fermi gas at unitarity is investigated in relation to the combined effects of the Heisenberg uncertainty principle and the Pauli principle. This lowest allowed quantum state is a superfluid state which has been studied extensively both experimentally and theoretically. The method used for the current investigation is based on a recent series of papers that proposed microscopic dynamics based on normal modes to describe superfluidity instead of real-space Cooper pairs. This approach yielded excellent agreement with experimental data for multiple properties and allowed the microscopic behavior underlying these results as well as the basis of universal behavior to be analyzed in detail using the group theoretic basis of this general N-body approach. This microscopic picture is now used to illucidate the roles played by the uncertainty principle and the Pauli principle in determining the energy and character of the lowest allowed quantum state including the squeezed character of this superfluid state and the suppression of the Pauli principle.

Quantum sensing exploits nonclassical states of light, including multiphoton entangled states and squeezed states, to achieve superresolution and/or super-sensitivity. However, its practical implementation is constrained by state-generation complexity, photon loss, and detection efficiency. Here, we present a quantum-operator analysis of coherence de Broglie wavelength (CBW) in an anti-symmetrically coupled Mach-Zehnder interferometer (MZI) architecture and clarify the origin of its superresolution and enhanced phase sensitivity. The two-mode SU(2) structure of the MZI, represented by Pauli operators, shows that successive basis-realigned transformations produce an Nth-order unitary U^N(phi), yielding N-fold phase accumulation (1+cosNphi). The quantum-operator description is particularly significant at the single-photon level, where even a single photon undergoes the Nth-order unitary evolution through its coherent evolution in the two-mode state space. This differs from entanglement-based quantum sensing based on photonic de Broglie wavelength interferometry, where N-fold phase accumulation is associated with an N-photon entangled state. The same SU(2) transformation also applies to coherent classical fields, establishing a classical-quantum correspondence of the CBW phase evolution. Fisher-information analysis further shows that the architecture-induced phase transformation yields an order-dependent enhancement of phase sensitivity without increasing the photon number or statistical sampling. CBW therefore provides an architecture-controlled route to high-order interferometric superresolution, accompanied by enhanced phase sensitivity, with potential applications to fringe-counting wavemetry and Fourier-transform-based sensing.

Limited circuit depth remains a central constraint for quantum optimization in the noisy intermediate-scale quantum (NISQ) regime, where shallow unitary dynamics may fail to sufficiently concentrate probability on low-energy configurations. We introduce Measurement-Guided Initialization (MGI), an iterative strategy that uses measurement outcomes from previous executions to update the initialization of subsequent runs. The method extracts single-qubit marginal probabilities from dominant measurement outcomes and prepares a biased product-state initialization, allowing information obtained during optimization to be reused without introducing classical parameter optimization. We implement this approach in the context of the Feedback-Based Algorithm for Quantum Optimization (FALQON) and evaluate its performance on weighted MaxCut instances. Numerical results show that measurement-guided initialization improves the performance of shallow-depth circuits and enables iterative refinement toward high-quality solutions while preserving the non-variational structure of the algorithm. These results indicate that measurement statistics can be exploited to improve shallow quantum optimization protocols compatible with NISQ devices.

We study the problem of maximizing a complex-valued quadratic form over the $K^{\text{th}}$ roots of unity. We show that when the objective matrix $\mathbf{Q}^\star \in \mathbb{C}^{n \times n}$ of the quadratic has rank $r$, the global maximizer belongs to a candidate set of size $O(rn^{2r-1})$. This set can be constructed deterministically in $O(rn^{2r+1})$ time by enumerating the vertices of a hyperplane arrangement in $\mathbb{R}^{2r}.$ The algorithm is embarrassingly parallel; with~$P$ processors, the time complexity drops to $O(r n^{2r+1}/P)$. For approximately low-rank settings, where the objective matrix is a noise-perturbed variant of a rank-$r$ matrix, we prove that applying our framework to a spectral truncation yields a multiplicative $(1 - O(\left\|\mathbf{H}\right\|_2 / \delta^{\star}))$-approximation guarantee, where $\delta^{\star}$ denotes the eigengap of the underlying rank-$r$ matrix and $\mathbf{H}$ represents the perturbation. To scale to high-dimensional problems, we establish a randomized sampling variant. We prove that uniformly sampling $S \geq O(1/\varepsilon^{r-1})$ candidates achieves a $(1-\varepsilon)\cos^2(\pi / K)$-approximation of the optimal rank-$r$ solution with high probability. Crucially, this sample size is entirely independent of $n$, reducing the overall runtime to $O(S \cdot n^2)$. Computational experiments on synthetic benchmarks and large-scale graphs for Max-3-Cut confirm that our algorithms match or exceed semi-definite programming solution quality on structured instances while enabling massive parallelization across heterogeneous hardware and scaling seamlessly to problems where $n \geq 10^6$.

Quantum machine learning (QML) is rapidly transitioning from theoretical promise to practical relevance across data-intensive scientific domains. In this Review, we provide a structured overview of recent advances that bridge foundational quantum learning principles with real-world applications. We survey foundational QML paradigms, including variational quantum algorithms, quantum kernel methods, and neural-network quantum states, with emphasis on their applicability to complex quantum systems. We examine neural-network quantum states as expressive variational models for correlated matter, non-equilibrium dynamics, and open quantum systems, and discuss fundamental challenges associated with training and sampling. Recent advances in quantum-enhanced sampling and diagnostics of learning dynamics, including information-theoretic tools, are reviewed as mechanisms for improving scalability and trainability. The Review further highlights application-driven QML frameworks in drug discovery, cancer biology, and agro-climate modeling, where data complexity and constraints motivate hybrid quantum-classical approaches. We conclude with a discussion of federated quantum machine learning as a route to distributed, privacy-preserving quantum intelligence. Overall, this Review presents a unified perspective on the opportunities and limitations of QML for complex systems.

This brief note is written with a somewhat similar purpose to Earman's 2011 paper on the conceptual problems on the Unruh effect. However, we confine ourselves to Sewell's modular approach to the Unruh effect, which is based on the theorems of Tomita-Takesaki and Bisognano-Wichmann. This approach is rigorous, and has an advantage of being model-independent. However, we will see that a number of conceptual problems remain unsolved on this approach.

Hilbert space fundamentalism (HSF) states that everything about the physical world is encoded in the Hamiltonian operator and the state vector (as a unit vector, not a wavefunction, which requires additional specification of a configuration space, a position basis, or the position observables). That all structures needed to describe reality, including subsystems, space, fields, emerge from these. I show that HSF can't account for our observations that the physical world changes in time.

An atomic Josephson junction realized with dipolar bosons in a double-well potential can be described by an extended Bose-Hubbard model in which dipolar interactions generate an effective on-site interaction and nearest-neighbor pair tunneling. Using mean-field theory and exact diagonalization, we investigate how this correlated process affects zero-temperature equilibrium and dynamical properties of the system. In equilibrium, we show that pair tunneling induces ground-state parity modulations and significantly reshapes the phase diagram, producing qualitative changes in the quantum phase transitions toward NOON and phase-NOON states, as well as quantitative shifts of the critical points. Out of equilibrium, we demonstrate that it modifies the conditions for macroscopic quantum self-trapping, and assess its impact by comparing mean-field and fully quantum evolution, including the emergence of dynamical quantum phase transitions.

Accurate calibration of coherent optical receivers is essential for reliable performance assessment in coherent communications, precision and quantum sensing, and continuous-variable quantum key distribution (CV-QKD), where the effective detection efficiency directly impacts channel parameter estimation. We present a methodology traceable to the International System of Units (SI) to determine the effective heterodyne detection efficiency of balanced receivers using shot-noise-referenced measurements. The protocol relies on two observables acquired with an electrical spectrum analyzer: the heterodyne beat-note power and the local oscillator shot-noise variance, with explicit treatment of the analyzer's equivalent noise bandwidth (ENBW). The photon flux in the signal path is referenced to SI units via calibrated radiometric standards. We first validate the protocol on a free-space receiver, demonstrating consistency with an independently constructed optical loss chain across a wide range of signal powers and under controlled, calibrated attenuation. Extending the same estimator to a fiber-coupled, polarization-maintaining balanced receiver confirms that the protocol is robust for practical coherent-receiver architectures and intermediate frequencies in the MHz range. These results establish a traceable, uncertainty-bounded framework for real-time receiver calibration, providing a practical route for CV-QKD and other coherent optical systems.

We approach the 3-SAT satisfiability problem with the quantum-inspired method of imaginary time propagation (ITP) applied to matrix product states (MPS) on a classical computer. This ansatz is fundamentally limited by a quantum entanglement barrier that emerges in imaginary time, reflecting the exponential hardness expected for this NP-complete problem. Strikingly, we argue based on careful analysis of the structure imprinted onto the MPS by the 3-SAT instances that this barrier arises from classical computational complexity. To reveal this connection, we elucidate with stochastic models the specific relationship between the classical hardness of the $\sharp$P $\supseteq$ NP-complete counting problem $\sharp$3-SAT and the entanglement properties of the quantum state. Our findings illuminate the limitations of this quantum-inspired approach and demonstrate how purely classical computational complexity can manifest in quantum entanglement. Furthermore, we present estimates of the non-stabilizerness required by the protocol, finding a similar resource barrier. Specifically, the necessary amount of non-Clifford operations scales superlinearly in system size, thus implying extensive resource requirements of ITP on different architectures such as Clifford circuits or gate-based quantum computers.

In this work, we present a technique for quantum state preparation in transmon qubit system that employs optimized electromagnetic pulse sequences rather than discrete quantum gates. By focusing directly on quantum correlations rather than specific target states, we optimize the pulse parameters to generate the desired entanglement structures in two and three qubits systems. The resulting protocols reproduce the characteristic entanglement properties associated with the Bell, GHZ, and W classes, reaching values of the corresponding entanglement measures consistent with these entanglement structures. The approach uses a reduced set of parameters to characterize the control pulses, thereby restricting the space explored during optimization while retaining the entanglement properties of interest.

Resonant inelastic X-ray scattering (RIXS) is the workhorse experimental technique for probing the structural degradation of higher-capacity cathode materials. However, the interpretation of experimental spectra is challenging due to the lack of accurate simulations. In this work, we propose a quantum algorithm for simulating the RIXS spectrum of molecular clusters hypothesized to form in Li-excess cathodes. The algorithm uses quantum phase estimation to sample the spectrum from a state encoding the scattering transition amplitudes of the cluster valence excitations. We prepare this state in the quantum computer using a block-encoding of the dipole operator and quantum signal processing to implement the Green's function propagator over intermediate core-excited states. To showcase the algorithm, we use a model cluster proposed in recent experimental works consisting of an oxygen dimer bonded to a manganese atom. Using the PennyLane software platform, we report resource estimation for simulating RIXS spectra for chemically motivated active spaces of increasing sizes. For a classically challenging active space with 20 orbitals, the algorithm requires $2.0 \times 10^{10}$ Toffoli gates and $414$ logical qubits.

Passive error correction schemes have so far been limited to static memories rather than dynamical qubits. We demonstrate that a driven-dissipative bosonic system, the Bose-Hubbard dimer (BHD), can encode a persistently oscillating qubit within a dynamical noiseless subsystem (DNS). The strong parity symmetry of the system leads to degenerate stationary states, whose mutual coherence breaks the time translation symmetry, giving rise to a time crystal in the thermodynamic limit. This time crystal undergoes a dissipative phase transition controlled by the driving force, with the DNS present above the transition point. This noiseless subsystem, and hence the qubit, is resilient to collective loss and at most quadratically affected when the strong symmetry condition is weakened. The decoherence from collective dephasing also cancels in the leading order, with the cancellation being exact at a specific drive strength, set by the photon-number difference between the two logical states. Tuning the drive extends this cancellation to unbalanced dephasing. These results establish dissipative time crystals as a medium for autonomously stabilized oscillating qubits.

We develop a systematic theory of spectral decimation for quantum many-body Hamiltonians and show that it provides a quantitative probe of emergent symmetries in statistically mixed spectra. Building on an analytical description of statistical mixtures, we derive an explicit expression for the size of a characteristic symmetry sector (CSS), defined as the largest subsequence of levels exhibiting non-Poissonian correlations. The CSS dimension is shown to be the size-biased average of the underlying symmetry sectors, establishing a direct link between spectral statistics and Hilbert-space structure. We apply this framework to two paradigmatic settings: Hilbert-space fragmentation and disorder-induced many-body localization (MBL). In fragmented systems, the CSS reproduces the mixture prediction and isolates correlated subsectors even when the full spectrum appears nearly Poissonian. In the disordered Heisenberg chain, spectral decimation reveals the gradual emergence of integrability through a shrinking CSS, whose statistics exhibit signatures consistent with local integrals of motion. We introduce a characteristic symmetry entropy (CSE) as a finite-size scaling observable and extract, within accessible system sizes, the crossover exponents. Our results establish spectral decimation as a controlled, unbiased and computationally inexpensive diagnostic of hidden structure in many-body spectra, capable of distinguishing between chaotic dynamics, statistical mixtures, and emergent integrability.

Fast decoders that achieve strong error suppression are essential for fault-tolerant quantum computation (FTQC) from both practical and theoretical perspectives. The union-find (UF) decoder for the surface code is widely regarded as a promising candidate, offering almost-linear time complexity and favorable empirical error suppression supported by numerical evidence. However, the lack of a rigorous threshold theorem has left open whether the UF decoder can achieve fault tolerance beyond the error models and parameter regimes tested in numerical simulations. Here, we provide a rigorous proof of a finite threshold for the UF decoder on the surface code under the circuit-level local stochastic error model. To this end, we develop a refined error-clustering framework that extends techniques previously used to analyze cellular-automaton and renormalization-group decoders, by showing that error clusters can be separated by substantially larger buffers, thereby enabling analytical control over the behavior of the UF decoder. Using this guarantee, we further prove a quasi-polylogarithmic upper bound on the average runtime of a parallel UF decoder in terms of the code size. We also show that this framework yields a finite threshold for the greedy decoder, a simpler decoder with lower complexity but weaker empirical error suppression. These results provide a solid theoretical foundation for the practical use of UF-based decoders in the development of fault-tolerant quantum computers, while offering a unified framework for studying fault tolerance across these practical decoders.

A key challenge of extreme ultraviolet (EUV) lithography in semiconductor fabrication is the line edge roughness or "blur" produced by the electron cascades following absorption of a high-energy photon. Here we present quantum algorithms to compute EUV absorption and photoelectron emission spectra, which are key to predicting blur. The first is a time-domain algorithm resolving absorption at a given frequency; the second is a first-quantized plane-wave algorithm computing the photoemission spectrum via real-time dynamics that treats bound and continuum states on equal footing. For a model photoresist monomer IMePh, 92 eV absorption requires $200$ logical qubits and $10^{9}$ non-Clifford gates per circuit with $10^3$ shots, while the photoemission spectrum needs $\geq 10^{14}$ gates, $10^4$ shots, and several thousand logical qubits. These results establish high-fidelity quantum simulations as a key component to parameterize the multi-scale macroscopic models required to overcome the electron blur bottleneck in semiconductor miniaturization.

We present trainsum, a versatile Python package for doing computations with multidimensional quantics tensor trains: https://github.com/fh-igd-iet/trainsum. Using the Array API standard together with opt_einsum, trainsum allows the effortless approximation of tensors or functions by tensor trains independent of their shape or dimensionality. Once approximated, our package can perform normal arithmetic operations with quantics tensor trains, including addition, Einstein summations and element-wise transformations. It can be therefore used for generic computations with applications in simulation, data compression, machine learning and data analysis.

We study two-dimensional translation-invariant CSS stabilizer codes over prime-dimensional qudits on the square lattice under twisted boundary conditions, generalizing the Kitaev $\mathbb{Z}_p$ toric code by augmenting each stabilizer with two additional qudits. Using the Laurent-polynomial formalism, we adapt the Gröbner basis to compute the logical dimension $k$ efficiently, without explicitly constructing large parity-check matrices. We then perform a systematic search over various stabilizer realizations and lattice geometries for $p\in\{3,5,7,11\}$, identifying qudit low-density parity-check codes with the optimal finite-size performance. Representative examples include $[[242,10,22]]_3$ and $[[120,6,20]]_{11}$, both achieving $k d^{2}/n=20$. Across the searched regime, the best observed $k d^{2}$ at fixed $n$ increases with $p$, with an empirical relation $k d^{2} = 0.0541 \, n^{2}\ln p + 3.84 \, n$, compatible with a Bravyi–Poulin–Terhal-type tradeoff when the interaction range grows with system size.

We present a general framework for simulating quantum systems in the Heisenberg picture on quantum hardware. Based on the vectorization map, our framework fully exploits the mapping between operators and quantum states, allowing any task defined on Heisenberg operators to be mapped to standard Schrödinger-picture tasks that are naturally accessible via quantum computers and simulators. This yields new or improved protocols for tasks such as operator sampling, the computation of OTOCs/superoperator expectation values and their higher order moments, two-point correlators, and operator stabilizer and entanglement entropies. Our approach is also amenable to implementation, as it inherits the structure and resource requirements of the (forward and time-reversed) Schrödinger-picture quantum simulation problem. We demonstrate this by proposing implementations of our framework for a 2D problem on digital and analog quantum simulators, taking into account device connectivity constraints.

We consider bosonization of supersymmetry in the context of Wess-Zumino quantum mechanics. Our motivation for this investigation is the flexibility the bosonic fock space affords as any classical probability distribution can be realized on it making it a versatile framework to work with for quantum processes. We proceed by constructing a minimal bosonization of a system with one bosonic and two fermionic degrees of freedom. We iterate this process to construct a tower of SUSY systems that is akin to unfolded Adinkras. We then identify an osp(2|2) symmetry of the system constructed. To build an irreducible representation of the system we induce representations across the sectors, a first to our knowledge, as the previous work have focused on induction only within the bosonic sector. First, we start with a fermionic representation using Clifford algebras and then induce a representation to gl(2|2) and restrict it to osp(2|2). In the second method, we induce a representation from that of the bosonic sector. In both cases, our representations are in terms of qubit operators that provide a way to solve SUSY problems using quantum information based approaches. Depending upon the direction of induction the representations are suitable for implementation on a hybrid qubit and fermionic or bosonic quantum computers.

Accurate characterization of coherent and non-Markovian errors remains a central challenge in quantum information processing, as conventional benchmarking techniques typically rely on Markovian and time-independent noise assumptions. In practice, however, quantum devices exhibit both systematic coherent miscalibrations and temporally correlated fluctuations, which complicate error diagnosis and mitigation. Here, we apply a technique based on tangent-space decomposition to characterize such error in single-qubit quantum gates implemented on a trapped ion platform. Small imperfections in a quantum operation are treated as perturbations of the target quantum map, represented as tangent vectors in the space of quantum channels. This formulations enables a natural decomposition of the deviation into three components corresponding to coherent, Markovian and non-Markovian processes.The relative weights of these components provide a quantitative measure of the contribution from each type of error mechanism, directly from a single tomographic snapshot. We experimentally validate this method on a single-qubit gates implemented on a trapped $^{40}$Ca$^+$ ion, where control is achieved through laser-driven optical transitions. By analyzing experimentally reconstructed process matrices, expressed in the Pauli Transfer Matrix and Choi representations, we identify and quantify non-Markovian effects arising from controlled injection of slow fluctuations in the experimental environment. We also characterize deterministic coherent miscalibrations using the same technique. This approach provides a physically transparent and experimentally accessible tool for diagnosing complex error sources in quantum control systems.