SimShadow: Astrophysical & Quantum Simulation

• SimShadow is a multi-disciplinary framework integrating black-hole shadow simulation, quantum noise fingerprinting, and compressed quantum dynamics to optimize system-level analysis.
• Its astrophysical module uses GRMHD models and modular Jones matrices to simulate mm-VLBI visibilities, supporting robust evaluation of imaging pipelines like the EHT.
• The quantum components leverage shadow-inspired estimation to reduce measurement costs by ~2.5×10⁶× and to compress operator dynamics into a low-dimensional state for scalable simulations.

SimShadow encompasses a set of distinct but related frameworks and protocols across computational astrophysics and quantum computing, each leveraging the notion of a "shadow"—as either a physical observable (e.g., black hole silhouette) or a compressed representation of system dynamics or noise. The term SimShadow specifically refers to (i) black-hole shadow simulation pipelines for mm-VLBI, (ii) quantum device noise “fingerprinting” protocols inspired by classical shadow tomography for quantum software engineering (QSE), and (iii) shadow Hamiltonian simulation—a compressed quantum simulation paradigm for evolving operator expectation values. Each instantiation combines high-efficiency data reduction with formal mathematical structures, supporting tasks from event-horizon-scale imaging to noise-aware quantum compilation and scalable dynamical simulation.

1. Black-Hole Shadow Simulation for mm-VLBI

The SimShadow pipeline for black-hole shadow simulation builds on the “Measurement Equation” formalism and modular signal corruption tree from MeqSilhouette (Blecher et al., 2016). It is designed to provide end-to-end simulated observation sets for the Event Horizon Telescope (EHT) and other VLBI arrays operating at (sub)millimeter wavelengths.

At its core, the simulation computes, per baseline, dual-polarization visibilities:

$V_{pq}(t,ν) = J_p(t,ν)\; X_{pq}(t,ν)\; J_q^H(t,ν),$

where $V_{pq}$ is the complex visibility matrix, $X_{pq}$ is the Fourier transform of the sky's intrinsic Stokes vector brightness distribution, and $J_p, J_q$ are station-based cumulative Jones matrices encoding all instrumental corruptions (e.g., tropospheric, ISM, pointing errors).

The physical source model is generated by GRMHD simulations coupled with polarized ray-tracing and radiative-transfer codes (e.g., BHOSS, IPOLE, GRTRANS), producing time- and polarization-resolved FITS cubes as direct inputs to the simulator. Interstellar scattering is implemented using Kolmogorov phase-screen models and the “ScatterBrane” approximation, while the tropospheric corruptions combine mean radiative transfer (ATM code) with turbulent phase screens.

Key instrumental effects, including time-dependent pointing offsets and receiver gain fluctuations, are implemented as Jones nodes that can be parameterized per the observing configuration or drawn from stochastic models. Calibration and imaging strategies (e.g., self-cal, closure modeling, use of Water-Vapor Radiometers) can be benchmarked, with systematic uncertainties evaluated via Monte Carlo over, for example, phase screen realizations.

This architecture enables synthetic data set generation for pipeline validation, parameter estimation studies, and algorithmic development under realistic, variable corruption scenarios, providing a quantitative foundation for assessing EHT performance and parameter inference in the strong-field regime of general relativity (Blecher et al., 2016).

2. SimShadow in Quantum Software Engineering: Live Noise Fingerprinting

SimShadow for QSE is a live, empirical noise-fingerprinting protocol enabling on-the-fly characterization and comparison of noise behaviors across quantum software stacks and hardware platforms (Bensoussan et al., 21 Dec 2025). It addresses the challenge of cross-platform reproducibility in quantum program execution due to opaque or divergent vendor noise model implementations.

The protocol operates in four principal phases:

1. Reference-State Selection: A compact set of $k$ states (computational, superposition, and entangled, e.g., $|00⟩$, $|+⟩|0⟩$, $|\Phi^+⟩$) is selected to probe amplitude, phase, and correlated errors.
2. State Preparation & Measurement: Each reference state $|\psi_i⟩$ is prepared, and a fixed set of $n$ Pauli observables $\{O_j\}$ are measured over $R$ shots.
3. Shadow-Inspired Estimation: Rather than reconstructing full density matrices, SimShadow computes empirical expectation values directly: $$\langle O_j\rangle_{\mathrm{obs},i} = \frac{1}{R} \sum_{r=1}^R o_{i,j}^{(r)}$$ for observed outcome $o_{i,j}^{(r)}$, and subtracts the ideal prediction to form the deviation matrix $$F_{ij} = \langle O_j\rangle_{\mathrm{obs},i} - \langle O_j\rangle_{\mathrm{ideal},i}$$.
4. Deviation-Fingerprint Construction & Comparison: The resulting $F$ encodes noise-induced deviations as a matrix fingerprint, supporting platform comparison via the Frobenius norm $\|F^{(A)} - F^{(B)}\|_F$.

This approach demonstrates efficiency, attaining a $\sim$2.5$\times$10⁶$\times$ reduction in measurement cost relative to process tomography for an 8-qubit system. Empirical studies show that, for standard channels (depolarizing, amplitude and phase damping), cross-platform fingerprint distances are 9–10$\times$ shot noise, revealing systematic divergence in nominally “identical” noise models between simulators (e.g., Qiskit vs Cirq).

SimShadow enables immediate integration into quantum development workflows for noise-aware compilation, automated validation, error mitigation calibration, CI/CD regression detection, and formal verification under empirically observed noise (Bensoussan et al., 21 Dec 2025).

3. Shadow Hamiltonian Simulation for Quantum Dynamics

The SimShadow (shadow Hamiltonian simulation) paradigm encodes the time evolution of expectation values of a finite, user-selected set of Hermitian “probe” observables $\{O_1, ..., O_M\}$ as amplitudes of a compressed “shadow state” living in an $M$-dimensional Hilbert space (Somma et al., 31 Jul 2024).

For a system Hamiltonian $H$ and quantum state $\rho(t)$, the (unnormalized) operator expectation vector is $$v(t) = (\langle O_1 \rangle_t, ..., \langle O_M \rangle_t)^T$$, and the normalized shadow state is

$$|\psi_s(t)\rangle = v(t)/\|v(t)\| = \frac{1}{\sqrt{A(t)}} \sum_{m=1}^M \langle O_m \rangle_t |m\rangle.$$

The time evolution is determined by the invariance property $[H, O_m] = -\sum_{m'} h_{m m'} O_{m'}$ for all $O_m \in S$, defining a “shadow Hamiltonian” $H_S$ on $\mathbb{C}^M$. The shadow amplitudes obey

$$i \partial_t |\psi_s(t)\rangle = H_S |\psi_s(t)\rangle$$

whenever $H_S$ is Hermitian.

The algorithm prepares $|\psi_s(0)\rangle$, constructs a block-encoding of $H_S/\Lambda$ in the sparse-matrix access or $k$-local model, and implements $U_s(t) = e^{-i H_S t}$ via quantum signal processing (QSP) or qubitization. For physical scenarios such as free-fermion and free-boson systems, $H_S$ is sparse or otherwise efficiently implementable, allowing simulation of expectation dynamics for exponentially large systems in time polynomial or even polylogarithmic in system size.

Extensions include simulating two-time correlators (via higher-dimensional shadow states) and the time evolution of operators in the Heisenberg picture—essential for studying operator growth and quantum chaos (Somma et al., 31 Jul 2024).

4. Core Algorithms and Mathematical Structures

Domain	SimShadow Core Object	Key Mathematical Structure
mm-VLBI simulation	Black hole shadow & corrupted visibilities	Measurement Equation formalism, modular Jones chains
QSE noise fingerprinting	Empirical deviation fingerprint matrix	Shadow tomography–inspired estimation, Frobenius distance
Quantum dynamics simulation	Compressed shadow state	Operator expectation encoding, shadow Schrödinger equation

The black hole shadow simulator is fundamentally constructed by composing Jones matrices for each physical corruption/module, acting multiplicatively on the “true” sky coherence. In the QSE context, empirical deviation-fingerprint matrices $F$ are constructed by direct measurement and subtracted analytic predictions, using a specifically selected reference set for maximal error sensitivity. In shadow Hamiltonian simulation, the shadow state's amplitudes directly encode the evolving observables, and the induced evolution is governed by a commutator-closed, efficiently described $H_S$.

5. Practical Applications and Impact

mm-VLBI and Black-Hole Imaging

SimShadow enables end-to-end data generation and analysis for EHT- and VLBI-scale imaging, including the robust assessment of calibration, parameter inference pipelines, and detection limits under variable physical and instrumental corruption. Its modularity allows systematic exploration of the impact of ISM scattering, atmospheric turbulence, pointing errors, and intrinsic source variability on shadow size, shape, and observable features, supporting robust interpretation of high-resolution black-hole images (Blecher et al., 2016).

Quantum Software Engineering

In QSE, SimShadow provides actionable, empirical metrics of platform-specific noise behavior, enabling drift detection, automated cross-platform validation, and routine integration into compiler cost modeling and continuous integration pipelines. By matching noise-aware compilation and transpilation to the actual deviation structure, it supports reliability and transferability in quantum development (Bensoussan et al., 21 Dec 2025).

Scalable Quantum Dynamics

Shadow Hamiltonian simulation facilitates the study of operator expectation evolution for large-scale free-fermion, free-boson, and certain interacting systems (with compact Lie algebra bases), including applications in time-dependent energy computation, multi-time correlation functions, and operator growth. This approach yields exponential savings in resources by sacrificing access to the full system state in favor of tracking only the relevant observables (Somma et al., 31 Jul 2024).

6. Efficiency, Validation, and Extensions

Each SimShadow framework attains efficiency by focusing the computational and experimental budget on the subspace or set of parameters most relevant for the task. In mm-VLBI, this is realized through modular model toggling, parameter scans, and MC validation of result distributions. In QSE, orders-of-magnitude shot-reduction is achieved compared to full process tomography, with direct implications for scalability and workflow integration. In quantum simulation, efficiency arises from reduction to a closed, low-dimensional shadow space under commutator invariance and judicious probe selection.

Validation in each instance involves comparing the simulated result, fingerprint, or expectation trajectory with either synthetic ground truth (pipeline closure) or analytic baseline. Quantitative uncertainty assessment (e.g., MC over phase screens or fingerprints) and cross-tool comparison (e.g., themis, eht-imaging, formal verifiers) are standard in the SimShadow pipelines.

Extensions include, for shadow Hamiltonian simulation, encoding multi-time correlators and Heisenberg-evolved operators, and in the QSE context, automated error-mitigation calibration and tight integration with formal methods for quantum program verification (Bensoussan et al., 21 Dec 2025, Somma et al., 31 Jul 2024).

7. Conclusion

SimShadow represents a family of frameworks spanning signal corruption simulation in astrophysical imaging, empirical noise fingerprinting for quantum software engineering, and efficient compressed-state simulation of quantum dynamics. Across all contexts, the focus is on extracting or tracking relevant subspaces—whether visibilities, deviations, or operator expectations—leading to scalable, modular, and robust protocols. These approaches constitute essential infrastructure for systems-level validation and analysis at the frontier of both observational astrophysics and quantum information processing (Blecher et al., 2016, Bensoussan et al., 21 Dec 2025, Somma et al., 31 Jul 2024).