Project Description

Abstract

The SpinQC4EO project, conducted by Equal1 Laboratories Ireland Ltd (Equal1) in collaboration with ESA Φ-lab at ESRIN (Frascati, Italy), investigates the applicability of hybrid spin-based quantum–classical computing (HQC) to computational problems arising in Earth Observation (EO) data processing, quality control, and satellite mission optimization. The project combines a feasibility study with the deployment and integration of a silicon-spin quantum processor within ESA's existing High-Performance Computing (HPC) environment, providing an on-premises platform for the development and experimental evaluation of hybrid quantum–classical workflows.

As part of the project, Equal1 is deploying its six-qubit silicon-spin quantum computing system, RacQ-1 (formerly Bell-1), at ESRIN. The compact, rack-mounted system is integrated directly with the HPC infrastructure, enabling classical resources to perform data preparation, optimization, and post-processing. At the same time, selected computational kernels are executed on the Quantum Processing Unit (QPU). Equal1's scope encompasses system delivery, installation, HPC integration, commissioning, and operations.

The technical investigation addresses two representative EO problem classes. The first concerns Synthetic Aperture Radar (SAR) tomography, where Quantum Singular Value Transformation (QSVT) is investigated for matrix operations associated with adaptive Capon beamforming. The application targets the reconstruction of forest vertical scattering profiles and the retrieval of structural parameters, including canopy height. The second concerns satellite mission planning, formulated as a constrained combinatorial optimization problem and investigated using variational quantum methods, including approaches based on the Variational Quantum Eigensolver (VQE).

The quantum and hybrid implementations are benchmarked against corresponding state-of-the-art classical methods using representative EO datasets and problem instances. The assessment considers numerical accuracy and solution quality, as well as quantum resource requirements, circuit complexity, hardware noise, data-encoding costs, classical–quantum communication overhead, and scalability with problem size. The objective is to establish the current capabilities and limitations of spin-based hybrid quantum computing for EO applications and to identify the algorithmic and hardware requirements for progression towards larger-scale implementations.

Detailed Description

Scientific and Technical Context

Earth Observation processing comprises a broad range of inverse, estimation, and optimization problems. Examples include SAR image formation and tomography, parameter retrieval, adaptive filtering, classification, sensor calibration, and satellite acquisition planning. As spatial, temporal, and spectral resolution increase, these applications require processing large multidimensional datasets and, in several cases, repeated execution of computationally expensive linear algebra or optimization operations.

SpinQC4EO investigates whether selected computational components of these workflows can be reformulated for execution on a quantum processor and embedded within an HPC-based processing chain.

The project is explicitly based on a hybrid quantum–classical architecture. The QPU is therefore treated as an accelerator for selected computational kernels rather than as a replacement for the classical computing infrastructure. This distinction is particularly relevant for current quantum processors, for which qubit number, circuit depth, gate fidelity, and data-loading requirements constrain the size and structure of executable problems.

The investigation consequently addresses both the mathematical properties of the candidate quantum algorithms and their implementation on physical quantum hardware.

Quantum Computing Platform and HPC Integration

Equal1 is deploying a six-qubit silicon-spin quantum computing system, RacQ-1, within ESA's on-premises computing infrastructure at ESRIN. The processor is based on semiconductor spin-qubit technology and is implemented as a rack-mounted system incorporating the cryogenic, control, and computing subsystems required for operation.

The QPU is integrated with ESA's HPC environment to enable execution of hybrid computational workflows. In this configuration, classical computing resources are used for operations such as input preparation, parameter optimization, and processing measurement results, while quantum circuits are submitted to the QPU for execution.

Equal1's technical scope includes:

• delivery and installation of the quantum computing system;
• integration with ESA's HPC infrastructure;
• system commissioning and acceptance activities;
• QPU calibration and characterization;
• establishment of the software interface required for hybrid execution;
• operational and remote technical support.

The integrated platform provides an experimental environment in which quantum algorithms can be evaluated under the conditions imposed by a physical QPU rather than exclusively through ideal or noise-model simulation.

Methodology

The work is organized into five technical phases.

1. Requirements and Use-Case Definition

Candidate EO applications are analyzed to identify computational kernels suitable for quantum implementation. For each selected problem, the mathematical formulation, input-data characteristics, classical reference algorithm, and evaluation metrics are defined.

The selection criteria include computational complexity, compatibility with available quantum algorithms, quantum-resource requirements, and the possibility of constructing meaningful classical reference implementations.

2. System Architecture and Integration

The quantum system is integrated into the ESA computing environment. The work addresses the hardware and software interfaces required for communication between HPC resources and the QPU and establishes the execution workflow for hybrid algorithms.

The resulting architecture supports the sequence

classical preprocessing → quantum circuit preparation and execution → measurement → classical post-processing or optimization.

For variational algorithms, this sequence is executed iteratively until the specified convergence criterion is reached.

3. Algorithm Development and Adaptation

Quantum and hybrid algorithms are developed for the selected EO use cases. The work includes transforming the original mathematical problems into representations compatible with quantum computation, constructing the corresponding circuits, and implementing the required classical components.

The principal algorithmic approaches considered include:

• Quantum Singular Value Transformation (QSVT) as a Fault Tolerant algorithm for Use Case 1 (Earth Observation, SAR) and Use Case 3 (Quantum Chemistry and Materials)
• Variational quantum algorithms as NISQ hardware demonstrations, the three Use cases
• Quantum neural network classifier for Use Case 1 (Earth Observation, classification)
• Quantum Approximate Optimization Algorithm for Use Case 2 (Satellite planning)
• Variational Quantum Eigensolver for Use Case (Ground state estimation)

Algorithm development is performed with explicit consideration of the limitations of the available QPU.

4. Experimental Benchmarking

Quantum implementations are evaluated against appropriate classical reference methods. Where applicable, experiments are conducted using representative EO datasets or problem instances derived from EO applications.

The benchmarking methodology depends on the use case considered.

• Numerical accuracy relative to the baseline reference is a key consideration, particularly for Use Case 1; in this case, reconstruction or estimation error is provided.
• Objective-function value for optimization problems is a key consideration for Use Case 2.
• Number of qubits, quantum circuit depth, number of circuit executions, and measurements are important for resource estimation in all cases.
• Classical preprocessing and post-processing costs are accounted for in the architecture.
• Quantum data-encoding costs are a key factor for fault tolerant algorithms such as QSVT.

This allows algorithmic performance to be separated from the additional costs of executing on physical quantum hardware.

5. Scalability Assessment

Scalability assessments have been performed for the Fault Tolerant methods, as they identify requirements for qubit count and quantum circuit depth and influence the time and energy required for computation.

SAR tomography with QSVT as Fault Tolerant Method

Earth surface classification with QNN as a NISQ Hardware Demonstration

The first application concerns Synthetic Aperture Radar tomography (TomoSAR).

TomoSAR exploits multiple complex SAR observations acquired with different spatial baselines to estimate the distribution of radar scattering along the elevation direction. For forest observations, the reconstructed vertical reflectivity profile contains information on the distribution of scattering within the vegetation layer and can be used to derive parameters related to forest vertical structure and canopy height.

Adaptive spectral estimators, such as the Capon beamformer, provide greater resolution than conventional non-adaptive beamforming approaches. Their application requires operations involving the covariance matrix of the observations and its inverse, or equivalent linear-algebra operations.

SpinQC4EO investigates a quantum formulation in which Quantum Singular Value Transformation (QSVT) is applied to computational components associated with the adaptive Capon estimator as a Fault Tolerant method with potential for quantum advantage.

Synthetic Aperture Radar tomography (TomoSAR) is evaluated using P-band ESA AfriSAR data over the Mondah tropical forest site in Gabon with LiDAR CHM and DTM from LVIS as ground truth. Specifically, SpinQC4EO investigates a quantum formulation in which Quantum Singular Value Transformation (QSVT) is applied to approximate R-1 via a polynomial transformation of singular values of a block-encoded matrix over condition numbers and tolerance.

The analysis evaluates whether the quantum formulation reproduces classical behavior. For high kappa, the results match classical Capon, which is the state of the art in terms of accuracy.

Satellite Mission Planning

The second application concerns EO satellite mission planning, formulated as a constrained combinatorial optimization problem over satellite constellations (e.g., Menut, Platero, Accenture-1, Hammer).

A mission-planning problem consists of selecting acquisition opportunities subject to kinematic slew rate (0.1°/s), stabilization time (60 s), cloud cover, sun zenith angle, and ground panel coverage constraints across Areas of Interest.

For quantum optimization, the problem is formulated as a Constraint Programming (CP) model and converted into Quadratic Unconstrained Binary Optimization (QUBO) format with quadratic weights encoding opportunity conflict constraints and linear weights rewarding panel acquisition.

SpinQC4EO investigates a variational quantum approach based on the Quantum Approximate Optimization Algorithm (QAOA) mapped to Ising spin Hamiltonians:

• preparation of a parameterized state |psi(gamma, beta)> using cost and mixer Hamiltonians;
• execution of the l-layer QAOA circuit on quantum hardware or simulators;
• measurement of cost expectation values;
• classical parameter optimization using Nelder-Mead and random sampling;
• repetition until parameter convergence.

The experimental analysis evaluates the approximation ratio alpha = C(x_QAOA) / C(x_best), achieving alpha > 0.9 across random QUBO benchmarks and demonstrating competitive quality compared with classical Simulated Annealing and Tabu search solvers.

Resource scaling indicates linear qubit requirements, O(n), in the number of opportunity decision variables, and a worst-case circuit depth of O(l n^2), highlighting QAOA's potential to provide warm-start states to classical solvers in hybrid execution workflows.

Performance Assessment

The assessment of the use cases distinguishes between algorithmic complexity and end-to-end computational performance.

The following quantities are therefore considered in the performance evaluation:

• accuracy: agreement with classical reference results or known solutions;
• solution quality: objective value obtained for optimization problems;
• quantum resources: qubit count, circuit depth, and number of circuit executions;
• hardware effects: sensitivity to noise and finite gate fidelity;
• data preparation: computational cost of mapping classical EO data to the quantum representation;
• hybrid overhead: cost of classical–quantum communication and iterative classical processing;
• scalability: evolution of these quantities with increasing problem dimension.

The analysis incorporates state preparation, block encoding, circuit depth execution, repeated measurements, classical parameter optimization, and post-selection/rescaling costs.

The resulting measurements provide the basis for comparing the investigated quantum formulations with established classical implementations.

Project Outcomes

SpinQC4EO has produced an experimental assessment of silicon-spin quantum computing applied to representative EO processing and optimization problems within an operational HPC environment.

The project established:

• Hardware & Algorithmic Validation - Successful validation of QSVT Capon matrix inversion on ESA AfriSAR P-band data (matching classical Capon peak height RMSE to +/- 0.05 m and achieving SSIM > 0.95), and hardware characterization of RacQ-1 (Bell-1) silicon-spin processor through single/two-qubit randomized benchmarking and GHZ entanglement state preparation.
• Scalability & Memory Advantage Study - Quantification of FABLE block encoding logarithmic memory scaling (O(log N) qubits vs O(N^2) classical storage bits), establishing runtime crossover for matrix inversion at N >= 1500 for kappa <= 3.

Combinatorial Optimization Utility - Execution of QAOA on mission planning QUBO formulations, achieving approximation ratios alpha > 0.9 and demonstrating utility for hybrid warm-starting of classical solvers.

The project is expected to establish:

• Hardware demonstration - whether the selected quantum formulations can be implemented on physical silicon-spin hardware
• Scalability study - quantum and classical resources required by quantum algorithms
• Technology study - the principal limitations associated with present hardware;

The results will provide a technical basis for assessing future integration of quantum processing resources into EO HPC and ground-segment architectures and for identifying the algorithmic and hardware developments required for subsequent implementations.