JIJ Launches SQOA Solver in IBM Quantum Functions Catalog to Tackle Combinatorial Optimization Beyond Qubit Counts

A Solver That Packs More Variables Than Qubits

Tokyo‑based JIJ Inc. has added its Sampling‑based Quantum Optimization Algorithm with Quantum Relaxation (SQOA‑QR) to IBM’s Quantum Functions Catalog. The new SQOA Solver lets IBM Quantum Premium, Flex, and On‑Prem users attack combinatorial optimization tasks that would normally exceed the number of physical qubits available.

Variable‑Compression Encoding

SQOA‑QR uses a Quantum Random Access Code (QRAC) to map up to three binary variables onto a single qubit by employing the Pauli‑X, Y, and Z operators. This “variable‑compression” step reduces the qubit‑to‑variable ratio from the one‑to‑one mapping typical of QAOA and other variational algorithms. By eliminating iterative quantum‑classical loops, the algorithm performs a single‑pass quantum sampling followed by classical subspace diagonalization, which dramatically cuts circuit depth and exposure to hardware noise.

Benchmark Results on IBM Heron r2

The team reported two benchmark cases from the QOBLIB suite:

• 384‑node MaxCut solved on 129 qubits, achieving 98.5 % approximation ratio in 12 seconds of QPU time.
• 200‑node Maximum Independent Set solved on 67 qubits, reaching 100 % approximation ratio.

These results illustrate how the solver can handle problem instances that would otherwise require far more qubits than are physically present.

Integration and Usage

The SQOA Solver is exposed as a catalog function (`jij/sqoa-solver`) that accepts QUBO dictionaries, Qiskit‑addon‑opt‑mapper inputs, and OMMX‑formatted models via JIJ’s JijModeling 2 library. Users can select from three compute tiers—Small (≤50 variables), Medium (≤100 variables), and Large (up to 48 vCPU / 768 GB RAM)—to match their workload size. After quantum sampling, the classical post‑processing stage projects the relaxed Hamiltonian onto the sampled subspace, diagonalizes it, and applies rounding plus local‑search refinement to produce feasible classical solutions.

What This Means for Quantum‑Accelerated Optimization

By compressing variables onto shared qubits and removing the costly variational loop, SQOA‑QR offers a practical pathway for near‑term quantum hardware to contribute to real‑world optimization problems. While the approach still relies on classical post‑processing, the reduction in quantum circuit depth makes it more tolerant of noise, potentially widening the range of applications that can benefit from quantum sampling.

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The underlying SQOA‑QR paper was presented at IEEE Quantum Week 2025 and is available on IEEE Xplore and arXiv. The official announcement, catalog entry, technical documentation, API reference, and a tutorial on Maximum Independent Set are linked in the original release.