I will present a hybrid quantum–HPC workflow that turns a shallow, NISQ-realistic constrained quantum core into end-to-end approximation pipelines for structured combinatorial optimization. The target problem class live the CE–QAOA kernel. Such problems admit a block one-hot (fixed-Hamming-weight) encoding, a diagonal objective, and a structured penalty Hamiltonian built from squared affine one-hot/degree/capacity constraints with bounded integer coefficients and strong pattern symmetries (block permutations and symbol relabelings). The quantum core uses a normalized block-XY mixer that preserves the encoded sector and a uniform one-hot product initialization (W-state per block), and is assumed to provide an instance-independent, dimension-free inverse-polynomial optimum hit probability.

The HPC layer then performs two structure-aware steps: (i) deterministic feasibility repair via Hamming-nearest projection and (ii) heavy-hitter extraction exploiting block factorization to shrink the retained candidate set dramatically before scoring. A total-variation robustness bound converts device noise and compilation/approximation error into explicit shot budgets, thresholds, and depth-compression rules. I will close by posing concrete open problems for JLESC collaborations on workflow integration, compiler–noise co-design, scalable repair beyond permutations, and cross-site benchmarking protocols.

Pattern recognition for track reconstruction at future particle colliders presents a highly combinatorial challenge. The problem is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) model, where candidate track segments are constructed from grouped detector hits in a classical preprocessing stage.

The QUBO encodes geometric compatibility between hit groupings and penalizes mutually conflicting combinations. Depending on event complexity, QUBO sizes range from a few hundred up to about 10⁵ variables. The study is based on 10,000 simulated events from a muon collider detector scenario, characterized by around 10⁶ background hits per event, with segment construction and QUBO generation parallelized across HPC resources.

Preprocessing and QUBO construction are executed on classical clusters. Due to current hardware size constraints, large QUBOs are decomposed into subproblems of 100 variables. These subproblems are solved either on the D-Wave Systems quantum annealer or with classical solvers such as Gurobi Optimization within the same workflow. The QUBO coefficients can additionally be tuned using machine learning techniques to improve discrimination between compatible and incompatible hit groupings. This enables a direct comparison of quantum annealing and classical optimization for identical problem instances.

A state-vector simulator of quantum computers has been developed for use on supercomputers. Our simulator, RIKEN-braket, removes the conventional limitations on the number of MPI processes and the size of the state-vector data array imposed by commonly used parallelization methods. We demonstrate that our simulator scales efficiently up to 46 qubits on the supercomputer Fugaku, using up to 55,296 computing nodes. We also describe recent enhancements to the simulator, including gate fusion and support for multiple circuits to enable simulations of variational algorithms.

Near-term quantum computing is expected to rely on distributed quantum computing (DQC) across multiple interconnected quantum processing units rather than on monolithic devices. Such systems inherently depend on quantum interconnects and require substantial classical computation for coordination, control, and error correction. As a result, meaningful hybrid quantum classical computing in the near term is fundamentally a hybrid DQC-HPC problem.

In this work, we present an ongoing effort to simulate hybrid DQC-HPC workflows using a software-driven, system-level approach. Building on our existing distributed quantum computing simulation framework implemented using the SeQUeNCe quantum network simulator, we have developed abstractions for DQC nodes that integrate data qubits, communication qubits, and non-local quantum operations such as teleportation, teledata, and telegate. Using this framework, we have successfully simulated distributed Grover’s algorithm across networked quantum nodes with full correctness.

We propose to extend this work toward end-to-end simulation of hybrid DQC-HPC applications by explicitly modeling three interacting components. First, quantum interconnects are simulated to capture entanglement generation, communication latency, and error behavior across QPU boundaries. Second, distributed quantum programs are modeled at the level of execution structure and inter-node dependencies rather than detailed hardware timing. Third, classical HPC resources are introduced as first-class participants responsible for distributed compilation, execution coordination, classical control, and in particular distributed quantum error correction (dQEC) decoding, which is computationally intensive and latency sensitive.

The goal of this effort is not to predict quantum hardware performance, but to expose software and systems challenges that arise when quantum networks, distributed quantum programs, and classical HPC runtimes interact at scale. By enabling simulation of hybrid DQC-HPC workflows, this work aims to support exploration of scheduling strategies, communication patterns, classical control and coordination with quantum execution, and resource trade-offs across architectures.

This contribution aligns directly with JLESC’s focus on hybrid QC-HPC software challenges and is intended to seed cross-institution collaboration on system-level abstractions for scalable, networked quantum computing.