Quantum-HPC Workflows Across Multiple Quantum Computing Platforms: Two Case Studies

I. INTRODUCTION

• Quantum-HPC applications are often bespoke collections of programs, schedulers, classical methods, glue code, and scripts, while growing complexity makes teams spend more time maintaining infrastructure than algorithms.The workflows must accommodate facility restrictions, device characteristics, hardware limitations, and networking topologies.Source: §I · p. 1
• Existing general-purpose and quantum workflow tools do not primarily target quantum-HPC integration, and the quantum-computing community has not consolidated around a software stack for it.The paper positions Tierkreis as a workflow-management adaptation and demonstration, not a microbenchmark or a new quantum algorithm.Source: §I · pp. 1–2
• Tierkreis is adapted to sit between quantum-computing frameworks and HPC, with support for batch and quantum submission and reusable worker interfaces.The resulting workflows can be adapted to different quantum and HPC backends.Source: §I · pp. 1–2
• The Reimei–ibm_kobe workflow uses ibm_kobe to warm-start QPE on Reimei, which the authors describe as the first end-to-end multi-modality quantum-HPC workflow.It also improves on a classically prepared initial state.Source: §I · p. 2
• The Fugaku–Reimei workflow computes biomolecular excited states, using conventional HPC quantum-chemistry packages and reusable parallelisation of quantum optimisation and submission.Reimei is used for the quantum part of the workflow.Source: §I · p. 2

II. QUANTUM-HPC HYBRID SYSTEM ARCHITECTURE

• Users access Fugaku and both quantum computers through a Fugaku login node, while low-latency connections let the HPC system submit quantum jobs.Figure 1 presents the hybrid system overview.Source: §II · p. 2, Figure 1 · p. 2

A. Fugaku

• Fugaku is an ultra-scale manycore system with 158,976 nodes and uses Fujitsu’s proprietary TCS scheduler, optimized for its network topology.pjsub is Fugaku’s job-submission command.Source: A. Fugaku · p. 2
• The sqcsub framework submits quantum jobs over direct Fugaku-to-QPU connections, with a lightweight scheduler at each computer and SQC APIs for circuits from HPC applications or workflows.pjsub corresponds to commands such as qsub and sbatch on other HPC systems.Source: A. Fugaku · p. 2

B. Quantinuum Reimei

• Reimei is a 20-qubit trapped-ion computer using the System Model H1 design [19], located about 500 km from Fugaku and connected by virtual LAN.Source: B. Quantinuum Reimei · p. 2
• Reimei’s qsubmit gRPC service provides low-latency circuit submission and result retrieval through sqcsub on Fugaku.Reimei is also accessible through the cloud-based Quantinuum Nexus API.Source: B. Quantinuum Reimei · p. 2
• Jobs submitted from Fugaku receive highest priority, and simultaneous HPC-submitted jobs are scheduled first-in-first-out.Source: B. Quantinuum Reimei · p. 2

C. ibm_kobe

• ibm_kobe is a 156-qubit Heron R2 computer in Fugaku’s building, connected by a low-latency network and available as a Qiskit backend.It can be accessed through direct submission integrated in sqcsub or through the IBM Quantum API.Source: C. ibm_kobe · p. 2

III. TIERKREIS EXTENSIONS FOR QUANTUM-HPC SYSTEMS

• Tierkreis represents workflows as DAGs of independent, loosely coupled tasks, allowing graph sections to run in parallel and the controller to orchestrate execution.The runtime tracks node states and dependencies, dispatching tasks when their dependencies are satisfied.Source: §III · pp. 2–3
• Executors connect worker tasks to classical, quantum, GPU, or FPGA backends and handle task inputs, execution, and output collection.Execution may dispatch a local process, submit a scheduler job, or send a circuit to a quantum device.Source: §III · p. 3
• Workers define tasks independently, with typed interfaces that can detect incorrect usage when a workflow is constructed rather than at runtime.The add-task example uses type annotations to specify two floating-point inputs and one floating-point output.Source: §III · p. 3
• Tierkreis passes data in file batches at task boundaries and persists workflow state and intermediate values, enabling workflows to pause, resume, or restart without losing task data.The primary HPC storage implementation uses a shared filesystem, while the storage interface is abstract; metadata, errors, logs, and task status are also stored.Source: §III · p. 3
• The runtime manages global workflow state and dependencies, and workflows encountering errors can resume from the last checkpoint after user intervention.The runtime can be suspended to pause and later resume workflows.Source: §III · p. 3
• The example workflow defines task dependencies and its final output, while the add function is registered separately and the workflow leaves task execution unspecified.Its two add tasks compute x = a + b and then y = x + c.Source: §III · p. 3

A. Adapting Tierkreis for HPC Platforms

• Tierkreis’s architecture-independent abstraction layer makes integration with HPC platforms straightforward, with backends determining how workflow tasks are executed.The adaptation adds custom workers for the HPC software stack.Source: A. Adapting Tierkreis for HPC Platforms · p. 3
• Tierkreis uses pjsub to submit HPC tasks annotated with resource requirements, while quantum resources can be exposed through the scheduler, for example via QRMI [3].Loosely coupled environments are managed by sqcsub through a shell executor.Source: A. Adapting Tierkreis for HPC Platforms · p. 3
• For sqcsub, a custom worker exposes the submission command in the workflow graph for execution by the shell executor, while the host environment handles credentials and access controls.The SQC client library authenticates users with tokens by communicating with the scheduler.Source: A. Adapting Tierkreis for HPC Platforms · pp. 3–4

B. Workflow Design

• Tierkreis separates task definitions from environment-specific implementations, allowing workflows to be built without knowledge of implementation and deployed with suitable workers and executors.Shared workers can encapsulate classical or quantum functionality for reuse across workflows.Source: B. Workflow Design · p. 4
• Tierkreis can compose existing subworkflows, including workflows for compiling and submitting quantum circuits to different backends.This supports composition of loosely coupled tasks.Source: B. Workflow Design · p. 4

IV. COMPUTING BIOMOLECULAR EXCITED STATES

• Biomolecular excited-state calculations can be costly when strong electron correlation must be treated in large active spaces, and they help investigate photochemical processes.The section describes these states as arising from biological molecules’ interactions with light.Source: §IV · p. 4
• The excited-state workflow reproduces key results from Yamamoto et al. [37] with minor modifications, omits error correction, and uses reimei-simulator2 during a Reimei hardware upgrade.The authors note that results may differ slightly from [37]; the experiment is intended to demonstrate feasibility despite the changed setup.Source: §IV · p. 4

A. Application Overview

• The application uses subtractive ONIOM with CASCI as the low-level method and TE-QSCI as the high-level method, combining quantum sampling with classical diagonalisation.Its software combines NTChem, TKET, and custom error-correction and QSCI components.Source: A. Application Overview · p. 4

B. Workflow

• Fugaku performs initial HF+CASCI calculations and final subspace diagonalisation, while Reimei executes time-evolution circuits that sample configurations for an expanded (8e, 8o) active space.Samples from target states and evolution times are merged into a common configuration space before diagonalisation; the initial calculation uses a (6e, 6o) active space.Source: B. Workflow · p. 4, Figure 2 · p. 5

C. Preliminary Experiments

• Tierkreis workflows can submit jobs directly to ibm_kobe and the Quantinuum reimei-simulator from Fugaku, with minimal application-code modifications.A local simulator is also invoked directly from the workflow on a single workflow-server core.Source: C. Preliminary Experiments · p. 4
• The demonstration omits Quantinuum QPU error correction and uses 64 Fugaku nodes, 16-qubit circuits, and 200 shots for the simulators versus 20,000 for ibm_kobe.The shot counts differ because of backend access costs, latency profiles, and execution fidelities.Source: C. Preliminary Experiments · p. 4
• NTChem accounts for approximately 80% of total workflow execution time, while circuit preparation is non-negligible and identified for future optimization and parallelization.Table IV summarizes execution time for the workflow at evolution time 7.5; measured task times include preprocessing, postprocessing, and job-queue waiting.Source: Table IV · p. 5, C. Preliminary Experiments · p. 5
• Task timings include preprocessing, postprocessing, and queue waiting; Circuit Exec also includes submission, communication, and result-return time.Queue waiting for NTChem is separately shown and depends on supercomputer workload and congestion.Source: C. Preliminary Experiments · p. 5, Table IV · p. 5
• Tierkreis reduces orchestration complexity and verbosity compared with bash scripts, and switching from reimei to reimei-simulator changes a single line.The paper identifies this backend-switching flexibility as a practical benefit of the workflow system.Source: A. Application Overview · p. 4, C. Preliminary Experiments · p. 5
• Table V presents excitation energies for CASCI with (6e, 6o) and (8e, 8o) active spaces and for TE-QSCI; the CASCI results are taken from [37].TE-QSCI values are reproduced in the paper; the supplied passages do not state the table's individual values.Source: C. Preliminary Experiments · p. 5, Table V · p. 6

V. COMBINING QPU MODALITIES

• For a 16-site transverse-field Ising model, Reimei and ibm_kobe coordinate on one computation, each handling a task suited to its strengths for a better result than either alone.The model is defined on a square lattice with periodic boundary conditions.Source: §V · p. 6
• VQE [18] warm-starts QPE, [5],,, with a ground-state-like input, while VQE runs on faster ibm_kobe because convergence takes many rounds and shots.QPE requires relatively deep circuits near the limit of what Reimei can successfully execute; the warm start increases ground-state overlap and hence the chance of success.Source: §V · p. 6
• VQE’s ansatz and optimal parameters provide a classical description of the prepared state, allowing it to be recreated on Reimei for QPE without quantum communication.Source: §V · p. 6

A. Experiment Design · 1) VQE:

• VQE approximates the ground state of Hamiltonian (2) by minimizing the energy expectation value of |ψ(θ)⟩.The trial state is varied through parameters θ.Source: 1) VQE · p. 6
• The chosen parameterized Hamiltonian variational ansatz uses a uniform product state classically pre-optimized over a single parameter α.Source: 1) VQE · p. 6
• Variational parameters {λd, ϕd, θd}D_d=1 are shared across qubits within each layer, reflecting lattice translational and rotational symmetry.Source: 1) VQE · p. 6
• SPSA, evaluates energy at two points per iteration; X and ZZ terms require measurements in both bases, totaling four measurements.The SPSA optimization uses the InQuanto implementation.Source: 1) VQE · p. 6

2) QPE:

• VQE supplies a candidate input state for QPE, where the ground-state phase divided by λ is most likely the ground-state energy.The phase is obtained using U = e^(iλH).Source: 2) QPE · p. 6
• Information Theory QPE [30] uses a single ancillary qubit and a relatively shallow circuit with state preparation, controlled evolution, an RZ(β) phase shift, and X-basis ancilla measurement.The controlled evolution applies U^k, with U approximating time evolution under H.Source: 2) QPE · p. 6
• QPE accuracy increases with kmax, shot count NS, and the ground-state population |a0|^2 in the input state; kmax also sets maximum circuit depth.The circuit is repeated NS times, with sampled k and β parameters.Source: 2) QPE · p. 6
• Circuit performance is optimized through symmetry-based compression, coherent-noise suppression using periodic Pauli X insertions [33], and leakage detection with post-selection.Leakage gadgets are appended to the 16-qubit system and one-qubit ancilla registers, using Reimei’s remaining three qubits.Source: 2) QPE · p. 6

B. Implementation Details

• Tierkreis combines VQE and QPE in one hierarchical workflow, with QPE as the primary output and VQE available as a comparison baseline.The user supplies QPE parameters, the Hamiltonian, and VQE parameters when starting the workflow.Source: B. Implementation Details · pp. 6–7
• The QPE workflow prepares circuits classically, executes them on Reimei, then processes results classically; higher-order map turns circuit lists into tasks that ran locally.Mapping compilation over circuits creates corresponding jobs and reunites their results; tasks could in principle run concurrently on different HPC nodes.Source: B. Implementation Details · p. 7, Figure 4 · p. 7
• The VQE loop implements SPSA gradient and parameter updates, repeats until its stopping condition, and stops after 500 iterations in this experiment.The loop emits its outputs only when it terminates; gradient and energy evaluation use the same energy-evaluation workflow.Source: B. Implementation Details · p. 7
• VQE energy evaluation generates quantum circuits and maps compilation and execution on ibm_kobe; it queries fresh device parameters inside the loop to account for queue delays.Fresh parameters are needed for best compilation when workflow execution includes long queue times.Source: B. Implementation Details · p. 7
• Tierkreis automates list handling and dynamic sub-workflow execution, using built-in functions, pytket, and custom workers; Fugaku's login node dispatched quantum kernels to the QPUs.The experiment used custom Python workers and sqcsub-based Fugaku access to the QPUs; its small classical workload did not use Fugaku compute nodes.Source: B. Implementation Details · pp. 7–8

C. Results

• The end-to-end workflow used periodic boundary conditions with h = 3J and a VQE ansatz of D = 2 layers, with NS = 500 for each.Source: C. Results · p. 8
• The estimated energy offset was (E−Eexact)/J = 0.61±0.36 after 300 QPE shots, against Eexact = −51.45J and EVQE = −48.00J.The opaque orange region in Fig. 7 represents statistical uncertainty.Source: Figure 7 · p. 8

• Tierkreis integrates Fugaku and two QPUs through dedicated executors and custom workers that expose software stacks via typed task interfaces.The extensions support HPC job submission and quantum resource access.Source: §VI · p. 8
• The first application incorporates existing software packages into a centrally controlled workflow while retaining flexibility to switch underlying implementations.Source: §VI · p. 9
• The second application demonstrates an end-to-end workflow across two quantum modalities, exploiting their speed and accuracy advantages while keeping the workflow hardware-agnostic.Executor design and worker assignment handle device switching.Source: §VI · p. 9
• The case studies demonstrate the feasibility and advantages of hybrid quantum-HPC workflows and provide a blueprint for shifting integration burdens from scientists to infrastructure.The workflow system separates application development from the hardware environment.Source: §VI · p. 9