📊 Tracking Issue: Structured Quantum Programs

This issue tracks the effort to extend MQT Bench with support for structured quantum programs.

By structured quantum programs we mean hybrid quantum–classical programs that go beyond straight-line circuits and include:

• Structured control flow operations (if, for, while, etc.)
• Dynamic quantum circuit primitives (mid-circuit measurements, resets, classically controlled quantum gates)

The goal of this roadmap is to provide an overview of the different available kinds of structured programs and to act as a tracking hub for adding them to the MQT Bench suite.

👉 Contributions are highly encouraged! Even adding a single primitive or algorithm is already a great start. Please see our contribution guidelines before getting started.
👉 Important: Checkboxes should only be marked once the corresponding PR has been merged.

These benchmarks are expected to serve not only as functional tests but also as challenges for compilers, visualization engines, runtimes, and emulators, since they combine quantum and classical control in nontrivial ways.

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🔁 Loops and Iteration

Loops are a fundamental control-flow construct. They can appear with static bounds (fixed iteration counts) or dynamic bounds (e.g., repeat-until-success). Many important algorithms can be expressed naturally in this form.

• Static loops

  • Example: Grover’s Algorithm (repeated oracle + diffusion steps)
    Ref: Grover, 1996
  • Example: GHZ state preparation (iterative entangling gates)
  • Example: Quantum Fourier Transform (QFT) (nested controlled rotations)
  • Example: Iterative Phase Estimation (iQPE) (looped controlled unitaries)
    Ref: Iterative QPE
  • Example: X-ray Absorption Spectroscopy (XAS)
    Ref: Quantum simulation of XAS and https://pennylane.ai/qml/demos/tutorial_xas

• Dynamic loops (Repeat-Until-Success)

  • Example: Quantum Metropolis Sampling
    Ref: Temme et al., 2011
  • Example: ML-QAE (Quantum Amplitude Estimation)
    Ref: Suzuki et al., 2020

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🧱 Block Encoding

Block encoding embeds classical data or operators into quantum states. It underpins advanced algorithms like QSVT.

• Block encoding primitive
  Ref: Quantum Singular Value Transformation (QSVT)
  • Example: QSVT / QSP
    Ref: Low & Chuang, 2016

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✨ Teleportation

Quantum teleportation is a canonical primitive for quantum communication and distributed computing.

• Teleportation primitive
  Ref: Bennett et al., 1993
  • Example: Teleportation-based subroutines (used in distributed algorithms, fault-tolerant protocols)

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🎛 Multiplexers

Quantum multiplexers allow conditional application of gates and are widely used in circuit synthesis and algorithm design.

• Multiplexer primitive
  Ref: Quantum multiplexers in circuit synthesis
  • Example: Grover’s Algorithm (oracle construction often uses multiplexed operations)

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🔄 Dynamic Qubit (Re)-Allocation

Dynamic allocation and reuse of qubits is crucial for resource-efficient algorithms. This often involves mid-circuit measurement and reset.

• Dynamic qubit allocation primitive
  • Example: Iterative Phase Estimation (iQPE)
  • Example: Iterative QFT
  • Example: Shor’s Algorithm
    Ref: Shor, 1994

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⚛️ Loosely Coupled Hybrid Programs

Variational and hybrid algorithms naturally combine quantum circuits with classical optimization loops. They are loosely coupled because the quantum and classical parts interact only at well-defined synchronization points.

• VQE (Variational Quantum Eigensolver)
  Ref: Peruzzo et al., 2014

• QAOA (Quantum Approximate Optimization Algorithm)
  Ref: Farhi et al., 2014

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🧩 Fault-Tolerance & Resource States

Structured programs also include primitives for error correction and fault-tolerant computation.

• Magic State Distillation
  Ref: Bravyi & Kitaev, 2005

Start with the linked MQT Bench contribution guidelines, then choose one unchecked primitive or algorithm from the relevant section of this tracking issue. Review how existing MQT Bench benchmarks are organized before defining the contribution scope. Done means the selected structured-program benchmark is added and its checkbox is marked only after the corresponding PR is merged.