📊 Tracking Issue: Dynamic Circuits

[flowerthrower]

As opposed to more general structured quantum programs, Qiskit natively supports classical feedforward and explicit control flow as described in the Qiskit documentation. A range of quantum algorithms has been proposed that rely on mid-circuit measurements. With the rapidly growing capabilities of modern compiler infrastructures, for example, those based on MLIR, and of emerging hardware platforms supporting dynamic circuits, such algorithms are becoming increasingly relevant.

This tracking issue is intended to collect benchmark circuits that exhibit dynamic behavior and are therefore of particular interest for integration into MQT Bench. After discussion with and acceptance by the maintainers, each proposed benchmark will be tracked in its own dedicated sub-issue covering its implementation, documentation, and validation.

The current list of candidate dynamic circuits includes:

• State preparation by shallow circuits using feed forward
• ...

Each sub-issue is expected to follow the structure outlined below.

Add … to the list of available benchmarks, including
	•	documentation (explanation, constraints, parameters, …),
	•	implementation (as a Qiskit circuit), and
	•	testing (if not covered by existing tests).

[adnathanail]

• Iterative QPE
  • Requires only 1 ancilla qubit for arbitrary precision QPE, using controlled rotations depending on the previous bits of precision measured
  • https://medium.com/quantum-untangled/iterative-quantum-phase-estimation-qpe-algorithms-ced794341487
• Error correcting codes
  • Shor's 9 qubit/Steane's 7 qubit/Surface code/others
• Dynamic GHZ preparation
  • Create arbitrary sized GHZ states with constant circuit depth
  • Removes requirement for cascading CNOTs, using "fusion measurement" to join together pairs of Bell states
  • https://journals.aps.org/prxquantum/pdf/10.1103/PRXQuantum.5.030339 (section III)

[morrishuismans]

QFT using Dynamical Circuits

• Uses O(n) mid-circuit measurements instead of O(n^2) 2-qubit gates and removes the assumption of all-to-all connectivity
• https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.150602

QAOA Protocol for MaxCut problem

• https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.041057
• The example in this paper managed to compress an 80-qubit QAOA circuit to a 20-qubit circuit for the MaxCut problem, aswell as an example where the number of qubits is reduced from 10 to 4.

[TomasVF]

Bernstein-Vazirani with qubit reuse

• Uses only 2 qubits instead of n+1 to solve the exact same problem by measuring and resetting the ancilla n times sequentially.
• https://arxiv.org/abs/2308.00194

Repeat-Until-Success (RUS)

• Approximate an arbitrary single-qubit unitary within distance e, for example an arbitrary Z-axis rotation. Executes the circuit, then does the measurement, depending on the result we either got the exact desired unitary or an undesired unitary that can be reversed at little or no cost. Repeat until the desired unitary is obtained.
• https://arxiv.org/abs/1404.5320, https://arxiv.org/abs/1311.1074

Holographic quantum simulation

• Maps the spatial structure of a tensor network into the time evolution of the circuit, repeatedly entangling, measuring, and resetting qubits to "recycle" them as the simulation moves along the chain.
• https://arxiv.org/abs/2203.00886