Clifford Circuit Initialization Improves QAOA And VQE
Clifford Circuit Initialization
Clifford Circuit Initialisation Revolutionises Quantum Computing: More Effective Algorithms
Fraunhofer ITWM researchers Théo Lisart-Liebermann and Arcesio Castanadena Medina developed and demonstrated Clifford Circuit Initialisation, a crucial step towards quantum computing. The Quantum Approximate Optimisation Algorithm (QAOA) and Variationally Quantum Eigensolver (VQE) employ complex quantum circuits, although this could improve their optimisation. In “Clifford Accelerated Adaptive QAOA,” they offer a unique technique that improves quantum-classical interactions and reduces QPU calls by combining classical simulation capabilities.
Clifford Circuit Initialisation improves parametric quantum circuit (PQC) parameter guesses. It exploits the intrinsic efficiency of Clifford Group gate circuits, which the Gottesmann-Knill theorem allows classical hardware to simulate quickly. The researchers found a way to increase circuit parameter initialisation and optimisation efficiency by exploring the parameter space with a smaller set of “Clifford-expressible points” (Clifford Points).
This invention is easily integrated into dynamic circuit reconfiguration methods like ADAPT-QAOA, which optimise QAOA performance by iteratively changing gate designs. The researchers' Clifford approximations improved ADAPT-QAOA at many levels.
Three Improvement Pillars
The study finds Clifford approximations advantageous in three areas:
Clifford Point pre-optimization gives ADAPT non-trivial gate selection behaviour, which may accelerate convergence. Early results suggest that this can accelerate initial convergence for challenges like the Transverse Field Ising Model (TFIM). As the TFIM Hamiltonian's gz control parameter grows, single-qubit Z-gates' benefits become more apparent. The Clifford Point projection on the Z-basis decreases continuous optimisation errors in some cases. The MaxCut problem is more complicated. Some pre-optimization methods failed, perhaps leading ADAPT to enter local minima. This suggests that MaxCut may need momentum transfer or objective function data for Clifford Point optimisation.
Fully Classical and Parallel Operator Selection: ADAPT operator selection that is fully parallel and classical is a major development. Clifford circuit assessments can be mimicked on classical hardware, so operator selection does not require costly QPU calls. Due to Clifford Point selection, better choices were made when extending the QAOA mixer layer for MaxCut, resulting in convergence behaviour at lower parameter counts. It recommended using two-qubit RZZ gates instead of single-qubit RY rotations, which improve expressivity and circuit performance. Similar benefits were reported for TFIM. This allows for substantial quantum-classical integration, which reduces computing time and cost by offloading workloads without quantum speedup to classical hardware.
Optimisation using T-gate Error Approximation: One of the most significant breakthroughs is the treatment of T-gates, non-Clifford gates essential to universal quantum processing. The researchers showed that low-rank stabiliser decomposition to apply a 10–30% error approximation on T-gates improves MaxCut and TFIM convergence quality. This unexpected finding suggests that T-gates are overused in modern quantum circuit design. This realisation could enable aggressive circuit compilation optimisations, reducing quantum resource requirements for complex algorithm implementation. The T-gate approximation improved convergence even when MaxCut's Clifford Point pre-optimization yielded contradictory results.
Towards Scalable Quantum Algorithms
This study advances the development of scalable and effective quantum algorithms. By actively integrating classical approximations, the team has improved hybrid quantum-classical computation prospects by better handling the trainability-expressivity trade-off in PQC design.
The researchers acknowledge that MaxCut and TFIM benefits depend on parameters and issue topologies and are problem-dependent. Future study will create automated methods to detect and reduce T-gate over-representation in quantum circuits and test them with different issue formats and larger system sizes. To explain the observed traits, more theoretical research is needed, notably on Clifford Point operator selection.
This endeavour, financed by BMWK-Project “EniQmA,” shows the ongoing commitment to creating practical quantum technologies and increasing hybrid quantum computing applications.
