Researchers develop new approach for optimizing quantum circuits

One of the problems facing current quantum computing devices is noise from the quantum gates. Since the circuit consists of a relatively large number of gates, and since the number of gates directly impacts circuit execution time, reducing the number of gates seems like an obvious objective. And indeed, scientists have developed ways to maximize gate cancellation. But such methods have limitations. In particular, they often fail to leverage the properties of the quantum simulation circuits. 

The best of both possible worlds

Motivated by this situation, researchers from the U.S. Department of Energy’s (DOE) Argonne National Laboratory and the University of Chicago asked the question: Can we convert a quantum circuit into a smaller quantum circuit and optimize them with classical postprocessing?

Their answer was a resounding ​“yes,” and their solution was a new framework called QuCLEAR (Quantum Clifford Extraction and Absorption). The work was presented March 1, 2025, at the IEEE International Symposium on High-Performance Computer Architecture (HPCA 2025), a prestigious conference in computer architecture.

As the name implies, QuCLEAR involves two techniques: Clifford Extraction and Clifford Absorption. Clifford Extraction moves all operations that can be simulated on a classical computer to the end of the quantum circuit, while Clifford Absorption handles these operations using a classical computer. Combining these two methods converts a quantum circuit into a hybrid quantum-classical circuit.  

“Our optimizations leverage the unique properties of both Clifford circuits and quantum simulations,” said Ji Liu, an assistant computer scientist in Argonne’s Mathematics and Computer Science division. ​“With QuCLEAR, we can significantly lower the number of quantum operations necessary to execute on a quantum computer.” 

The researchers acknowledged, however, that extracting Clifford subcircuits is not always advantageous. ​“The trick is to identify the best structure for the Clifford extraction,” Liu said. To this end, they developed a recursive algorithm for synthesizing CNOT trees to be extracted in quantum simulation circuits.

Fewer gates, multiple benefits

The research team evaluated 19 benchmarks, including different sizes and applications: a chemistry eigenvalue problem, several QAOA variations, and a Hamiltonian simulation for three different compounds. Compared with four state-of-the-art methods, QuCLEAR reduced the CNOT gate count up to 68.1% (50.6% on average) in the number of two-qubit quantum gates compared with IBM’s industrial compiler Qiskit.  

Moreover, the QuCLEAR framework is designed to be modular, and it is both platform and software independent. ​“Thus, the optimized circuit can be executed on quantum devices using any quantum software stack and hardware,” Liu said.

This work was funded by Q-NEXT, one of five U.S. Department of Energy National Quantum Information Science Research Centers, and by the AIDE-QC project, which address critical aspects of computer science research that accelerate the integration of near-term intermediate-scale quantum devices for scientific exploration. For the full paper, see Ji Liu, Alvin Gonzales, Benchen Huang, Zain Hamid Saleem, and Paul Hovland, “: Clifford Extraction and Absorption for Significant Reduction in Quantum Circuit Size,” preprint arXiv:2408.13316v2.