QuCLEAR: Clifford Extraction and Absorption for Quantum Circuit Optimization

TL;DR

QuCLEAR tackles the challenge of noisy quantum devices by converting parts of quantum circuits into classically simulable subcircuits through Clifford Extraction and Absorption. It leverages the weak commutation between Pauli rotations and Clifford circuits to move Clifford blocks to the circuit end and absorb them into measurements or probability processing, reducing CNOT counts and entangling depth for quantum simulation tasks. The framework introduces a recursive CNOT-tree synthesis and a scalable Clifford Extraction algorithm, achieving up to 77.7% CNOT reduction and 84.1% entangling-depth reduction across 19 benchmarks, and performs well on devices with limited connectivity. Its modular, hardware-agnostic design and favorable CA-runtime scaling make it practical for near-term and beyond-NISQ regimes.

Abstract

Quantum computing carries significant potential for addressing practical problems. However, currently available quantum devices suffer from noisy quantum gates, which degrade the fidelity of executed quantum circuits. Therefore, quantum circuit optimization is crucial for obtaining useful results. In this paper, we present QuCLEAR, a compilation framework designed to optimize quantum circuits. QuCLEAR significantly reduces both the two-qubit gate count and the circuit depth through two novel optimization steps. First, we introduce the concept of Clifford Extraction, which extracts Clifford subcircuits to the end of the circuit while optimizing the gates. Second, since Clifford circuits are classically simulatable, we propose Clifford Absorption, which efficiently processes the extracted Clifford subcircuits classically. We demonstrate our framework on quantum simulation circuits, which have wide-ranging applications in quantum chemistry simulation, many-body physics, and combinatorial optimization problems. Near-term algorithms such as VQE and QAOA also fall within this category. Experimental results across various benchmarks show that QuCLEAR achieves up to a $77.7\%$ reduction in CNOT gate count and up to an $84.1\%$ reduction in entangling depth compared to state-of-the-art methods.

Figures (11)

• Figure 1: Equivalent quantum simulation circuits for $e^{iZYIXt}$
• Figure 2: Optimizing quantum simulation circuit $e^{iZZZZt_1}e^{iYYXXt_2}$. (a) Original quantum simulation circuit, which can not be optimized with gate cancellation. The observable being measured is XXZZ. (b) Circuit after extracting the Clifford subcircuit in $e^{iZZZZt_1}$. The second Pauli rotation circuit is optimized to $e^{iYYIIt_2}$. (c) Circuit after absorbing the Clifford subcircuit in the observable measurement. The new observable is ZIXZ.
• Figure 3: Clifford circuits weakly commute with Pauli rotation circuits, meaning that interchanging their positions transforms the Pauli string $P_1$ to another Pauli string $P_2$.
• Figure 4: Extracting the Clifford subcircuit from a sequence of Pauli rotation blocks. (a) Identifying the best Clifford subcircuit design $U_{CL1}$ that maximizes the optimization of subsequent Pauli blocks. (b) Sequentially extracting Clifford subcircuits from each block to the end of the circuit.
• Figure 5: (a) The Clifford subcircuit at the end can be absorbed into the observable measurements. (b) The CNOT network at the end can be absorbed into the probability measurements.

Theorems & Definitions (2)

• Proposition 1
• Lemma 1