A 12-CNOT Double Qubit Excitation Gate

The paper presents the first reported 12-CNOT decomposition of the double qubit excitation operator, improving upon state-of-the-art (SOTA) implementations with 13 CNOTs. The new circuit has the lowest CNOT count (12), lowest CNOT depth (10), and lowest total circuit depth (16) among all previous SOTA circuits. Further, it only adds 2 extra one-qubit gates compared to the lowest one-qubit gate count (11) among previous SOTA circuits.

The double qubit excitation gate implements a continuous rotation between the two states 0011⟩ and 1100⟩ in a 4-qubit system, as shown in equation (2). It is used as a building block for several quantum algorithms, both near-term and fault-tolerant, including variational ground-state ansätze such as UCCSD in VQE, adaptive variants such as QEB-ADAPT-VQE and FAST-VQE, Trotterized Hamiltonian simulation, and state preparation for quantum phase estimation.

The paper first describes a 14-CNOT baseline decomposition using Gray-code expansion of the C3Ry(2θ) rotation, which uses 8 CNOTs and 8 Ry rotations. It then reviews previous SOTA 13-CNOT implementations, including circuits by Yordanov et al. (with lowest CNOT depth of 11 but 16 one-qubit gates) and Nam (with lowest one-qubit gate count of 11 but 13 CNOT depth), as well as a circuit by Wang with 15 one-qubit gates and 13 CNOT depth.

The new 12-CNOT circuit, shown in Figure 5, was found using various circuit synthesis and optimization tools such as Q-Synth, Qiskit Transpiler, and Tket, along with techniques like Clifford Synthesis, CNOT+Rz Synthesis, and KAK decomposition. Table 1 compares the new circuit with previous implementations across four metrics: CNOT count, CNOT depth, single-qubit gate count, and total circuit depth. The new circuit achieves 12 CNOTs, 10 CNOT depth, 13 one-qubit gates, and 16 total depth, outperforming all previous SOTA circuits in CNOT count, CNOT depth, and total circuit depth.

Improvements to AI Systems:

1. Automated Quantum Circuit Optimization: The AI can be enhanced to automatically discover and verify minimal-CNOT decompositions for arbitrary multi-qubit gates (beyond just double excitation). By integrating synthesis tools (Q-Synth, Qiskit, Tket) with a search heuristic that targets CNOT count, CNOT depth, and total depth simultaneously, the AI can generate hardware-efficient circuits for any rotation gate, reducing error rates in near-term quantum devices.

2. Adaptive Ansatz Construction for VQE: The AI can use the 12-CNOT decomposition as a drop-in replacement for the double excitation operator in UCCSD, QEB-ADAPT-VQE, and FAST-VQE. This improves the AI’s ability to design variational circuits with fewer entangling gates, leading to faster convergence and lower noise sensitivity in molecular ground-state simulations on real quantum hardware.

3. Trotterized Hamiltonian Simulation: The AI can incorporate the new circuit into Trotter-step implementations for 4-qubit interactions (e.g., in fermionic systems). This reduces the per-step CNOT overhead by 8% compared to SOTA, enabling longer-time simulations with the same error budget—critical for quantum chemistry and condensed matter physics.

4. State Preparation for Quantum Phase Estimation (QPE): The AI can leverage the lower total depth (16 vs. previous 18–20) to prepare the 0011⟩↔1100⟩ superposition more reliably. This improves the fidelity of initial states in QPE, which is essential for fault-tolerant algorithms like Shor’s factoring or eigenvalue estimation.

5. Cross-Layer Circuit Compilation: The AI can be trained to combine the new decomposition with Clifford synthesis and KAK-based optimizations to automatically re-synthesize larger circuits containing multiple double excitations. This yields global CNOT reductions beyond single-gate optimization, improving scalability of quantum compilers.

6. Benchmarking and Verification: The AI can be used to generate a benchmark suite of minimal-CNOT circuits for all 4-qubit excitation gates, enabling automated validation of future synthesis algorithms. This helps the AI learn to predict which decomposition strategies yield optimal trade-offs between CNOT count, depth, and single-qubit gate overhead.

What the improved AI system can do:

• Design quantum circuits for chemistry and physics simulations with up to 8% fewer CNOTs and 20% lower total depth than current best methods.

• Automatically compile high-level quantum algorithms (UCCSD, Trotter, QPE) into noise-resilient, hardware-native circuits with minimal entangling operations.

• Predict and synthesize optimal decompositions for new, user-defined multi-qubit gates in real time, reducing manual design effort.

• Improve the accuracy of variational quantum eigensolvers on noisy intermediate-scale quantum (NISQ) devices by lowering the circuit’s susceptibility to decoherence and gate errors.

Effective implementation of high-level quantum gates is essential for practical quantum computing. To the best of our knowledge, we present the first reported 12-CNOT decomposition of the double qubit excitation operator, improving upon state-of-the-art (SOTA) implementations with 13 CNOTs. Our new circuit has the lowest CNOT count (12), lowest CNOT depth (10), and lowest total circuit depth (16) among all the previous SOTA circuits. Further, we only added 2 extra one-qubit gates compared to the lowest one-qubit gate count (11) among the previous SOTA circuits.