Quantum State Preparation Using an Exact CNOT Synthesis Formulation

TL;DR

This work reframes quantum state preparation as an exact CNOT synthesis problem by modeling state transitions as a shortest-path search on a graph of amplitude-preserving moves. Using an A* search with an entanglement-informed admissible heuristic and a canonicalization-based state compression, the method finds optimal circuits with minimal CNOT cost while keeping computation tractable. Empirical results show 9%–32% average CNOT reductions for general states up to 20 qubits and a 2x reduction for Dicke states, surpassing prior design automation methods and matching manual designs in efficiency. The approach offers a scalable, exact, and automation-friendly pathway to more robust quantum state preparation on NISQ hardware, with potential extensions to larger systems and more complex amplitude structures.

Abstract

Minimizing the use of CNOT gates in quantum state preparation is a crucial step in quantum compilation, as they introduce coupling constraints and more noise than single-qubit gates. Reducing the number of CNOT gates can lead to more efficient and accurate quantum computations. However, the lack of compatibility to model superposition and entanglement challenges the scalability and optimality of CNOT optimization algorithms on classical computers. In this paper, we propose an effective state preparation algorithm using an exact CNOT synthesis formulation. Our method represents a milestone as the first design automation algorithm to surpass manual design, reducing the best CNOT numbers to prepare a Dicke state by 2x. For general states with up to 20 qubits, our method reduces the CNOT number by 9% and 32% for dense and sparse states, on average, compared to the latest algorithms.

Figures (7)

• Figure 1: 6-CNOT circuit using the qubit reduction method.
• Figure 2: 7-CNOT circuit using the cardinality reduction method.
• Figure 3: 2-CNOT circuit using the exact synthesis (ours).
• Figure 4: Example of exploring a (portion of a) state transition graph from the target state $\ket{\psi} = \frac{1}{\sqrt{4}}(\ket{000} + \ket{011} + \ket{101} + \ket{110})$.
• Figure 5: Evaluation workflow of exact CNOT synthesis.