Logical-to-Physical Compilation for Reducing Depth in Distributed Quantum Systems

Abstract

Quantum computing is expected to become a foundational technology for solving problems that exceed the capabilities of classical systems. As quantum algorithms and hardware technologies continue to advance, the need for scalable architectures becomes increasingly clear. Distributed quantum computing offers a promising path forward by interconnecting multiple smaller processors into a larger, more powerful system. However, distributed quantum computing introduces significant circuit depth overhead, as logical operations are typically decomposed into sequential physical procedures that require entanglement generation. These sequential operations limit the reliability of quantum algorithms in the NISQ era due to noise. In this work, we present a compiler that integrates logical-to-physical decomposition with depth-aware rescheduling to reduce the execution cost of distributed quantum circuits. The compiler identifies sequences of logical CNOT gates that share a control or target qubit, reschedules them into parallel instruction groups, and applies decompositions that allow multiple gates to be executed simultaneously using distributed shared entanglement resources. An algorithm is proposed that ensures parallelism is created when possible while keeping logical equivalence and that circuit depth is never increased. Benchmark results demonstrate that the compiler consistently reduces circuit depth for circuits containing inherently sequential CNOT structures, while leaving already-parallel circuits unchanged. These results highlight the value of combining scheduling and hardware-aware decomposition, and establish the compiler as a practical tool for improving the fidelity of distributed quantum computations.

Figures (11)

• Figure 1: Two NV‑center nodes in a distributed quantum computer. Each node contains an electron spin used as a communication qubit and four C‑13 nuclear spins used as memory qubits. Entanglement is generated between the electron spins of different nodes via photonic links, enabling distributed quantum gates between the carbon qubits.
• Figure 2: Standard implementation of a distributed CNOT gate. The logical CNOT is decomposed into physical operations involving entanglement generation, classical communication, and physical qubit operations. This construction serves as the baseline against which parallel decompositions are compared.
• Figure 3: Standard implementation of two distributed CNOT gates sharing a common control qubit. Each logical CNOT is decomposed into a sequence of physical operations involving entanglement generation, classical communication, and local qubit operations. Because both gates use the same control qubit, their physical decompositions must be executed sequentially, illustrating the baseline case against which parallel decompositions are compared.
• Figure 4: Example of a sequence of CNOT gates that all share the same control qubit. Although these gates appear sequential in the logical circuit, their shared-control structure allows them to be decomposed into a parallel physical implementation.
• Figure 5: Parallel decomposition of n number of distributed CNOT gates that share a control qubit across n number of nodes. A shared multipartite entangled state enables all CNOTs to be executed simultaneously, reducing circuit depth without increasing entanglement requirements.