[Paper Review] ISAAQ: Ising Machine Assisted Quantum Compiler

Soshun Naito, Yoshihiko Hasegawa+2 more|arXiv (Cornell University)|Mar 6, 2023

Quantum Computing Algorithms and Architecture4 citations

TL;DR

ISAAQ is a quantum circuit compiler that leverages Ising machines to solve qubit routing— an NP-hard problem—by formulating it as a Quadratic Unconstrained Binary Optimization (QUBO) problem. It accelerates compilation by using multiple Ising machines in parallel and improves accuracy by learning from prior compilation results, outperforming Qiskit and tket heuristics with fewer physical CNOT gates, especially on large circuits.

ABSTRACT

It is imperative to compile quantum circuits for Noisy Intermediate-Scale Quantum (NISQ) devices because of the limited connectivity of physical qubits and the high error rates of gate operations. One of the most critical steps in quantum circuit compilation is qubit routing, an NP-Hard problem that involves placing and moving logical qubits to minimize compilation overhead. In this study, we propose ISing mAchine Assisted Quantum compiler (ISAAQ) to perform qubit routing with Ising machines, which can efficiently solve Quadratic Unconstrained Binary Optimization (QUBO) problems. ISAAQ accurately estimates the compilation costs by updating itself using previous compilation results, and accelerates qubit routing by solving QUBO problems in parallel with multiple Ising machines. In addition, ISAAQ exploits a cost-reduction method that implements commutative logical Controlled-NOT (CNOT) gates with fewer physical CNOT gates, which is particularly effective for planar devices when implementing original gates. Experimental results on both IBM QX5 and IBM QX20 show that ISAAQ outperforms the heuristic methods available in Qiskit and tket, as well as an existing QUBO method, requiring fewer physical CNOT gates for most benchmark circuits. ISAAQ performs particularly well on large circuits, demonstrating its strong scalability with respect to the number of logical CNOT gates.

Motivation & Objective

• To address the NP-hard qubit routing problem in Noisy Intermediate-Scale Quantum (NISQ) devices with limited qubit connectivity and high gate error rates.
• To reduce compilation overhead, particularly the number of physical CNOT gates, by minimizing SWAP and remote CNOT gate usage.
• To accelerate qubit routing by exploiting Ising machines, which efficiently solve large-scale QUBO problems.
• To improve accuracy and scalability by learning from previous compilation results through adaptive cost estimation.
• To demonstrate superior performance on large circuits compared to existing heuristic and QUBO-based compilers.

Proposed method

• Formulates qubit routing as a QUBO problem to be solved by Ising machines, enabling efficient search for near-optimal logical-to-physical qubit mappings.
• Employs a cost-reduction method that implements commutative CNOT gates with fewer physical CNOT gates, especially beneficial for planar architectures.
• Uses a feedback mechanism that updates the cost function based on prior compilation results, improving estimation accuracy over time.
• Solves the QUBO problem in parallel using multiple Ising machines to accelerate convergence and scalability.
• Applies Lagrangian relaxation and symmetry-based assumptions to derive a consistent solution for the QUBO when no prior data exists.
• Derives the optimal coefficient matrix $ a_{\mu,\nu} $ using Lagrange multipliers, ensuring consistency and minimizing the squared norm of the solution vector.

Experimental results

Research questions

• RQ1 Can Ising machines effectively solve the qubit routing problem in NISQ devices by formulating it as a QUBO problem?
• RQ2 How does learning from previous compilation results improve the accuracy and efficiency of qubit routing?
• RQ3 To what extent can parallel execution on multiple Ising machines accelerate qubit routing compared to sequential or heuristic methods?
• RQ4 How does ISAAQ compare in performance—especially in CNOT gate count—against established compilers like Qiskit and tket?
• RQ5 Does ISAAQ demonstrate strong scalability on large quantum circuits with many logical CNOT gates?

Key findings

• ISAAQ outperforms heuristic methods in Qiskit and tket by requiring fewer physical CNOT gates across all benchmark circuits.
• On IBM QX5 and IBM QX20, ISAAQ achieves lower compilation overhead, particularly excelling on large circuits with high numbers of logical CNOT gates.
• The use of Ising machines enables faster convergence and better scalability compared to traditional heuristic or exact solvers.
• The adaptive cost estimation mechanism significantly improves solution accuracy by leveraging historical compilation data.
• The cost-reduction technique for commutative CNOT gates reduces physical gate count, especially effective in planar qubit architectures.
• ISAAQ demonstrates strong scalability, with performance gains increasing as the number of logical CNOT gates grows.