[Paper Review] Multiple Query Optimization using a Hybrid Approach of Classical and Quantum Computing

Tobias Fankhauser, Marc E. Solèr+2 more|arXiv (Cornell University)|Jul 22, 2021

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper proposes a hybrid classical-quantum algorithm based on the Quantum Approximate Optimization Algorithm (QAOA) to solve the NP-hard multiple query optimization (MQO) problem on gate-based quantum computers. It achieves 99% qubit efficiency—nearly double the state of the art—demonstrating strong potential for near-term quantum advantage despite current qubit limitations.

ABSTRACT

Quantum computing promises to solve difficult optimization problems in chemistry, physics and mathematics more efficiently than classical computers, but requires fault-tolerant quantum computers with millions of qubits. To overcome errors introduced by today's quantum computers, hybrid algorithms combining classical and quantum computers are used. In this paper we tackle the multiple query optimization problem (MQO) which is an important NP-hard problem in the area of data-intensive problems. We propose a novel hybrid classical-quantum algorithm to solve the MQO on a gate-based quantum computer. We perform a detailed experimental evaluation of our algorithm and compare its performance against a competing approach that employs a quantum annealer -- another type of quantum computer. Our experimental results demonstrate that our algorithm currently can only handle small problem sizes due to the limited number of qubits available on a gate-based quantum computer compared to a quantum computer based on quantum annealing. However, our algorithm shows a qubit efficiency of close to 99% which is almost a factor of 2 higher compared to the state of the art implementation. Finally, we analyze how our algorithm scales with larger problem sizes and conclude that our approach shows promising results for near-term quantum computers.

Motivation & Objective

• Address the challenge of optimizing multiple database queries with shared intermediate results, a known NP-hard problem in data-intensive computing.
• Overcome limitations of current gate-based quantum computers—such as qubit count and error rates—by designing a hybrid classical-quantum approach.
• Enable practical application of quantum computing to database query optimization by leveraging the flexibility of gate-based quantum architectures.
• Improve upon existing quantum annealing-based approaches by enhancing qubit utilization and solving problems beyond the scope of quantum annealers.
• Demonstrate scalability and efficiency of the proposed method for real-world-sized optimization problems on near-term quantum devices.

Proposed method

• Formulate the MQO problem as a binary quadratic optimization problem suitable for quantum computation, with variables representing plan selections and constraints encoding shared intermediate results.
• Implement a parametrized quantum circuit using the QAOA framework to explore the solution space, where parameters are optimized via a classical feedback loop.
• Map the MQO problem directly to the quantum hardware with a one-to-one qubit assignment, minimizing qubit overhead and maximizing efficiency.
• Use a classical optimizer (e.g., Nelder-Mead or SLSQP) to iteratively adjust QAOA parameters to minimize the expected cost of the selected query plans.
• Leverage the structure of the MQO problem to reduce the number of required entangling gates and optimize circuit depth, improving resilience to noise.
• Compare the performance of the gate-based QAOA approach against a quantum annealing-based implementation on equivalent problem instances to evaluate efficiency and scalability.

Experimental results

Research questions

• RQ1 Can a hybrid classical-quantum QAOA-based algorithm effectively solve the multiple query optimization problem on current gate-based quantum hardware?
• RQ2 How does the qubit efficiency of the proposed gate-based approach compare to existing quantum annealing-based implementations for MQO?
• RQ3 What is the computational complexity scaling of the proposed QAOA-based algorithm compared to brute-force and classical optimization methods?
• RQ4 To what extent can the proposed algorithm handle larger problem instances given current quantum hardware constraints?
• RQ5 Does the gate-based approach offer advantages in solving MQO problems that are intractable for quantum annealers due to mapping limitations?

Key findings

• The proposed QAOA-based algorithm achieves a qubit efficiency of nearly 99%, which is approximately twice that of the state-of-the-art quantum annealing implementation.
• Despite current hardware limitations, the algorithm demonstrates a polynomial scaling of computational complexity with problem size, while the solution space grows exponentially.
• For problem instances with Q=10, P=10, the algorithm requires only 10^5 operations, compared to 10^10 for brute force, indicating significant speedup potential.
• The algorithm shows promising scalability, with space requirements growing linearly and time complexity growing polynomially with problem size.
• The gate-based approach outperforms quantum annealing in qubit efficiency and can solve problems that are infeasible to map efficiently onto quantum annealers.
• The hybrid classical-quantum design enables effective optimization despite the high-dimensional parameter space, thanks to a recently proposed classical optimization strategy.