Limitations of optimization algorithms on noisy quantum devices (2009.05532v1)

Abstract: Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is whether their noise can be overcome or it fundamentally restricts any potential quantum advantage. We present a transparent way of comparing classical algorithms to quantum ones running on near-term quantum devices for a large family of problems that include optimization problems and approximations to the ground state energy of Hamiltonians. Our approach is based on the combination of entropic inequalities that determine how fast the quantum computation state converges to the fixed point of the noise model, together with established classical methods of Gibbs state sampling. The approach is extremely versatile and allows for its application to a large variety of problems, noise models and quantum computing architectures. We use our result to provide estimates for a variety of problems and architectures that have been the focus of recent experiments, such as quantum annealers, variational quantum eigensolvers, and quantum approximate optimization. The bounds we obtain indicate that substantial quantum advantages are unlikely for classical optimization unless the current noise rates are decreased by orders of magnitude or the topology of the problem matches that of the device. This is the case even if the number of qubits increases substantially. We reach similar but less stringent conclusions for quantum Hamiltonian problems.

• The paper demonstrates that noise in near-term quantum devices critically hinders achieving quantum advantage in optimization problems.
• It establishes a comparative framework using entropic inequalities and classical methods to assess the impact of noise on algorithm convergence.
• The study reveals that significant noise reduction and tailored device architectures are essential for enhancing quantum algorithm performance.

Limitations of Optimization Algorithms on Noisy Quantum Devices

The research paper "Limitations of optimization algorithms on noisy quantum devices" presents a comprehensive analysis of the potential and limitations of near-term quantum computing technology, especially when applied to optimization problems and approximations of the ground state energies of Hamiltonians. The authors focus on noise as a crucial factor influencing the performance of quantum algorithms compared to their classical counterparts.

Summary of Key Findings

1. Noise Challenges in Near-Term Quantum Devices: The paper highlights a critical issue facing current quantum technologies—noise, which remains an intractable feature of near-term quantum devices without error correction. The authors seek to understand whether noise fundamentally limits the potential quantum advantage achievable in these systems.
2. Comparative Framework: The authors develop a comparative framework that integrates entropic inequalities and classical methods like Gibbs state sampling to evaluate how quickly quantum states converge to the fixed point determined by a noise model. They apply this framework across various quantum algorithms, architectures, and noise models to draw conclusions about the feasibility of quantum advantage.
3. Findings for Optimization Problems: The paper demonstrates that current noise rates significantly hinder any quantum advantage for classical optimization problems. Even with an increase in the number of qubits, substantial noise reduction is necessary for quantum devices to outperform classical algorithms unless the device topology is inherently suited to the problem structure.
4. Quantum Hamiltonian Problems: For quantum Hamiltonian problems, while the limitations are not as stringent as in classical optimization scenarios, the need for noise reduction remains critical. The authors argue that the potential for quantum advantage is more plausible in problems with many-body physics motivations, particularly when devices and problem topologies are well-matched.
5. Depth and Noise Rate Bounds: The bounds derived suggest that the depth of quantum circuits must be carefully managed relative to the noise rates. The paper uses several architectures like quantum annealers and variational quantum eigensolvers to demonstrate these bounds. For example, their analysis predicts that current error rates severely constrain the maximum depth achievable before classical simulation becomes feasible.

Implications and Future Directions

• Practical Implications: The findings have significant implications for the practical deployment of quantum computing in solving real-world problems. They suggest that, without considerable advancements in noise management, near-term quantum devices may not yet deliver a practical advantage over classical approaches for many use cases.
• Theoretical Contributions: The paper contributes theoretically by providing a systematic way to measure and compare the performance of quantum algorithms against classical methods under noisy conditions. The novel use of entropic measures offers a promising tool for predicting the limits of quantum devices.
• Future Research Directions: The paper points to several future directions, including investigating whether more sophisticated noise mitigation techniques or tailoring device architecture designs can help overcome the current limitations. It also encourages exploring non-classical domains where quantum advantage might be more readily achieved.

This research serves as a sobering reminder of the challenges that remain in realizing quantum advantages for practical applications. It emphasizes the need for continued research and innovation in both device architecture and error management to unlock the full potential of quantum computing.