QAOA for Max-Cut requires hundreds of qubits for quantum speed-up (1812.07589v1)

Abstract: Computational quantum technologies are entering a new phase in which noisy intermediate-scale quantum computers are available, but are still too small to benefit from active error correction. Even with a finite coherence budget to invest in quantum information processing, noisy devices with about 50 qubits are expected to experimentally demonstrate quantum supremacy in the next few years. Defined in terms of artificial tasks, current proposals for quantum supremacy, even if successful, will not help to provide solutions to practical problems. Instead, we believe that future users of quantum computers are interested in actual applications and that noisy quantum devices may still provide value by approximately solving hard combinatorial problems via hybrid classical-quantum algorithms. To lower bound the size of quantum computers with practical utility, we perform realistic simulations of the Quantum Approximate Optimization Algorithm and conclude that quantum speedup will not be attainable, at least for a representative combinatorial problem, until several hundreds of qubits are available.

• The paper demonstrates through realistic noise simulations that QAOA for Max-Cut requires hundreds of qubits for quantum speedup.
• It compares QAOA performance on small graphs with classical solvers, revealing that classical methods outperform current NISQ devices.
• The findings underscore the necessity for enhanced qubit coherence, gate fidelity, and connectivity to make quantum algorithms practically competitive.

Critical Evaluation of "QAOA for Max-Cut requires hundreds of qubits for quantum speed-up"

The paper "QAOA for Max-Cut requires hundreds of qubits for quantum speed-up" by G.G. Guerreschi and A.Y. Matsuura presents an insightful analysis of the practicality and limitations of using the Quantum Approximate Optimization Algorithm (QAOA) to achieve quantum speedup in solving the Max-Cut problem. This paper is particularly pertinent in the context of the Noisy Intermediate-Scale Quantum (NISQ) era, aiming to quantify the threshold at which quantum computers might surpass classical solutions in addressing NP-hard problems.

Overview of the Research Framework

The authors conduct realistic noise simulations of QAOA applied to Max-Cut, a problem widely regarded within the NP-hard complexity class and with applications in domains like machine scheduling, image recognition, and electronic circuit layout. The paper explicitly investigates whether current NISQ devices, with limited coherence times and inter-qubit connections, can provide computational advantages over classical algorithms. The primary contribution of this research is determining that quantum speedup for Max-Cut may not be attainable until quantum devices are equipped with several hundreds of qubits.

Technical and Computational Aspects

The authors simulate QAOA circuits on a 2D grid of qubits and incorporate realistic noise through an approach grounded in the stochastic Schrödinger equation. The paper details how they compile quantum circuits for optimal depth and minimal gate overhead, acknowledging constraints like limited qubit connectivity and gate fidelities relevant to superconducting qubit platforms.

A noteworthy element is the comparison of QAOA with state-of-the-art classical solvers such as the AKMAXSAT for Max-Cut, focusing on computational time and absolute performance metrics. The paper shows that, for small graphs (up to 20 vertices), classical methods significantly outperform QAOA in terms of computational time. These findings highlight the necessity for hundreds of qubits in quantum hardware before QAOA can surpass classical solutions in terms of computational efficiency.

Results and Implications

The simulations indicate that the quantum-classical crossover in computational performance might occur only for instances involving several hundreds to a few thousand variables, contingent on manageable coherence and noise levels. This implies that immediate quantum speedup with NISQ devices may be overanticipated. Furthermore, concerns regarding the scalability of QAOA with respect to increasing problem sizes and the circuit depth parameter, $p$, are addressed. The empirical results add weight to the argument that significant strides in hardware improvements are required to make QAOA practically competitive.

Future Directions

This work raises pertinent questions about future pathways for quantum algorithm research and highlights benchmarks that future quantum technologies should aim to surpass. It advocates for enhancement in both quantum hardware—focusing on coherence times and error rates—and algorithmic strategies, perhaps through hybrid advancements or entirely novel approaches.

Beyond the straightforward goal of solving NP-hard problems efficiently, the paper fuels the conversation on the theoretical applicability of quantum computing in real-world scenarios, pivoting from theoretical supremacy to practical utility. Given the dynamic developments in quantum technologies, it is likely that further refinements to quantum algorithms and better utilization of qubit resources could lower the barriers highlighted in this paper.

In conclusion, this paper serves as a technical roadmap identifying both the current limitations of NISQ devices and the vast potential awaiting realization through improvements in quantum algorithm design and hardware scaling. It forms a foundational benchmark for practitioners and researchers aiming to transition from theoretical demonstrations of quantum capabilities to their applications in tackling complex computational challenges.