[Paper Review] Disentangling Hype from Practicality: On Realistically Achieving Quantum Advantage

Torsten Hoefler, Thomas Haener+1 more|arXiv (Cornell University)|Jul 2, 2023

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper establishes practical guidelines for identifying realistic quantum advantage by analyzing the trade-offs between quantum speedup and classical performance, concluding that only small-data problems and algorithms with super-quadratic speedups—particularly in quantum chemistry and materials science—can achieve practical quantum advantage within realistic hardware constraints. The study uses a conservative benchmark of a 10,000 logical qubit quantum computer against a modern GPU, showing that I/O bottlenecks and high gate latencies severely limit quantum advantage in big-data applications.

ABSTRACT

Quantum computers offer a new paradigm of computing with the potential to vastly outperform any imagineable classical computer. This has caused a gold rush towards new quantum algorithms and hardware. In light of the growing expectations and hype surrounding quantum computing we ask the question which are the promising applications to realize quantum advantage. We argue that small data problems and quantum algorithms with super-quadratic speedups are essential to make quantum computers useful in practice. With these guidelines one can separate promising applications for quantum computing from those where classical solutions should be pursued. While most of the proposed quantum algorithms and applications do not achieve the necessary speedups to be considered practical, we already see a huge potential in material science and chemistry. We expect further applications to be developed based on our guidelines.

Motivation & Objective

• To distinguish between hype and practical quantum advantage by identifying which quantum algorithms can realistically outperform classical computers.
• To establish performance benchmarks for future quantum computers under conservative assumptions about error correction, gate speed, and I/O bandwidth.
• To evaluate whether widely cited quantum applications—such as database search, optimization, and machine learning—can achieve practical speedup given realistic hardware constraints.
• To provide clear, quantitative guidelines for identifying promising quantum applications based on required speedup and problem size.
• To demonstrate that only specific domains like quantum chemistry and materials science currently show viable potential for practical quantum advantage.

Proposed method

• Compares a hypothetical future quantum computer with 10,000 logical qubits, 10 µs gate time, and all-to-all connectivity against a modern NVIDIA A100 GPU with 54 billion transistors.
• Estimates I/O bandwidth as 1 Gbit/s for the quantum computer, assuming one gate per input bit, and compares it to 10,000 Gbit/s for the classical GPU.
• Models quantum operation rates using fault-tolerant surface code with distillation factories, estimating 10.5 kop/s for fp16, 0.83 kop/s for int32, and 235 kop/s for binary logic.
• Applies the crossover time analysis: determines the maximum oracle complexity M for which a quantum computer completes a problem faster than a classical computer within 10^6 seconds.
• Uses the inequality $ M \leq 10^6 \cdot \sqrt[k-1]{t_c / t_q^k} $ to compute the upper bound on operations per oracle call for polynomial speedups (e.g., Grover’s algorithm with $k=2$).
• Assesses parallelism by assuming both classical and quantum oracles operate in depth one; considers worst-case scenarios where classical parallelism is limited to evaluate sensitivity.

Figure 1. Quantum speedup : The time needed to solve certain problems with quantum algorithms increases more slowly than that of any known classical algorithm as the problem size N increases. To be practical, however, we need more than an asymptotic speedup: the crossover time where quantum advantag

Experimental results

Research questions

• RQ1 Which quantum algorithms can realistically achieve practical quantum advantage given current and projected hardware constraints?
• RQ2 What is the maximum number of operations per oracle call for which a quantum computer can outperform a classical computer within a 10^6-second window?
• RQ3 How do I/O bandwidth limitations and gate latencies affect the feasibility of quantum advantage in big-data applications?
• RQ4 To what extent do super-quadratic speedups (e.g., Grover’s algorithm) enable practical quantum advantage despite high gate costs?
• RQ5 Which application domains—such as quantum chemistry or materials science—demonstrate the most promise for practical quantum advantage under conservative hardware assumptions?

Key findings

• Quantum computers with 10,000 logical qubits and 10 µs gate time can achieve only 10.5 kop/s for 16-bit floating-point operations, far below the 195 Top/s of a modern GPU.
• I/O bandwidth is the dominant bottleneck: the quantum computer’s 1 Gbit/s I/O rate is 10,000× slower than the GPU’s 10,000 Gbit/s, making big-data problems impractical for quantum advantage.
• For Grover’s algorithm ($k=2$), the maximum number of operations per oracle call that allows quantum advantage within 10^6 seconds is bounded by $ M \leq 10^6 \cdot \sqrt{t_c / t_q^2} $, which limits practical use to small-scale problems.
• Only applications with super-quadratic speedups and small input data—such as quantum chemistry simulations—can realistically achieve quantum advantage under the given assumptions.
• Most proposed applications, including optimization, machine learning, and database search, fail to achieve practical speedup due to insufficient speedup and high I/O costs.
• Even with optimistic assumptions, the crossover point where quantum advantage becomes practical is too large and too slow for most widely cited quantum algorithms, indicating that significant algorithmic improvements are needed for broader practicality.