We study the complexity of Decoded Quantum Interferometry (DQI), a quantum algorithm for approximate optimization. First, we show that the algorithm resists classical simulation strategies based on locating outputs with large probabilities. We then prove that DQI can be simulated at a low level of the polynomial hierarchy, posing challenges to standard quantum supremacy arguments. We further show that DQI is a constructive solution to a classical coding-theoretic bound based on the MacWilliams identity. Lastly, we interpret DQI as preparing low-energy states of a quantum simple harmonic oscillator, a viewpoint we believe suggests a physics-motivated route to generalizing DQI.

翻译：我们研究了解码量子干涉测量法（DQI）的复杂性，这是一种用于近似优化的量子算法。首先，我们证明该算法能抵抗基于定位高概率输出的经典模拟策略。接着，我们证明DQI可在多项式谱系的低层级进行模拟，这对标准的量子霸权论点提出了挑战。进一步地，我们表明DQI是基于麦克威廉姆斯恒等式的经典编码理论界的一种构造性解决方案。最后，我们将DQI解释为制备量子简谐振子的低能态，我们认为这一视角为推广DQI提供了基于物理动机的路径。