Quantum computers promise the ability to solve problems that are intractable in the classical setting¹, but in many cases this is not rigorously proven. It is often possible to establish a provable theoretical advantage for quantum computations by restricting the computational power^{2,3,4,5,6,7,8}. In multiple cases, quantum advantage over these restricted models was demonstrated experimentally^9,10,11,12. Here we consider space-restricted computations that use only one computational classical or quantum bit with a read-only memory as input. We show that n-bit symmetric Boolean functions can be implemented exactly in this framework through the use of quantum signal processing¹³ and O(n²) gates, but in the analogous classical computations some of the functions may only be evaluated with probability \(1/2 + O\left(n/{\sqrt{2}}^n\right)\). We experimentally demonstrate computations of three-bit to six-bit symmetric Boolean functions by quantum circuits with an algorithmic success probability that exceeds the classical limit. This shows that in computations, quantum scrap space offers an advantage over analogous classical space, and calls for an in-depth exploration of space–time trade-offs in quantum circuits.

量子计算机承诺能够解决经典环境中难以解决的问题¹，但在许多情况下，这并没有得到严格证明。^{通过限制计算能力2,3,4,5,6,7,8}通常可以为量子计算建立可证明的理论优势。在多种情况下，实验证明了这些受限模型的量子优势^9,10,11,12。在这里，我们考虑仅使用一个具有只读存储器的计算经典或量子位作为输入的空间受限计算。我们通过使用量子信号处理¹³和O (n ² ) 门，但在类似的经典计算中，某些函数只能以概率\(1/2 + O\left(n/{\sqrt{2}}^n\right)\)进行评估。我们通过实验证明了通过量子电路计算 3 位到 6 位对称布尔函数，其算法成功概率超过了经典限制。这表明在计算中，量子废料空间比类比经典空间具有优势，需要深入探索量子电路中的时空权衡。