We show that quantum algorithms of time $T$ and space $S\ge \log T$ with unitary operations and intermediate measurements can be simulated by quantum algorithms of time $T \cdot \mathrm{poly} (S)$ and space $ {O}(S\cdot \log T)$ with unitary operations and without intermediate measurements. The best results prior to this work required either $\Omega(T)$ space (by the deferred measurement principle) or $\mathrm{poly}(2^S)$ time [FR21,GRZ21]. Our result is thus a time-efficient and space-efficient simulation of algorithms with unitary operations and intermediate measurements by algorithms with unitary operations and without intermediate measurements. To prove our result, we study pseudorandom generators for quantum space-bounded algorithms. We show that (an instance of) the INW pseudorandom generator for classical space-bounded algorithms [INW94] also fools quantum space-bounded algorithms. More precisely, we show that for quantum space-bounded algorithms that have access to a read-once tape consisting of random bits, the final state of the algorithm when the random bits are drawn from the uniform distribution is nearly identical to the final state when the random bits are drawn using the INW pseudorandom generator. This result applies to general quantum algorithms which can apply unitary operations, perform intermediate measurements and reset qubits.
翻译：我们展示了时间的量子算法$T$和空间 $S\ge\log T$,使用单一操作和中间测量的量子算法$T\cdott\mathrm{poly}(S)美元和空间${O}(S\cdot\log T)$,使用单一操作和没有中间测量的量子算法。在这项工作之前的最佳结果要求要么$Omega(T) 空间(根据推迟测量原则) 或$\mathrm{poly}(2QS) 时间[FR21,GRZ21]。因此,我们的结果可以模拟时间算法的量子算法($T\cddd\\\c\\\\c\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\h\
相关内容
微信扫码咨询专知VIP会员