Eliminating Intermediate Measurements using Pseudorandom Generators
Abstract
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 timeefficient and spaceefficient 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 spacebounded algorithms. We show that (an instance of) the INW pseudorandom generator for classical spacebounded algorithms [INW94] also fools quantum spacebounded algorithms. More precisely, we show that for quantum spacebounded algorithms that have access to a readonce 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.11877
 Bibcode:
 2021arXiv210611877G
 Keywords:

 Quantum Physics;
 Computer Science  Computational Complexity