Eliminating Intermediate Measurements using Pseudorandom Generators

@article{Girish2021EliminatingIM,
  title={Eliminating Intermediate Measurements using Pseudorandom Generators},
  author={Uma Girish and Ran Raz},
  journal={Electron. Colloquium Comput. Complex.},
  year={2021},
  volume={28},
  pages={87}
}
  • Uma Girish, R. Raz
  • Published 22 June 2021
  • Computer Science
  • Electron. Colloquium Comput. Complex.
We show that quantum algorithms of time $T$ and space $S\ge \log T$ with intermediate measurements can be simulated by quantum algorithms of time $T \cdot \mathrm{poly}(S)$ and space $O(S\cdot \log T )$ without intermediate measurements. The best simulations 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 intermediate… 

Figures from this paper

Quantum circuits with classical channels and the principle of deferred measurements

References

SHOWING 1-10 OF 31 REFERENCES
Quantum Logspace Algorithm for Powering Matrices with Bounded Norm
TLDR
This result proves a quantum analogue of the result of Lange, McKenzie and Tapp that deterministic logspace is equal to reversible logspace [LMT00], and uses the results to show non-trivial classical simulations of quantum logspace learning algorithms.
A Note on Bennett's Time-Space Tradeoff for Reversible Computation
TLDR
Bennett shows how to construct an equivalent reversible program with running time T and space complexity O and proves that the reversible program actually runs in time $\Theta ({{T^{1 + \varepsilon}} / {S^{\varePSilon}}})$ and space $\TheTA (S(1+\ln ({T / S})))$.
Space-Bounded Quantum Complexity
  • J. Watrous
  • Computer Science
    J. Comput. Syst. Sci.
  • 1999
TLDR
It is shown that unbounded error, space O(s) bounded quantum Turing machines and probabilistic Turing machines are equivalent in power and, furthermore, that any QTM running in space s can be simulated deterministically in NC2(2s)?DSPACE(s2)?DTIME(2O(s).
Eliminating intermediate measurements in space-bounded Quantum computation
TLDR
This work exhibits a procedure to eliminate all intermediate measurements that is simultaneously space efficient and time efficient, and shows that the definition of a space-bounded quantum complexity class is robust to allowing or forbidding intermediate measurements.
Small-bias probability spaces: efficient constructions and applications
It is shown how to efficiently construct a small probability space on n binary random variables such that for every subset, its parity is either zero or one with “almost” equal probability. They are
Space Pseudorandom Generators by Communication Complexity Lower Bounds
  • A. Ganor, R. Raz
  • Computer Science
    Electron. Colloquium Comput. Complex.
  • 2013
TLDR
A lower bound for the communication complexity of conservative one-way unicast communication protocols that compute a family of functions obtained by compositions of strong extractors is proved.
Pseudorandom Generators for Regular Branching Programs
TLDR
It is shown that if a (possibly non-regular) branching program of length $n$ and width $d$ has the property that every vertex in the program is traversed with probability at least $\gamma$ on a uniformly random input, then the error of the generator above is at most $2 \epsilon/\gamma^2$.
Time/Space Trade-Offs for Reversible Computation
TLDR
Using a pebbling argument, this paper shows that, for any $\varepsilon > 0$, ordinary multitape Turing machines using time T and space S can be simulated by reversible ones using time $O(T^{1 + \varpsilon } )$ and space $O (S\log T)$ or in linear time and space$O(ST^\varePSilon )$.
Pseudorandom generators for space-bounded computation
  • N. Nisan
  • Computer Science, Mathematics
    Comb.
  • 1992
TLDR
Pseudorandom generators are constructed which convertO(SlogR) truly random bits toR bits that appear random to any algorithm that runs inSPACE(S) that can be simulated using onlyO(Slogn) random bits.
...
...