## Abstract

It was recently shown that SVD and matrix inversion can be approximated in quantum log-space [1] for well formed matrices. This can be interpreted as a fully logarithmic quantum approximation scheme for both problems. We show that if prBQL=prBPL then every fully logarithmic quantum approximation scheme can be replaced by a probabilistic one. Hence, if classical algorithms cannot approximate the above functions in logarithmic space, then there is a gap already for languages, namely, prBQL prBPL. On the way we simplify a proof of Goldreich for a similar statement for time bounded probabilistic algorithms. We show that our simplified algorithm works also in the space bounded setting (for a large set of functions) whereas Goldreich's approach does not seem to apply in the space bounded setting.

Original language | English |
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Pages (from-to) | 750-753 |

Number of pages | 4 |

Journal | Information Processing Letters |

Volume | 115 |

Issue number | 10 |

DOIs | |

State | Published - 15 Sep 2014 |

Externally published | Yes |

## Keywords

- Approximation algorithms
- Computational complexity
- Randomized algorithms
- Space bounded approximation schemes
- Space bounded computation
- Space bounded quantum computation