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Eliminating intermediate measurements in space-bounded Quantum computation

Authors:

Bill Fefferman,

Zachary RemscrimAuthors Info & Claims

STOC 2021: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing

Pages 1343 - 1356

https://doi.org/10.1145/3406325.3451051

Published: 15 June 2021 Publication History

Abstract

A foundational result in the theory of quantum computation, known as the "principle of safe storage," shows that it is always possible to take a quantum circuit and produce an equivalent circuit that makes all measurements at the end of the computation. While this procedure is time efficient, meaning that it does not introduce a large overhead in the number of gates, it uses extra ancillary qubits, and so is not generally space efficient. It is quite natural to ask whether it is possible to eliminate intermediate measurements without increasing the number of ancillary qubits. We give an affirmative answer to this question by exhibiting a procedure to eliminate all intermediate measurements that is simultaneously space efficient and time efficient. In particular, this shows that the definition of a space-bounded quantum complexity class is robust to allowing or forbidding intermediate measurements. A key component of our approach, which may be of independent interest, involves showing that the well-conditioned versions of many standard linear-algebraic problems may be solved by a quantum computer in less space than seems possible by a classical computer.

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Cited By

Wang QZhang Z(2024)Fast Quantum Algorithms for Trace Distance EstimationIEEE Transactions on Information Theory10.1109/TIT.2023.332112170:4(2720-2733)Online publication date: Apr-2024
https://doi.org/10.1109/TIT.2023.3321121
Metger TYuen H(2023)stateQIP = statePSPACE2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00082(1349-1356)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00082
Blocki JHolman BLee S(2022)The Parallel Reversible Pebbling Game: Analyzing the Post-quantum Security of iMHFsTheory of Cryptography10.1007/978-3-031-22318-1_3(52-79)Online publication date: 7-Nov-2022
https://dl.acm.org/doi/10.1007/978-3-031-22318-1_3

Index Terms

Eliminating intermediate measurements in space-bounded Quantum computation
1. Theory of computation
  1. Models of computation
    1. Quantum computation theory
      1. Quantum complexity theory

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cover image ACM Conferences

STOC 2021: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing

June 2021

1797 pages

ISBN:9781450380539

DOI:10.1145/3406325

General Chair:
Samir Khuller
Northwestern University, USA
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Program Chair:
Virginia Vassilevska Williams
Massachusetts Institute of Technology, USA

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Published: 15 June 2021

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STOC '21: 53rd Annual ACM SIGACT Symposium on Theory of Computing

June 21 - 25, 2021

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Cited By

Wang QZhang Z(2024)Fast Quantum Algorithms for Trace Distance EstimationIEEE Transactions on Information Theory10.1109/TIT.2023.332112170:4(2720-2733)Online publication date: Apr-2024
https://doi.org/10.1109/TIT.2023.3321121
Metger TYuen H(2023)stateQIP = statePSPACE2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00082(1349-1356)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00082
Blocki JHolman BLee S(2022)The Parallel Reversible Pebbling Game: Analyzing the Post-quantum Security of iMHFsTheory of Cryptography10.1007/978-3-031-22318-1_3(52-79)Online publication date: 7-Nov-2022
https://dl.acm.org/doi/10.1007/978-3-031-22318-1_3

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