On the Need for Large Quantum Depth

Fuente: arXiv
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Main Authors: Chia, Nai-Hui, Chung, Kai-Min, Lai, Ching-Yi
Format: Preprint
Published: 2019
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author Chia, Nai-Hui
Chung, Kai-Min
Lai, Ching-Yi
author_facet Chia, Nai-Hui
Chung, Kai-Min
Lai, Ching-Yi
contents Near-term quantum computers are likely to have small depths due to short coherence time and noisy gates, and thus a potential way to use these quantum devices is using a hybrid scheme that interleaves them with classical computers. For example, the quantum Fourier transform can be implemented by a hybrid of logarithmic-depth quantum circuits and a classical polynomial-time algorithm. Along the line, it seems possible that a general quantum computer may only be polynomially faster than a hybrid quantum-classical computer. Jozsa raised the question of whether $BQP = BPP^{BQNC}$ and conjectured that they are equal, where $BQNC$ means $polylog$-depth quantum circuits. Nevertheless, Aaronson conjectured an oracle separation for these two classes and gave a candidate. In this work, we prove Aaronson's conjecture for a different but related oracle problem. Our result also proves that Jozsa's conjecture fails relative to an oracle.
format Preprint
id arxiv_https___arxiv_org_abs_1909_10303
institution arXiv
publishDate 2019
record_format arxiv
spellingShingle On the Need for Large Quantum Depth
Chia, Nai-Hui
Chung, Kai-Min
Lai, Ching-Yi
Quantum Physics
Computational Complexity
Near-term quantum computers are likely to have small depths due to short coherence time and noisy gates, and thus a potential way to use these quantum devices is using a hybrid scheme that interleaves them with classical computers. For example, the quantum Fourier transform can be implemented by a hybrid of logarithmic-depth quantum circuits and a classical polynomial-time algorithm. Along the line, it seems possible that a general quantum computer may only be polynomially faster than a hybrid quantum-classical computer. Jozsa raised the question of whether $BQP = BPP^{BQNC}$ and conjectured that they are equal, where $BQNC$ means $polylog$-depth quantum circuits. Nevertheless, Aaronson conjectured an oracle separation for these two classes and gave a candidate. In this work, we prove Aaronson's conjecture for a different but related oracle problem. Our result also proves that Jozsa's conjecture fails relative to an oracle.
title On the Need for Large Quantum Depth
topic Quantum Physics
Computational Complexity
url https://arxiv.org/abs/1909.10303