DeepAI AI Chat
Log In Sign Up

On the Need for Large Quantum Depth

by   Nai-Hui Chia, et al.

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.


page 1

page 2

page 3

page 4


Oracle separations of hybrid quantum-classical circuits

An important theoretical problem in the study of quantum computation, th...

Learning DNFs under product distributions via μ-biased quantum Fourier sampling

We show that DNF formulae can be quantum PAC-learned in polynomial time ...

Computations with Greater Quantum Depth Are Strictly More Powerful (Relative to an Oracle)

A conjecture of Jozsa states that any polynomial-time quantum computatio...

Rotational Abstractions for Verification of Quantum Fourier Transform Circuits

With the race to build large-scale quantum computers and efforts to expl...

Learning quantum symmetries with interactive quantum-classical variational algorithms

A symmetry of a state |ψ⟩ is a unitary operator of which |ψ⟩ is an eigen...

Hybrid divide-and-conquer approach for tree search algorithms

As we are entering the era of real-world small quantum computers, findin...

The Complexity of NISQ

The recent proliferation of NISQ devices has made it imperative to under...