Limitations of Noisy Quantum Devices in Computational and Entangling
Power
- URL: http://arxiv.org/abs/2306.02836v1
- Date: Mon, 5 Jun 2023 12:29:55 GMT
- Title: Limitations of Noisy Quantum Devices in Computational and Entangling
Power
- Authors: Yuxuan Yan, Zhenyu Du, Junjie Chen, Xiongfeng Ma
- Abstract summary: We show that noisy quantum devices with a circuit depth of more than $O(log n)$ provide no advantages in any quantum algorithms.
We also study the maximal entanglement that noisy quantum devices can produce under one- and two-dimensional qubit connections.
- Score: 5.178527492542246
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Quantum computing devices have been rapidly developed in the past decade.
Tremendous efforts have been devoted to finding quantum advantages for useful
but classically intractable problems via current noisy quantum devices without
error correction. It is important to know the fundamental limitations of noisy
quantum devices with the help of classical computers. For computation with
general classical processing, we show that noisy quantum devices with a circuit
depth of more than $O(\log n)$ provide no advantages in any quantum algorithms.
This rigorously rules out the possibility of implementing well-known quantum
algorithms, including Shor's, Grover's, Harrow-Hassidim-Lloyd, and linear-depth
variational algorithms. Then, we study the maximal entanglement that noisy
quantum devices can produce under one- and two-dimensional qubit connections.
In particular, for a one-dimensional qubit chain, we show an upper bound of
$O(\log n)$. This finding highlights the restraints for quantum simulation and
scalability regarding entanglement growth. Additionally, our result sheds light
on the classical simulatability in practical cases.
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