Classically simulating quantum circuits with local depolarizing noise
| Autor: | Seiichiro Tani, Yuki Takeuchi, Yasuhiro Takahashi |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Quantum Physics General Computer Science Computer science Computation FOS: Physical sciences Quantum Circuit Extension (predicate logic) Computational Complexity (cs.CC) Classical Simulation Topology Noise (electronics) Local Depolarizing Noise Theoretical Computer Science Computer Science - Computational Complexity Computer Science::Emerging Technologies Theory of computation → Quantum computation theory Qubit Probability distribution Quantum Physics (quant-ph) Quantum Electronic circuit Communication channel |
| Zdroj: | Theoretical Computer Science. 893:117-132 |
| ISSN: | 0304-3975 |
| DOI: | 10.1016/j.tcs.2021.07.025 |
| Popis: | We study the effect of noise on the classical simulatability of quantum circuits defined by computationally tractable (CT) states and efficiently computable sparse (ECS) operations. Examples of such circuits, which we call CT-ECS circuits, are IQP, Clifford Magic, and conjugated Clifford circuits. This means that there exist various CT-ECS circuits such that their output probability distributions are anti-concentrated and not classically simulatable in the noise-free setting (under plausible assumptions). First, we consider a noise model where a depolarizing channel with an arbitrarily small constant rate is applied to each qubit at the end of computation. We show that, under this noise model, if an approximate value of the noise rate is known, any CT-ECS circuit with an anti-concentrated output probability distribution is classically simulatable. This indicates that the presence of small noise drastically affects the classical simulatability of CT-ECS circuits. Then, we consider an extension of the noise model where the noise rate can vary with each qubit, and provide a similar sufficient condition for classically simulating CT-ECS circuits with anti-concentrated output probability distributions. 19 pages, 2 figures |
| Databáze: | OpenAIRE |
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