Noise-induced barren plateaus in variational quantum algorithms

@article{Wang2021NoiseinducedBP,
  title={Noise-induced barren plateaus in variational quantum algorithms},
  author={Samson Wang and Enrico Fontana and Mar{\'i}a Cerezo and Kunal Sharma and Akira Sone and Lukasz Cincio and Patrick J. Coles},
  journal={Nature Communications},
  year={2021},
  volume={12}
}
Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the… 
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References

SHOWING 1-10 OF 120 REFERENCES
Barren plateaus in quantum neural network training landscapes
TLDR
It is shown that for a wide class of reasonable parameterized quantum circuits, the probability that the gradient along any reasonable direction is non-zero to some fixed precision is exponentially small as a function of the number of qubits.
Cost-Function-Dependent Barren Plateaus in Shallow Quantum Neural Networks
TLDR
Two results are rigorously proved that establish a connection between locality and trainability in VQAs and illustrate these ideas with large-scale simulations of a particular VQA known as quantum autoencoders.
Cost function dependent barren plateaus in shallow parametrized quantum circuits
TLDR
This work rigorously proves two results, assuming V(θ) is an alternating layered ansatz composed of blocks forming local 2-designs, that establish a connection between locality and trainability.
Entanglement devised barren plateau mitigation
TLDR
This work defines barren plateaus in terms of random entanglement and proposes and demonstrates a number of barren plateau ameliorating techniques, including initial partitioning of cost function and non-cost function registers, meta-learning of lowentanglement circuit initializations, selective inter-register interaction, entanglements regularization, and rotation into preferred cost function eigenbases.
Noise resilience of variational quantum compiling
TLDR
A surprising form of noise resilience for variational hybrid quantum-classical algorithms is reported, finding one often learns the correct gate sequence $V$ despite various sources of incoherent noise acting during the cost-evaluation circuit.
Variational quantum state diagonalization
Variational hybrid quantum-classical algorithms are promising candidates for near-term implementation on quantum computers. In these algorithms, a quantum computer evaluates the cost of a gate
Noisy intermediate-scale quantum (NISQ) algorithms
TLDR
A thorough summary of NISQ computational paradigms and algorithms, which discusses the key structure of these algorithms, their limitations, and advantages, and a comprehensive overview of various benchmarking and software tools useful for programming and testing NISZ devices.
Hybrid Quantum-Classical Algorithms and Quantum Error Mitigation
TLDR
The basic results for hybrid quantum-classical algorithms and quantum error mitigation techniques are reviewed and it is expected that this review to be a useful basis for future studies.
Noise-resilient variational hybrid quantum-classical optimization
TLDR
This work considers a minimization problem with respect to a variational state, iteratively obtained via a parametric quantum circuit, taking into account both the role of noise and the stochastic nature of quantum measurement outcomes, and shows the robustness of the algorithm against different noise strengths.
The theory of variational hybrid quantum-classical algorithms
TLDR
This work develops a variational adiabatic ansatz and explores unitary coupled cluster where it is shown how the use of modern derivative free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques.
...
...