Noise-induced barren plateaus in variational quantum algorithms

@article{Wang2020NoiseinducedBP,
  title={Noise-induced barren plateaus in variational quantum algorithms},
  author={Samson Wang and Enrico Fontana and Marco Cerezo and Kunal Sharma and Akira Sone and Lukasz Cincio and Patrick J. Coles},
  journal={Nature Communications},
  year={2020},
  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… 

Universal noise-precision relations in variational quantum algorithms

Analytic estimations of the error in the cost function of VQAs due to the noise are established and a quantum error mitigation method which is different from the extrapolation and the probabilistic error cancellation is proposed.

Entanglement devised barren plateau mitigation

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.

Absence of Barren Plateaus in Quantum Convolutional Neural Networks

This work rigorously analyze the gradient scaling for the parameters in the QCNN architecture and finds that the variance of the gradient vanishes no faster than polynomially, implying that QCNNs do not exhibit barren plateaus.

Accelerating Variational Quantum Algorithms Using Circuit Concurrency

This work shows that circuit-level concurrency provides a means to increase the performance of variational quantum algorithms on noisy quantum computers by mapping multiple instances of the same circuit onto the quantum computer at the same time, which allows multiple samples in a Variational quantum algorithm to be gathered in parallel for each training iteration.

Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers

This article presents a large-scale numerical study, simulating circuits with up to 40 qubits and 352 parameters, that demonstrates the potential of an iterative layer VQE (L-VQE) approach and shows that L-VZE is more robust to finite sampling errors and has a higher chance of finding the solution as compared with standard VZE approaches.

Quantum Generative Training Using R\'enyi Divergences

This work examines the assumptions that give rise to barren plateaus and shows that an unbounded loss function can circumvent the existing no-go results and proposes a training algorithm that minimizes the maximal Rényi divergence of order two and presents techniques for gradient computation.

Evaluating the noise resilience of variational quantum algorithms

This work uses a variational quantum eigensolver to find the ground state of a Hamiltonian in presence of noise, and finds that the inclusion of redundant parameterised gates makes the quantum circuits more resilient to noise.

Fast suppression of classification error in variational quantum circuits

Variational quantum circuits (VQCs) have shown great potential in near-term applications. However, the discriminative power of a VQC, in connection to its circuit architecture and depth, is not

Equivalence of quantum barren plateaus to cost concentration and narrow gorges

This work analytically proves the connection between three different landscape features that have been observed for PQCs: exponentially vanishing gradients, exponential cost concentration about the mean, and the exponential narrowness of minina.

Variational Quantum Algorithms

An overview of the field of Variational Quantum Algorithms is presented and strategies to overcome their challenges as well as the exciting prospects for using them as a means to obtain quantum advantage are discussed.
...

References

SHOWING 1-10 OF 109 REFERENCES

Barren plateaus in quantum neural network training landscapes

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

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

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

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

This work finds one often learns the correct gate sequence V despite various sources of incoherent noise acting during the cost-evaluation circuit, and suggests that variational quantum compiling, due to its robustness, could be practically useful for noisy intermediate-scale quantum devices.

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

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

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

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

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.
...