Capacity and quantum geometry of parametrized quantum circuits

@article{Haug2021CapacityAQ,
  title={Capacity and quantum geometry of parametrized quantum circuits},
  author={Tobias Haug and Kishor Bharti and M. S. Kim},
  journal={ArXiv},
  year={2021},
  volume={abs/2102.01659}
}
To harness the potential of noisy intermediate-scale quantum devices, it is paramount to find the best type of circuits to run hybrid quantum-classical algorithms. Key candidates are parametrized quantum circuits that can be effectively implemented on current devices. Here, we evaluate the capacity and trainability of these circuits using the geometric structure of the parameter space via the effective quantum dimension, which reveals the expressive power of circuits in general as well as of… Expand
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References

SHOWING 1-10 OF 79 REFERENCES
Expressibility and Entangling Capability of Parameterized Quantum Circuits for Hybrid Quantum‐Classical Algorithms
TLDR
This study quantifies the substantial improvement in performance of two-qubit gates in a ring or all-to-all connected arrangement compared to that of those on a line, and investigates how expressibility "saturates" with increased circuit depth. Expand
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. Expand
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. Expand
Quantum Chemistry in the Age of Quantum Computing.
TLDR
This Review provides an overview of the algorithms and results that are relevant for quantum chemistry and aims to help quantum chemists who seek to learn more about quantum computing and quantum computing researchers who would like to explore applications in quantum chemistry. Expand
Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets
TLDR
The experimental optimization of Hamiltonian problems with up to six qubits and more than one hundred Pauli terms is demonstrated, determining the ground-state energy for molecules of increasing size, up to BeH2. Expand
An initialization strategy for addressing barren plateaus in parametrized quantum circuits
TLDR
This technical note theoretically motivate and empirically validate an initialization strategy which can resolve the barren plateau problem for practical applications and shows empirically that variational quantum eigensolvers and quantum neural networks initialized using this strategy can be trained using a gradient based method. Expand
Quantum Computing in the NISQ era and beyond
TLDR
Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future, and the 100-qubit quantum computer will not change the world right away - but it should be regarded as a significant step toward the more powerful quantum technologies of the future. Expand
Quantum convolutional neural networks
TLDR
A quantum circuit-based algorithm inspired by convolutional neural networks is shown to successfully perform quantum phase recognition and devise quantum error correcting codes when applied to arbitrary input quantum states. Expand
Variational ansatz-based quantum simulation of imaginary time evolution
TLDR
This work proposes a variational algorithm that is hybrid, suitable for error mitigation and can exploit shallow quantum circuits, and can be implemented with current quantum computers, and uses it to find the ground-state energy of many-particle systems. Expand
An adaptive variational algorithm for exact molecular simulations on a quantum computer
TLDR
A new variational hybrid quantum-classical algorithm which allows the system being simulated to determine its own optimal state, and highlights the potential of the adaptive algorithm for exact simulations with present-day and near-term quantum hardware. Expand
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