# 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

#### Figures and Tables from this paper

#### 9 Citations

Fisher Information in Noisy Intermediate-Scale Quantum Applications

- Physics
- Quantum
- 2021

The recent advent of noisy intermediate-scale quantum devices, especially near-term quantum computers, has sparked extensive research efforts concerned with their possible applications. At the… Expand

Towards favorable landscapes in quantum combinatorial optimization

- 2021

The performance of variational quantum algorithms relies on the success of using quantum and classical computing resources in tandem. Here, we study how these quantum and classical components… Expand

On Assessing the Quantum Advantage for MaxCut Provided by Quantum Neural Network Ans\"atze

- Physics, Mathematics
- 2021

In this work we design a class of Ansätze to solve MaxCut on a parameterized quantum circuit (PQC). Gaining inspiration from properties of quantum optimal control landscapes, we consider the presence… Expand

Entanglement Diagnostics for Efficient Quantum Computation

- Computer Science, Physics
- ArXiv
- 2021

By analyzing the qualitative and quantitative differences in the respective optimization processes, it is demonstrated that the entanglement measures are robust diagnostics that are highly correlated with the optimization performance. Expand

Large-scale quantum machine learning

- Computer Science, Physics
- ArXiv
- 2021

This work measures quantum kernels using randomized measurements to gain a quadratic speedup in computation time and quickly process large datasets and efficiently encode high-dimensional data into quantum computers with the number of features scaling linearly with the circuit depth. Expand

Quantum variational optimization: the role of entanglement and problem hardness

- Physics
- 2021

Quantum variational optimization has been posed as an alternative to solve optimization problems faster and at a larger scale than what classical methods allow. In this manuscript we study… Expand

Towards a Unified Model of Quantum Computation

- 2021

In this work we provide a unifying framework from which to discuss the measures of computational complexity associated with different models of quantum computation, based on the resources being… Expand

Towards ultra-high fidelity quantum operations: SQiSW gate as a native two-qubit gate

- Physics
- 2021

Cupjin Huang,1 Dawei Ding,1 Qi Ye,2, 3 Feng Wu,4 Linghang Kong,5 Fang Zhang,1 Xiaotong Ni,4 Yaoyun Shi,1 Hui-Hai Zhao,2 and Jianxin Chen1 Alibaba Quantum Laboratory, Alibaba Group USA, Bellevue,… Expand

Theory of overparametrization in quantum neural networks

- Computer Science, Physics
- ArXiv
- 2021

This paper presents a meta-analyses of the LaSalle–Cerezo–Larocca–Bouchut–Seiden–Stein cellular automaton, a model derived from the model developed by J. J. Giambiagi in 2007, which states that the model derived in this paper can be modified for flows on rugous topographies varying around an inclined plane. Expand

#### References

SHOWING 1-10 OF 79 REFERENCES

Expressibility and Entangling Capability of Parameterized Quantum Circuits for Hybrid Quantum‐Classical Algorithms

- Computer Science, Physics
- Advanced Quantum Technologies
- 2019

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

- Computer Science, Physics
- Nature Communications
- 2018

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

- Computer Science, Physics
- 2015

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.

- Physics, Chemistry
- Chemical reviews
- 2019

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

- Physics, Medicine
- Nature
- 2017

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

- Computer Science, Physics
- 2019

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

- Computer Science, Physics
- Quantum
- 2018

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

- Computer Science, Physics
- Nature Physics
- 2019

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

- Computer Science, Mathematics
- npj Quantum Information
- 2019

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

- Physics, Computer Science
- Nature Communications
- 2019

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