# Quantum Approximation of Normalized Schatten Norms and Applications to Learning

@article{Chen2022QuantumAO,
title={Quantum Approximation of Normalized Schatten Norms and Applications to Learning},
author={Yiyou Chen and Hideyuki Miyahara and Louis-S. Bouchard and Vwani P. Roychowdhury},
journal={ArXiv},
year={2022},
volume={abs/2206.11506}
}
• Published 23 June 2022
• Computer Science
• ArXiv
Eﬃcient measures to determine similarity of quantum states, such as the ﬁdelity metric, have been widely studied. In this paper, we address the problem of deﬁning a similarity measure for quantum operations that can be eﬃciently estimated . Given two quantum operations, U 1 and U 2 , represented in their circuit forms, we ﬁrst develop a quantum sampling circuit to estimate the normalized Schatten 2-norm of their diﬀerence ( (cid:107) U 1 − U 2 (cid:107) S 2 ) with precision (cid:15) , using…

## References

SHOWING 1-10 OF 67 REFERENCES

### The Quantum Complexity of Computing Schatten $p$-norms

• Computer Science
TQC
• 2018
It is shown that the problem of approximating $\text{Tr}\, (|A|^p)$ for a log-local $n$-qubit Hamiltonian $A$ and $p=\text{poly}(n)$, up to a suitable level of accuracy, is contained in DQC1; and that approximating this quantityup to a somewhat higherlevel of accuracy is D QC1-hard.

### QUEST: systematically approximating Quantum circuits for higher output fidelity

• Computer Science
ASPLOS
• 2022
The results indicate that QUEST can reduce CNOT gate count by 30-80% on ideal systems and decrease the impact of noise on existing and near-future quantum systems.

### Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators.

• Physics
Physical review letters
• 2021
Electron transport in realistic physical and chemical systems often involves the nontrivial exchange of energy with a large environment, requiring the definition and treatment of open quantum

### Operational applications of the diamond norm and related measures in quantifying the non-physicality of quantum maps

• Physics
Quantum
• 2021
Although quantum channels underlie the dynamics of quantum states, maps which are not physical channels — that is, not completely positive — can often be encountered in settings such as entanglement

### Ansatz-Independent Variational Quantum Classifier

• Computer Science
• 2021
This letter addresses the open questions about VQCs and shows that they, including QCL, fit inside the well-known kernel method, and proposes a variational circuit realization (VCR) for designing efficient quantum circuits for a given unitary operator.

### Variational Quantum Algorithms

• Physics, Computer Science
Nature Reviews Physics
• 2021
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.

### On the natural gradient for variational quantum eigensolver

This paper gives some simple case-studies of how the natural gradient optimizer makes use of the geometric property to change and improve the ordinary gradient method.