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}
}
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… 

Figures and Tables from this paper

References

SHOWING 1-10 OF 67 REFERENCES

The Quantum Complexity of Computing Schatten $p$-norms

TLDR
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

TLDR
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.

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

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

TLDR
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

TLDR
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

TLDR
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.

Quantum Natural Gradient

TLDR
An efficient algorithm is presented for computing a block-diagonal approximation to the Fubini-Study metric tensor for parametrized quantum circuits, which may be of independent interest.

Gradients of parameterized quantum gates using the parameter-shift rule and gate decomposition

The parameter-shift rule is an approach to measuring gradients of quantum circuits with respect to their parameters, which does not require ancilla qubits or controlled operations. Here, I discuss

Ambiguous Discrimination of General Quantum Operations

We consider the problem of discriminating general quantum operations. Using the definition of mapping operator to vector, and by some calculating skills, we derive an explicit formulation as a new
...