Fock-Space Schrieffer–Wolff Transformation: Classically-Assisted Rank-Reduced Quantum Phase Estimation Algorithm

Round 1

Reviewer 1 Report

In the manuscript entitled  ``Fock-space Schrieffer–Wolff transformation: classically-assisted

rank-reduced quantum phase estimation algorithm", the authors present an extension of many-body downfolding methods to reduce the resources

required in the quantum phase estimation (QPE) algorithm. To be specific, they focus on the Schrieffer-Wolff (SW) transformation of the electronic Hamiltonians for molecular systems that provides significant simplifications of quantum circuits for simulations of quantum dynamics. It is shown that  the locality of the qubit-mapped similarity transformed Hamiltonians  can be significantly increased by employing Fock-space variants of the SW transformation (or rank-reducing similarity transformations (RRST))which serves as a design principle for developing new classes of approximate schemes that reduce the complexity of quantum circuits. In my opinion, the derivation follows the standard procedure and the results sound scientific and effective. Therefore, I am willing to provide my recommendation for publication of this manuscript in Applied Sciences after the authors address the following points.

1. The Reference number should be placed in front of punctuation.

2. In line 106, there is a extra box, which should be deleted.

3. In the sentence before Eq.~(39), the words ``in analogous was" may be replaced with ``in analogous as", the authors should examine the whole manuscript carefully to avoid mistakes.

 

 

Author Response

Our responses to the Reviewer's comments:

 

 

1. The Reference number should be placed in front of punctuation.

          Answer: We changed the punctuation.

2. In line 106, there is a extra box, which should be deleted.

          Answer: The box is the QED symbol at the end of the proof. It marks the                               end of the proof and should be there. 

3. In the sentence before Eq.~(39), the words ``in analogous was" may be replaced with ``in analogous as", the authors should examine the whole manuscript carefully to avoid mistakes.

            Answer: The section was changed to “can transform the $H$ operator to              the $\Gamma$ operator in an analogous way”

Reviewer 2 Report

Dear Editor,

I think the paper can be published as it is.

Author Response

We would like to thank the Reviewer for time to read the manuscript. 

Reviewer 3 Report

This manuscript studies the Schrieffer–Wolff (SW) transformation of the electronic Hamiltonians for molecular systems that provides significant simplifications of quantum circuits for simulations of quantum dynamics. We demonstrate that by employing Fock-space variants of the SW transformation (or rank-reducing similarity transformations (RRST)) one can significantly increase the locality of the qubit-mapped similarity transformed Hamiltonians.

The subject is timely, the paper is well written. Therefore, I conclude that the manuscript is suitable for publication in Appl. Sci..

Author Response

We would like to thank the Reviewer for time to read the manuscript.