The ITensor Software Library for Tensor Network Calculations

We thank the referees and editors while we prepared our resubmission and hope it reflects their many helpful suggestions. Thank you to the referees for the detailed reviews and taking the time to review such a long manuscript. Below we list the major changes. Of course we have also made many small changes that are too numerous to list, such as updating code examples to use newer syntax reflecting updates we have made to ITensor, or updates about features we are currently working on.

Major changes:

1. We have added two sections discussing benchmarks of ITensor. The first performs extensive benchmarks of ITensor itself, both the C++ and Julia implementations, across multiple algorithms and using various kinds of multi-threaded parallelism. The second set of benchmarks is more briefly discussed in the paper and is hosted externally. These compare ITensor to the state-of-the-art TeNPy software.

2. We have revised the introduction to discuss more aspects about the unusual choice to have "intelligent" tensor indices, why it is helpful, some drawbacks it can present (but how to handle them). We have also contrasted the ITensor interface against other tensor libraries and their interfaces in some more depth, while trying to make the writing broad enough to be "future proof" given that other libraries are always changing and adding features.

3. We discuss aspects of the various ITensor storage types in some additional depth, with more details of implementation and references to other parts of the paper where they are discussed more.

4. On a related note, the NDTensors section has been expanded, including a more detailed example of a block-sparse tensor with a figure.

5. Please note the link to further code examples online added to the end of Section 2 and beginning of Appendix A. We are continually updating and expanding these.

Specific Replies to Referees
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# Referee 1

Thank you for the suggestion of adding benchmarks, which does make the paper much stronger. We have now added extensive benchmarks of the Julia versus C++ versions of ITensor, showing they have similar performance, with the Julia version being even faster in many cases.

# Referee 2

Thank you for the detailed feedback, and especially for the suggestion of adding benchmarks.

Regarding point (1), we have added new material to the introduction to put ITensor in more context. Of course we feel the intelligent index design is a good one and are continually finding it to have many benefits (e.g. as we are now working on an automatic fermion system, automatic differentiation tools, etc.). But we certainly agree that there are risks or possible downsides of the design that have to be thought about: for example, we now specifically note how users can gain manual control over index ordering and memory layout when needed.

To address point (2), we have added references to relevant papers on conservation of quantum numbers i.e. symmetric tensors within the section on QN conserving ITensors. Thank you for this suggestion since there has been much work on this topic in the tensor literature of course.

Regarding (3), we have now added extensive benchmarks of the C++ versus Julia implementations of ITensor, and detailed benchmarks versus the TeNPy software online. We agree the paper greatly benefits from including these.

# Referee 3

Thank you for the detailed review. In the new section on benchmarks, we have also provided links to our ITensorBenchmarks Github repository, which includes further instructions for running or re-running the benchmark codes with various adjustable options. We plan to continue working on this repository over time by not only adding more benchmarks but also making it easier to use with more adjustable options etc.

We have also provided a link to the examples code folder, plus made this more prominent in our online ITensor documentation. Thank you for this suggestion as these examples were definitely too hard to find previously.

Thank you for the writing corrections which we have implemented.