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Quantum circuit simulation of linear optics using fermion to qubit encoding
by Seungbeom Chin, Jaehee Kim, Joonsuk Huh
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Joonsuk Huh |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202311_00007v2 (pdf) |
| Date accepted: | 2024-06-03 |
| Date submitted: | 2024-05-22 13:42 |
| Submitted by: | Huh, Joonsuk |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
This work proposes a digital quantum simulation protocol for the linear scattering process of bosons, which provides a simple extension to partially distinguishable boson cases. Our protocol is achieved by combining the boson-fermion correspondence relation and fermion to qubit encoding protocols. As a proof of concept, we designed quantum circuits for generating the Hong-Ou-Mandel dip by varying particle distinguishability. The circuits were verified with the classical and quantum simulations using the IBM Quantum and IonQ cloud services.
Author comments upon resubmission
Reviewer 1. 1- example of situation showcasing the advantages of the method, e.g where existing methods would fail while the proposed protocol does not.
Answer: The reviewer's claim is correct that other B2QE protocols can simulate HOM dip in principle. However, our protocol can achieve that more efficiently than other protocols based on integer-to-bit encodings optimized for ideal bosons. Our protocol is organized to preserve the exchange symmetry of bosons, resulting in a straightforward and efficient simulation of distinguishable bosons. As far as we know, the only research that has simulated HOM effect with digital quantum computers is Ref. [33] (recently posted in arXiv), which, however, is limited to ideal boson simulations with the gray code and acknowledges that a more general HOM dip simulation would require a significant amount of additional qubits. We have added a remark at the end of section III to demonstrate that our method can efficiently simulate the scattering process of distinguishable bosons. We left a remark in our manuscript (highlighted in blue) as follows:
"It is worth mentioning that our example of the HOM dip simulation with distinguishable bosons shows the advantage of our scheme over other integer-to-bit mappings in, e.g., Ref. [13-19]. Comparing Eq. (27) with Eq. (36), we see that bosonic system with a 2-dimensional internal degree of freedom is directly simulated by adding one copy of 4 qubits. Since our mapping from the bosonic system to qubits is set to preserve the exchange symmetry, the generalization from ideal bosons to distinguishable bosons is straightforward. Moreover, we do not need Schur transformation gates as in Ref. [12], hence more efficient. On the other hand, recent research on the digital simulation of the HOM experiment with ideal photons in Ref. [33] shows that a significant amount of qubits are needed to add distinguishability in integer-to-bit mappings, such as the gray code encoding."
Answer: The reviewer's claim is correct that other B2QE protocols can simulate HOM dip in principle. However, our protocol can achieve that more efficiently than other protocols based on integer-to-bit encodings optimized for ideal bosons. Our protocol is organized to preserve the exchange symmetry of bosons, resulting in a straightforward and efficient simulation of distinguishable bosons. As far as we know, the only research that has simulated HOM effect with digital quantum computers is Ref. [33] (recently posted in arXiv), which, however, is limited to ideal boson simulations with the gray code and acknowledges that a more general HOM dip simulation would require a significant amount of additional qubits. We have added a remark at the end of section III to demonstrate that our method can efficiently simulate the scattering process of distinguishable bosons. We left a remark in our manuscript (highlighted in blue) as follows:
"It is worth mentioning that our example of the HOM dip simulation with distinguishable bosons shows the advantage of our scheme over other integer-to-bit mappings in, e.g., Ref. [13-19]. Comparing Eq. (27) with Eq. (36), we see that bosonic system with a 2-dimensional internal degree of freedom is directly simulated by adding one copy of 4 qubits. Since our mapping from the bosonic system to qubits is set to preserve the exchange symmetry, the generalization from ideal bosons to distinguishable bosons is straightforward. Moreover, we do not need Schur transformation gates as in Ref. [12], hence more efficient. On the other hand, recent research on the digital simulation of the HOM experiment with ideal photons in Ref. [33] shows that a significant amount of qubits are needed to add distinguishability in integer-to-bit mappings, such as the gray code encoding."
Published as SciPost Phys. Core 7, 042 (2024)