Hardware-efficient bosonic quantum error-correcting codes based on symmetry operators
We establish a symmetry-operator framework for designing quantum error-correcting (QEC) codes based on fundamental properties of the underlying system dynamics. Based on this framework, we propose three hardware-efficient bosonic QEC codes that are suitable for χ²-interaction based quantum computati...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2018
|
| Online Access: | http://hdl.handle.net/1721.1/114512 https://orcid.org/0000-0002-0013-416X https://orcid.org/0000-0001-7296-523X https://orcid.org/0000-0002-6094-5861 |
| _version_ | 1826217262371045376 |
|---|---|
| author | Niu, Yuezhen Chuang, Isaac Shapiro, Jeffrey H |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Niu, Yuezhen Chuang, Isaac Shapiro, Jeffrey H |
| author_sort | Niu, Yuezhen |
| collection | MIT |
| description | We establish a symmetry-operator framework for designing quantum error-correcting (QEC) codes based on fundamental properties of the underlying system dynamics. Based on this framework, we propose three hardware-efficient bosonic QEC codes that are suitable for χ²-interaction based quantum computation in multimode Fock bases: the χ² parity-check code, the χ² embedded error-correcting code, and the χ² binomial code. All of these QEC codes detect photon-loss or photon-gain errors by means of photon-number parity measurements, and then correct them via χ² Hamiltonian evolutions and linear-optics transformations. Our symmetry-operator framework provides a systematic procedure for finding QEC codes that are not stabilizer codes, and it enables convenient extension of a given encoding to higher-dimensional qudit bases. The χ² binomial code is of special interest because, with m≤N identified from channel monitoring, it can correct m-photon-loss errors, or m-photon-gain errors, or (m−1)th-order dephasing errors using logical qudits that are encoded in O(N) photons. In comparison, other bosonic QEC codes require O(N²) photons to correct the same degree of bosonic errors. Such improved photon efficiency underscores the additional error-correction power that can be provided by channel monitoring. We develop quantum Hamming bounds for photon-loss errors in the code subspaces associated with the χ² parity-check code and the χ² embedded error-correcting code, and we prove that these codes saturate their respective bounds. Our χ² QEC codes exhibit hardware efficiency in that they address the principal error mechanisms and exploit the available physical interactions of the underlying hardware, thus reducing the physical resources required for implementing their encoding, decoding, and error-correction operations, and their universal encoded-basis gate sets. |
| first_indexed | 2024-09-23T17:00:35Z |
| format | Article |
| id | mit-1721.1/114512 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T17:00:35Z |
| publishDate | 2018 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1145122022-10-03T09:48:40Z Hardware-efficient bosonic quantum error-correcting codes based on symmetry operators Niu, Yuezhen Chuang, Isaac Shapiro, Jeffrey H Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Department of Physics Massachusetts Institute of Technology. Research Laboratory of Electronics Niu, Yuezhen Chuang, Isaac Shapiro, Jeffrey H We establish a symmetry-operator framework for designing quantum error-correcting (QEC) codes based on fundamental properties of the underlying system dynamics. Based on this framework, we propose three hardware-efficient bosonic QEC codes that are suitable for χ²-interaction based quantum computation in multimode Fock bases: the χ² parity-check code, the χ² embedded error-correcting code, and the χ² binomial code. All of these QEC codes detect photon-loss or photon-gain errors by means of photon-number parity measurements, and then correct them via χ² Hamiltonian evolutions and linear-optics transformations. Our symmetry-operator framework provides a systematic procedure for finding QEC codes that are not stabilizer codes, and it enables convenient extension of a given encoding to higher-dimensional qudit bases. The χ² binomial code is of special interest because, with m≤N identified from channel monitoring, it can correct m-photon-loss errors, or m-photon-gain errors, or (m−1)th-order dephasing errors using logical qudits that are encoded in O(N) photons. In comparison, other bosonic QEC codes require O(N²) photons to correct the same degree of bosonic errors. Such improved photon efficiency underscores the additional error-correction power that can be provided by channel monitoring. We develop quantum Hamming bounds for photon-loss errors in the code subspaces associated with the χ² parity-check code and the χ² embedded error-correcting code, and we prove that these codes saturate their respective bounds. Our χ² QEC codes exhibit hardware efficiency in that they address the principal error mechanisms and exploit the available physical interactions of the underlying hardware, thus reducing the physical resources required for implementing their encoding, decoding, and error-correction operations, and their universal encoded-basis gate sets. United States. Air Force Office of Scientific Research (Grant FA9550-14-1-0052) 2018-04-03T17:23:23Z 2018-04-03T17:23:23Z 2018-03 2017-12 2018-03-28T18:00:46Z Article http://purl.org/eprint/type/JournalArticle 2469-9926 2469-9934 http://hdl.handle.net/1721.1/114512 Niu, Murphy Yuezhen et al. "Hardware-efficient bosonic quantum error-correcting codes based on symmetry operators." Physical Review A 97, 3 (March 2018): 032323 © 2018 American Physical Society https://orcid.org/0000-0002-0013-416X https://orcid.org/0000-0001-7296-523X https://orcid.org/0000-0002-6094-5861 en http://dx.doi.org/10.1103/PhysRevA.97.032323 Physical Review A Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Niu, Yuezhen Chuang, Isaac Shapiro, Jeffrey H Hardware-efficient bosonic quantum error-correcting codes based on symmetry operators |
| title | Hardware-efficient bosonic quantum error-correcting codes based on symmetry operators |
| title_full | Hardware-efficient bosonic quantum error-correcting codes based on symmetry operators |
| title_fullStr | Hardware-efficient bosonic quantum error-correcting codes based on symmetry operators |
| title_full_unstemmed | Hardware-efficient bosonic quantum error-correcting codes based on symmetry operators |
| title_short | Hardware-efficient bosonic quantum error-correcting codes based on symmetry operators |
| title_sort | hardware efficient bosonic quantum error correcting codes based on symmetry operators |
| url | http://hdl.handle.net/1721.1/114512 https://orcid.org/0000-0002-0013-416X https://orcid.org/0000-0001-7296-523X https://orcid.org/0000-0002-6094-5861 |
| work_keys_str_mv | AT niuyuezhen hardwareefficientbosonicquantumerrorcorrectingcodesbasedonsymmetryoperators AT chuangisaac hardwareefficientbosonicquantumerrorcorrectingcodesbasedonsymmetryoperators AT shapirojeffreyh hardwareefficientbosonicquantumerrorcorrectingcodesbasedonsymmetryoperators |