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Kasai Lab
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The lab designs quantum error-correcting codes to fix errors in quantum computers.
AboutAbout the lab
Suppressing errors in quantum computation through code design
The Kasai Lab studies codes that correct errors occurring in quantum computer calculations.
In particular, it explores how to construct quantum LDPC codes, whose parity-check equations are sparse, and how to decode them.
The challenge is to satisfy several properties that are hard to achieve together: a practical code rate, a large girth, and low decoding complexity.
The lab aims to regain the design freedom of classical LDPC codes under the constraint of quantum commutativity.
Key terms
- Quantum error correction
- A mechanism that uses codes to detect and correct disturbances to the state during a quantum computer's calculation
- LDPC codes
- Error-correcting codes whose parity-check conditions are sparse (few nonzero entries). Even large codes can be decoded with limited computation
- Code rate
- The fraction of a code that actually carries information. The higher it is, the less wasteful the code
ResearchResearch themes
The lab designs quantum LDPC codes, which are described by sparse parity-check matrices, with clearly defined constructions and practical code rates and decoding performance. It approaches this from two directions: the binary CSS construction and non-binary constructions that use large finite fields.
*Illustrative imageNon-binary quantum LDPC codes
The lab constructs and decodes quantum LDPC codes over large finite fields. By combining this with methods that exploit the degeneracy of quantum errors, it aims to approach the theoretical limits with realistic computational complexity.
*Illustrative imageKasai codes (APM construction)
The APM construction controls the commutativity of permutation matrices to break through the orthogonality barrier in quantum LDPC codes. It is a method for building CSS codes with a large girth and uniform row and column weights.
*Illustrative imagePP codes
This construction satisfies the orthogonality condition required for CSS codes by pairing up overlaps between blocks. Because the codes can be expressed with circulant permutation matrices, their description is compact, and the construction is easy to reproduce and verify.
*Illustrative imageOther construction methods
The lab also studies code families that differ from both Kasai codes and PP codes, such as constructions based on affine cosets, two-branch constructions using finite fields, and constructions aimed at high code rates.
MembersFaculty
- Associate ProfessorKenta KasaiPublications ↗
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Quantum-computer-Chalmers 2017” Anita Fors (Chalmers) / CC BY-SA 4.0 (cropped)
- Non-binary quantum LDPC codes: “6 Transmon Superconducting Quantum Processor without Cheesing 013” OJB Quantum / CC BY 4.0 (cropped)
- Kasai codes (APM construction): “Heawood graph bipartite” Mathsci / CC BY-SA 3.0 (cropped)
- PP codes: “6 Transmon Superconducting Quantum Processor without Cheesing 012” OJB Quantum / CC BY 4.0 (cropped)
- Other construction methods: “AG(2,3)” Kmhkmh / CC BY 3.0 (cropped)
- Related lab (Matsumoto Lab): “Optical fiber cable-01ASD” Asurnipal / CC BY-SA 4.0 (cropped)
- Related lab (Ogata Lab): “Enigma-IMG 0487-black” Rama / CC BY-SA 2.0 fr (cropped)
- Related lab (Kuroda Lab): “Cosine Series Plus Noise TFM” Fourier1789 / CC BY-SA 4.0 (cropped)
- Related lab (Islam Lab): “Micromanipulator Semiautomatic Probe Station” Rgarrigan / CC BY-SA 4.0 (cropped)
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