Suggested reading
For the basis of the tableaux methods first read (Gottesman, 1998) followed by the more efficient approach described in (Aaronson and Gottesman, 2004).
The tableaux can be canonicalized (i.e. Gaussian elimination can be performed on them) in a number of different ways, and considering the different approaches provides useful insight. The following methods are implemented in this library:
- The default one: (Garcia et al., 2012)
- Useful when in need of tracing out a set of qubits: (Audenaert and Plenio, 2005)
- Useful when defining logical operators of codes: (Gottesman, 1997)
For the use of these methods in error correction and the subtle overlap between the two fields consider these resources. They are also useful in defining some of the specific constraints in commutation between rows in the tableaux:
These publications describe the uniform sampling of random stabilizer states:
For circuit construction routines (for stabilizer measurements for a given code):
- (Cleve and Gottesman, 1997)
- (Gottesman, 1997) (and its erratum)
- (Grassl, 2002)
- (Grassl, 2011)
For quantum code construction routines:
- (Cleve and Gottesman, 1997)
- (Gottesman, 1996)
- (Gottesman, 1997)
- (Yu et al., 2013)
- (Chao and Reichardt, 2017)
- (Kitaev, 2003)
- (Fowler et al., 2012)
- (Knill and Laflamme, 1996)
- (Steane, 1999)
- (Campbell et al., 2012)
- (Anderson et al., 2014)
- (Wang and Mueller, 2024)
- (Voss et al., 2024)
- (Lin and Pryadko, 2024)
- (Bravyi et al., 2024)
- (Haah, 2011)
- (Landahl et al., 2011)
- (Wang et al., 2023)
- (Naghipour et al., 2015)
For classical code construction routines:
- (Muller, 1954)
- (Reed, 1954)
- (Raaphorst, 2003)
- (Abbe et al., 2020)
- (Djordjevic, 2021)
- (Hocquenghem, 1959)
- (Bose and Ray-Chaudhuri, 1960)
- (Bose and Ray-Chaudhuri, 1960)
- (Lin and Costello, 2024)
- (Golay, 1949)
- (Huffman and Pless, 2010)
- (Bhatia and Kumar, 2018)
For minimum distance calculation of quantum codes:
- (Vardy, 1997)
- (Sabo, 2022)
- (Kapshikar and Kundu, 2023)
- (Landahl et al., 2011)
- (White and Grassl, 2006)
- (Pryadko et al., 2023)
- (Makhorin, 2008)
- (Lubin et al., 2023)
- (Huangfu and Hall, 2018)
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