Recent work established that, for independent erasures, storing $K$ logical qubits for $S$ time steps with error at most $\varepsilon$ requires a spacetime cost of $\Omega(S(K+\log(S/\varepsilon)))$. A matching construction was also given, but assumes ideal error correction. Here we show that the same scaling can be ac...
Kishor Bharti, Tobias Haug, Derek Khu et al.· 0 citations
We study a family of quantum subsystem codes defined on rectangular coordinate grids of any dimension, with even side lengths of at least four. The directly measured operators act along coordinate lines. For every member of the family, we derive the number of protected logical qubits and prove its dressed distance with...
Kishor Bharti, Tobias Haug, Run-Zhou Tao et al.· 0 citations
Non-Clifford gates are essential for universal quantum computation, yet implementing them fault-tolerantly remains a central challenge for stabilizer codes. Here, we show how a syndrome degree of freedom can mediate a logical non-Clifford gate. Releasing one stabilizer check makes an additional logical qubit available...
Kishor Bharti, Tobias Haug, Andrew Tanggara· 0 citations
This work establishes fundamental limits on the resources required for quantum fault tolerance, and gives a positive-rate CSS code construction that attains the memory bound, and identifies sufficient conditions under which the same scaling extends from quantum memory to fault-tolerant circuit implementations.
Kishor Bharti, Tobias Haug, Andrew Tanggara· 1 citation
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