We introduce an algebraic framework for constructing a new class of quantum error-correcting codes, bosonic algebraically-restricted constellation (BARC) codes. The code states are finite superpositions of coherent-state constellations constrained by symmetries of solution sets to multivariate complex polynomial system...
Praneel Gore, D. Aghamalyan, Varun Narasimhachar et al.· 0 citations
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
The most general strategy for estimating parameters of a quantum channel is to probe the channel many times sequentially with the help of coherent ancillary systems. However, finding the strategy that minimizes the mean-squared error (MSE) is a notoriously hard problem, requiring optimization over the initial probe sta...
Andrew Tanggara, Lorcán O. Conlon, Alexey V. Gorshkov 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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