A closed-form resource estimation tool for concatenated quantum error correction reveals that magic-state operations rarely dominate qubit costs, with general optimizations providing orders-of-magnitude larger reductions than magic-specific ones.
Codes and Protocols for Distilling $T$, controlled-$S$, and Toffoli Gates
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abstract
We present several different codes and protocols to distill $T$, controlled-$S$, and Toffoli (or $CCZ$) gates. One construction is based on codes that generalize the triorthogonal codes, allowing any of these gates to be induced at the logical level by transversal $T$. We present a randomized construction of generalized triorthogonal codes obtaining an asymptotic distillation efficiency $\gamma\rightarrow 1$. We also present a Reed-Muller based construction of these codes which obtains a worse $\gamma$ but performs well at small sizes. Additionally, we present protocols based on checking the stabilizers of $CCZ$ magic states at the logical level by transversal gates applied to codes; these protocols generalize the protocols of 1703.07847. Several examples, including a Reed-Muller code for $T$-to-Toffoli distillation, punctured Reed-Muller codes for $T$-gate distillation, and some of the check based protocols, require a lower ratio of input gates to output gates than other known protocols at the given order of error correction for the given code size. In particular, we find a $512$ T-gate to $10$ Toffoli gate code with distance $8$ as well as triorthogonal codes with parameters $[[887,137,5]],[[912,112,6]],[[937,87,7]]$ with very low prefactors in front of the leading order error terms in those codes.
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Heterogeneous quantum architectures with task-specific hardware and QEC encodings deliver up to 138x lower physical-qubit overhead than monolithic baselines for fault-tolerant algorithms, including RSA-2048 factoring at 190k-381k qubits.
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Magic states are rarely the best resource to optimize: An analytical tool for qubit resource estimation in concatenated codes
A closed-form resource estimation tool for concatenated quantum error correction reveals that magic-state operations rarely dominate qubit costs, with general optimizations providing orders-of-magnitude larger reductions than magic-specific ones.
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Heterogeneous architectures enable a 138x reduction in physical qubit requirements for fault-tolerant quantum computing under detailed accounting
Heterogeneous quantum architectures with task-specific hardware and QEC encodings deliver up to 138x lower physical-qubit overhead than monolithic baselines for fault-tolerant algorithms, including RSA-2048 factoring at 190k-381k qubits.