aiqbench analysis
This study reframes magic-state distillation protocols using classical error-correcting codes and SAT solvers to establish rigorous no-go theorems for compact quantum factories. By proving fundamental limits on error detection for protocols under eight qubits, the work provides essential analytical constraints for optimizing resource usage in fault-tolerant quantum computation. The paper also introduces new, minimal-qubit protocols for specific distances, offering a concrete reference point for hardware designers targeting scalable quantum architectures.
Exploring the landscape of compact magic-state distillation factories
arXiv:2606.07734v1 Announce Type: new Abstract: Producing high-fidelity magic states using the smallest possible amount of physical qubits and operations stands as a very important challenge to achieve fault-tolerant quantum computation at scale. Besides emerging proposals for alternative methods such as cultivation, magic state distillation remains essential for achieving very low error rates. Known distillation protocols are usually built through quantum codes derived from triorthogonal matrices. Here, exploiting the specific noise structure present in magic state distillation protocols, we show that classical error-correcting codes offer a simpler framework for deriving these protocols. This formulation is particularly well suited to systematic numerical and analytical studies of distillation protocols involving a fixed number of qubits. Specifically, we use a SAT solver to derive a series of no-go theorems that relate key figures of merit, including the number of qubits, the protocol depth, the factory distance, and the prefactor in the output error rate. For instance, we prove that any $T$-to-$T$ state distillation protocol using fewer than eight qubits can detect at most three errors, while any $T$-to-$\mathrm{CC}Z$ state distillation protocol using fewer than eight qubits can detect at most two errors. Our results also include new distillation protocols with the smallest number of qubits for a given distance in the literature, namely distance 4 and 5 $T$-to-$T$ state protocols supported on 10 and 11 qubits, as well as distance 3 and 4 $T$-to-$\mathrm{CC}Z$ state distillation protocols supported on 9 and 10 qubits.
Abstract:Producing high-fidelity magic states using the smallest possible amount of physical qubits and operations stands as a very important challenge to achieve fault-tolerant quantum computation at scale. Besides emerging proposals for alternative methods such as cultivation, magic state distillation remains essential for achieving very low error rates. Known distillation protocols are usually built through quantum codes derived from triorthogonal matrices. Here, exploiting the specific noise structure present in magic state distillation protocols, we show that classical error-correcting codes offer a simpler framework for deriving these protocols. This formulation is particularly well suited to systematic numerical and analytical studies of distillation protocols involving a fixed number of qubits. Specifically, we use a SAT solver to derive a series of no-go theorems that relate key figures of merit, including the number of qubits, the protocol depth, the factory distance, and the prefactor in the output error rate. For instance, we prove that any $T$-to-$T$ state distillation protocol using fewer than eight qubits can detect at most three errors, while any $T$-to-$\mathrm{CC}Z$ state distillation protocol using fewer than eight qubits can detect at most two errors. Our results also include new distillation protocols with the smallest number of qubits for a given distance in the literature, namely distance 4 and 5 $T$-to-$T$ state protocols supported on 10 and 11 qubits, as well as distance 3 and 4 $T$-to-$\mathrm{CC}Z$ state distillation protocols supported on 9 and 10 qubits.
arXiv:2606.07734 [quant-ph]
(or arXiv:2606.07734v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.07734 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 325 words