Exploring the landscape of compact magic-state distillation factories

• URL: http://arxiv.org/abs/2606.07734v1
• Date: Fri, 05 Jun 2026 18:00:00 GMT
• Title: Exploring the landscape of compact magic-state distillation factories
• Abstract summary: We show that classical error-correcting codes offer a simpler framework for deriving magic state distillation protocols.<n>We 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.<n>Our results also include new distillation protocols with the smallest number of qubits for a given distance in the literature.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Constant sized support state distillation with qubit recycling [0.0]
  We provide a family of protocols able to produce diagonal states at every level of the Clifford hierarchy.<n>We show that the protocols we derive can be performed at arbitrary high distance on a fix number of logical qubits.
  arXiv  Detail & Related papers  (2026-09-15T11:52:36Z)
• Constant Overhead Entanglement Distillation via Scrambling [0.6249768559720122]
  High-fidelity quantum entanglement enables key quantum networking capabilities such as secure communication and distributed quantum computing.<n>We introduce protocols that use quantum scrambling - the spreading of quantum information under chaotic dynamics.<n>We show this protocol remains effective even with noisy quantum gates, making it suitable for near-term devices.
  arXiv  Detail & Related papers  (2025-02-13T16:46:15Z)
• ParetoQ: Improving Scaling Laws in Extremely Low-bit LLM Quantization [73.60493264901359]
  We present a unified framework for rigorous comparisons across 1-bit, 1.58-bit, 2-bit, 3-bit, and 4-bit quantization settings.<n>We show that ternary, 2-bit, and 3-bit quantization maintains comparable performance in the size-accuracy trade-off.<n>Considering hardware constraints, 2-bit quantization offers promising potential for memory reduction and speedup.
  arXiv  Detail & Related papers  (2025-02-04T18:59:26Z)
• Universal quantum computation via scalable measurement-free error correction [45.29832252085144]
  We show that universal quantum computation can be made fault-tolerant in a scenario where the error-correction is implemented without mid-circuit measurements.<n>We introduce a measurement-free deformation protocol of the Bacon-Shor code to realize a logical $mathitCCZ$ gate.<n>In particular, our findings support that below-breakeven logical performance is achievable with a circuit-level error rate below $10-3$.
  arXiv  Detail & Related papers  (2024-12-19T18:55:44Z)
• Stabilizer Entanglement Distillation and Efficient Fault-Tolerant Encoders [3.496737164472548]
  Entanglement is essential for quantum information processing, but is limited by noise.<n>We develop high-yield entanglement distillation protocols with several advancements.
  arXiv  Detail & Related papers  (2024-08-12T17:09:24Z)
• Fast Flux-Activated Leakage Reduction for Superconducting Quantum Circuits [84.60542868688235]
  leakage out of the computational subspace arising from the multi-level structure of qubit implementations. We present a resource-efficient universal leakage reduction unit for superconducting qubits using parametric flux modulation. We demonstrate that using the leakage reduction unit in repeated weight-two stabilizer measurements reduces the total number of detected errors in a scalable fashion.
  arXiv  Detail & Related papers  (2023-09-13T16:21:32Z)
• Near-term $n$ to $k$ distillation protocols using graph codes [0.0]
  Noisy hardware forms one of the main hurdles to the realization of a near-term quantum internet. We consider here an experimentally relevant class of distillation protocols, which distill $n$ to $k$ end-to-end entangled pairs. We leverage this correspondence to find provably optimal distillation protocols in this class for several tasks important for the quantum internet.
  arXiv  Detail & Related papers  (2023-03-20T21:46:17Z)
• Transversal Injection: A method for direct encoding of ancilla states for non-Clifford gates using stabiliser codes [55.90903601048249]
  We introduce a protocol to potentially reduce this overhead for non-Clifford gates. Preliminary results hint at high quality fidelities at larger distances.
  arXiv  Detail & Related papers  (2022-11-18T06:03:10Z)
• Fault-tolerant operation of a logical qubit in a diamond quantum processor [0.21670084965090575]
  We demonstrate fault-tolerant operations on a logical qubit using spin qubits in diamond. Our realization of fault-tolerant protocols on the logical-qubit level is a key step towards large-scale quantum information processing.
  arXiv  Detail & Related papers  (2021-08-03T17:39:25Z)
• Fault-tolerant parity readout on a shuttling-based trapped-ion quantum computer [64.47265213752996]
  We experimentally demonstrate a fault-tolerant weight-4 parity check measurement scheme. We achieve a flag-conditioned parity measurement single-shot fidelity of 93.2(2)%. The scheme is an essential building block in a broad class of stabilizer quantum error correction protocols.
  arXiv  Detail & Related papers  (2021-07-13T20:08:04Z)
• Entanglement purification by counting and locating errors with entangling measurements [62.997667081978825]
  We consider entanglement purification protocols for multiple copies of qubit states. We use high-dimensional auxiliary entangled systems to learn about number and positions of errors in the noisy ensemble.
  arXiv  Detail & Related papers  (2020-11-13T19:02:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.