Stabilizer Code-Generic Universal Fault-Tolerant Quantum Computation

• URL: http://arxiv.org/abs/2601.10964v1
• Date: Fri, 16 Jan 2026 03:06:56 GMT
• Title: Stabilizer Code-Generic Universal Fault-Tolerant Quantum Computation
• Authors: Nicholas J. C. Papadopoulos, Ramin Ayanzadeh,
• Abstract summary: This work implements logical Clifford and T gates through novel ancilla-mediated protocols.<n>Our implementation is deterministic, does not consume ancilla registers, does not modify the underlying data codes or registers, and is generic over all stabilizer codes.
• Score: 0.47267770920095536
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Fault-tolerant quantum computation allows quantum computations to be carried out while resisting unwanted noise. Several error correcting codes have been developed to achieve this task, but none alone are capable of universal quantum computation. This universality is highly desired and often achieved using additional techniques such as code concatenation, code switching, or magic state distillation, which can be costly and only work for specific codes. This work implements logical Clifford and T gates through novel ancilla-mediated protocols to construct a universal fault-tolerant quantum gate set. Unlike traditional techniques, our implementation is deterministic, does not consume ancilla registers, does not modify the underlying data codes or registers, and is generic over all stabilizer codes. Thus, any single code becomes capable of universal quantum computation by leveraging helper codes in ancilla registers and mid-circuit measurements. Furthermore, since these logical gates are stabilizer code-generic, these implementations enable communication between heterogeneous stabilizer codes. These features collectively open the door to countless possibilities for existing and undiscovered codes as well as their scalable, heterogeneous coexistence.

Related papers

• Single-Shot Universality in Quantum LDPC Codes via Code-Switching [7.411709177042115]
  We present a single-shot, universal protocol that uses code-switching between high-rate quantum codes to perform fault-tolerant quantum computation.<n>We achieve this feat with single-shot code-switching between constant-rate 2D hypergraph product (HGP) codes and high-rate 3D HGP codes.<n>We prove the fault-tolerance of our code-switching protocol under both the adversarial and localstochastic noise models.
  arXiv  Detail & Related papers  (2025-10-09T17:57:46Z)
• Universal fault-tolerant logic with heterogeneous holographic codes [38.98035278249248]
  We introduce a new class of holographic codes that realize the ability to support universal fault-tolerant quantum logic.<n>Unlike standard tunabled codes, we establish that the new codes can encode more than a single logical qubit per code block.<n>Our work strengthens the case for the utility of holographic quantum codes for practical quantum computing.
  arXiv  Detail & Related papers  (2025-04-14T16:28:33Z)
• Measurement-free, scalable and fault-tolerant universal quantum computing [1.2600261666440378]
  We present a complete toolbox for fault-tolerant universal quantum computing without the need for measurements during algorithm execution. We develop new fault-tolerant, measurement-free protocols to transfer encoded information between 2D and 3D color codes. Our measurement-free approach provides a practical and scalable pathway for universal quantum computing on state-of-the-art quantum processors.
  arXiv  Detail & Related papers  (2024-10-17T14:04:14Z)
• Experimental fault-tolerant code switching [1.9088985324817254]
  We present the first experimental implementation of fault-tolerant code switching between two codes. We construct logical circuits and prepare 12 different logical states which are not accessible in a fault-tolerant way within a single code. Our results experimentally open up a new route towards deterministic control over logical qubits with low auxiliary qubit overhead.
  arXiv  Detail & Related papers  (2024-03-20T16:40:57Z)
• Fault-Tolerant Computing with Single Qudit Encoding [49.89725935672549]
  We discuss stabilizer quantum-error correction codes implemented in a single multi-level qudit. These codes can be customized to the specific physical errors on the qudit, effectively suppressing them. We demonstrate a Fault-Tolerant implementation on molecular spin qudits, showcasing nearly exponential error suppression with only linear qudit size growth.
  arXiv  Detail & Related papers  (2023-07-20T10:51:23Z)
• Homological Quantum Rotor Codes: Logical Qubits from Torsion [47.52324012811181]
  homological quantum rotor codes allow one to encode both logical rotors and logical qudits in the same block of code.<n>We show that the $0$-$pi$-qubit as well as Kitaev's current-mirror qubit are indeed small examples of such codes.
  arXiv  Detail & Related papers  (2023-03-24T00:29:15Z)
• Quantum process tomography of continuous-variable gates using coherent states [49.299443295581064]
  We demonstrate the use of coherent-state quantum process tomography (csQPT) for a bosonic-mode superconducting circuit. We show results for this method by characterizing a logical quantum gate constructed using displacement and SNAP operations on an encoded qubit.
  arXiv  Detail & Related papers  (2023-03-02T18:08:08Z)
• 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 Coding for Entanglement-Assisted Communication [46.0607942851373]
  This paper studies the study of fault-tolerant channel coding for quantum channels. We use techniques from fault-tolerant quantum computing to establish coding theorems for sending classical and quantum information in this scenario. We extend these methods to the case of entanglement-assisted communication, in particular proving that the fault-tolerant capacity approaches the usual capacity when the gate error approaches zero.
  arXiv  Detail & Related papers  (2022-10-06T14:09:16Z)
• Fault-tolerant circuit synthesis for universal fault-tolerant quantum computing [0.0]
  We present a quantum circuit synthesis algorithm for implementing universal fault-tolerant quantum computing based on geometricd codes. We show how to synthesize the set of universal fault-tolerant protocols for $[[7,1,3]]$ Steane code and the syndrome measurement protocol of $[[23, 1, 7]]$ Golay code.
  arXiv  Detail & Related papers  (2022-06-06T15:43:36Z)
• Finding the disjointness of stabilizer codes is NP-complete [77.34726150561087]
  We show that the problem of calculating the $c-disjointness, or even approximating it to within a constant multiplicative factor, is NP-complete. We provide bounds on the disjointness for various code families, including the CSS codes,$d codes and hypergraph codes. Our results indicate that finding fault-tolerant logical gates for generic quantum error-correcting codes is a computationally challenging task.
  arXiv  Detail & Related papers  (2021-08-10T15:00:20Z)
• Fault-tolerant Coding for Quantum Communication [71.206200318454]
  encode and decode circuits to reliably send messages over many uses of a noisy channel. For every quantum channel $T$ and every $eps>0$ there exists a threshold $p(epsilon,T)$ for the gate error probability below which rates larger than $C-epsilon$ are fault-tolerantly achievable. Our results are relevant in communication over large distances, and also on-chip, where distant parts of a quantum computer might need to communicate under higher levels of noise.
  arXiv  Detail & Related papers  (2020-09-15T15:10:50Z)

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.