Emergent coding phases and hardware-tailored quantum codes

• URL: http://arxiv.org/abs/2503.15483v1
• Date: Wed, 19 Mar 2025 17:57:12 GMT
• Title: Emergent coding phases and hardware-tailored quantum codes
• Authors: Gaurav Gyawali, Henry Shackleton, Zhu-Xi Luo, Michael Lawler,
• Abstract summary: Finding good quantum codes for a particular hardware application is central to quantum error correction.<n>For the $Z$ code, we provide two practical error correction procedures that fall short of the optimal codes and qualitatively alter the phase diagram.<n> carrying out our approach on current noisy devices could provide a systematic way to construct quantum codes for robust computation and communication.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Finding good quantum codes for a particular hardware application and determining their error thresholds is central to quantum error correction. The threshold defines the noise level where a quantum code switches between a coding and a no-coding \emph{phase}. Provided sufficiently frequent error correction, the quantum capacity theorem guarantees the existence of an optimal code that provides a maximum communication rate. By viewing a system experiencing repeated error correction as a novel form of matter, this optimal code, in analogy to Jaynes's maximum entropy principle of quantum statistical mechanics, \emph{defines a phase}. We explore coding phases from this perspective using the Open Random Unitary Model (ORUM), which is a quantum circuit with depolarizing and dephasing channels. Using numerical optimization, we find this model hosts three phases: a maximally mixed phase, a ``$Z_2$ code'' that breaks its U(1) gauge symmetry down to $Z_2$, and a no-coding phase with first-order transitions between them and a novel \emph{zero capacity multi-critical point} where all three phases meet. For the $Z_2$ code, we provide two practical error correction procedures that fall short of the optimal codes and qualitatively alter the phase diagram, splitting the multi-critical point into two second-order coding no-coding phase transitions. Carrying out our approach on current noisy devices could provide a systematic way to construct quantum codes for robust computation and communication.

Related papers

• Efficient and Universal Neural-Network Decoder for Stabilizer-Based Quantum Error Correction [44.698141103370546]
  We introduce a universal decoder based on linear attention sequence modeling and graph neural network. Our experiments demonstrate that this decoder outperforms specialized algorithms in both accuracy and speed.
  arXiv  Detail & Related papers  (2025-02-27T10:56:53Z)
• Approximate quantum error correcting codes from conformal field theory [0.0]
  We consider generic 1+1D CFT codes under extensive local dephasing channels. We show that a CFT code with continuous symmetry saturates a bound on the recovery fidelity for covariant codes.
  arXiv  Detail & Related papers  (2024-06-13T19:40:36Z)
• Near-optimal decoding algorithm for color codes using Population Annealing [44.99833362998488]
  We implement a decoder that finds the recovery operation with the highest success probability. We study the decoder performance on a 4.8.8 color code lattice under different noise models.
  arXiv  Detail & Related papers  (2024-05-06T18:17:42Z)
• Near-Term Distributed Quantum Computation using Mean-Field Corrections and Auxiliary Qubits [77.04894470683776]
  We propose near-term distributed quantum computing that involve limited information transfer and conservative entanglement production. We build upon these concepts to produce an approximate circuit-cutting technique for the fragmented pre-training of variational quantum algorithms.
  arXiv  Detail & Related papers  (2023-09-11T18:00:00Z)
• Single-shot decoding of good quantum LDPC codes [38.12919328528587]
  We prove that quantum Tanner codes facilitate single-shot quantum error correction (QEC) of adversarial noise. We show that in order to suppress errors over multiple repeated rounds of QEC, it suffices to run the parallel decoding algorithm for constant time in each round.
  arXiv  Detail & Related papers  (2023-06-21T18:00:01Z)
• Hardware efficient autonomous error correction with linear couplers in superconducting circuits [0.5428370406156905]
  Large-scale quantum computers will inevitably need quantum error correction (QEC) to protect information against decoherence. AQEC schemes work by transforming error states into excitations that can be efficiently removed through engineered dissipation. The recently proposed AQEC scheme by Li et al., called the Star code, can autonomously correct or suppress all single qubit error channels using two transmons as encoders with a tunable coupler and two lossy resonators as a cooling source.
  arXiv  Detail & Related papers  (2023-03-02T09:44:55Z)
• Achieving metrological limits using ancilla-free quantum error-correcting codes [1.9265037496741413]
  Existing quantum error-correcting codes generally exploit entanglement between one probe and one noiseless ancilla of the same dimension. Here we construct two types of multi-probe quantum error-correcting codes, where the first one utilizes a negligible amount of ancillas and the second one is ancilla-free.
  arXiv  Detail & Related papers  (2023-03-02T00:51:02Z)
• Deep Quantum Error Correction [73.54643419792453]
  Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. In this work, we efficiently train novel emphend-to-end deep quantum error decoders. The proposed method demonstrates the power of neural decoders for QECC by achieving state-of-the-art accuracy.
  arXiv  Detail & Related papers  (2023-01-27T08:16:26Z)
• Hardware optimized parity check gates for superconducting surface codes [0.0]
  Error correcting codes use multi-qubit measurements to realize fault-tolerant quantum logic steps. We analyze an unconventional surface code based on multi-body interactions between superconducting transmon qubits. Despite the multi-body effects that underpin this approach, our estimates of logical faults suggest that this design can be at least as robust to realistic noise as conventional designs.
  arXiv  Detail & Related papers  (2022-11-11T18:00:30Z)
• Quantum Error Correction via Noise Guessing Decoding [0.0]
  Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. This paper shows that it is possible to both construct and decode QECCs that can attain the maximum performance of the finite blocklength regime.
  arXiv  Detail & Related papers  (2022-08-04T16:18:20Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• 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.