Efficient Magic State Cultivation on the Surface Code

• URL: http://arxiv.org/abs/2502.01743v3
• Date: Mon, 06 Oct 2025 21:28:34 GMT
• Title: Efficient Magic State Cultivation on the Surface Code
• Authors: Yotam Vaknin, Shoham Jacoby, Arne Grimsmo, Alex Retzker,
• Abstract summary: We introduce three new cultivation protocols, each yielding a different magic state.<n>We demonstrate that our protocol achieves state-of-the-art infidelities and acceptance rates for magic state generation.<n>In platforms such as cold atoms and trapped ions, where idle error rates are lower than two-qubit gate errors, we demonstrate that cultivation exhibits an even greater advantage.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Magic state cultivation is a newly proposed protocol that represents the state of the art in magic state generation. It uses the transversality of the $H_{XY}$ gate on the 2D triangular color-code, together with a novel grafting mechanism to transform the color-code into a matchable code with minimal overhead. Still, the resulting code has a longer cycle time and some high weight stabilizers. Here, we introduce three new cultivation protocols, each yielding a different magic state. These protocols avoid grafting by exploiting transversal operations on the surface code using non-local connectivity, allowing for a much lower post-selection rates in the expansion process. Through numerical simulations, we demonstrate that our protocol achieves state-of-the-art infidelities and acceptance rates for magic state generation, on par with another recent proposal on the $\mathbb{RP}^2$ code, while still preserving the local geometry of the surface code. Moreover, in platforms such as cold atoms and trapped ions, where idle error rates are lower than two-qubit gate errors, we demonstrate that cultivation exhibits an even greater advantage, yielding an additional order-of-magnitude reduction in resource requirements. Lastly, we analyze the effect of erasure qubits on cultivation and show that \emph{algorithmically-relevant} infidelities can be achieved using only 9 erasure qubits on a distance-2 surface code with a single cultivation round.

Related papers

• Dual-Branch Center-Surrounding Contrast: Rethinking Contrastive Learning for 3D Point Clouds [55.5576033344795]
  We propose a novel DualBranch textbfCentertextbfSurrounding textbfContrast (CSCon) framework for 3D point clouds.<n>Under the FULL and ALL protocols, CSCon achieves performance comparable to generative methods.<n>Our method attains state-of-the-art results, even surpassing cross-modal approaches.
  arXiv  Detail & Related papers  (2025-12-09T14:56:35Z)
• Efficient magic state cultivation with lattice surgery [2.6945797019995363]
  Magic state distillation plays a crucial role in fault-tolerant quantum computation.<n>Traditional logical-level distillation offers significant overhead reduction by enabling direct implementation with physical gates.<n>Magic state cultivation is a state-of-the-art physical-level distillation protocol that is compatible with the square-grid connectivity.
  arXiv  Detail & Related papers  (2025-10-28T16:44:34Z)
• Fold-transversal surface code cultivation [0.5488290895559226]
  Magic state cultivation is a protocol to prepare ultra-high fidelity non-Clifford resource states for universal quantum computation.<n>We present a new cultivation scheme in which we measure the fold-transversal Hadamard of unrotated surface code.<n>We find that this approach achieves the lowest known spacetime overhead for magic state cultivation.
  arXiv  Detail & Related papers  (2025-09-05T16:14:46Z)
• Efficient Magic State Cultivation on $\mathbb{RP}^2$ [4.828791769306579]
  We propose a new magic state cultivation protocol that produces a logical $mathrmT$ state on a rotated surface code. Small $mathbbRP2$ codes are used to hold logical information and checked by syndrome extraction circuits. Our protocol requires about an order of magnitude smaller space-time volume to reach a target logical error rate around $10-9$ compared to the original MSC protocol.
  arXiv  Detail & Related papers  (2025-03-24T13:20:57Z)
• Demonstrating dynamic surface codes [118.67046728951689]
  We experimentally demonstrate three time-dynamic implementations of the surface code.<n>First, we embed the surface code on a hexagonal lattice, reducing the necessary couplings per qubit from four to three.<n>Second, we walk a surface code, swapping the role of data and measure qubits each round, achieving error correction with built-in removal of accumulated non-computational errors.<n>Third, we realize the surface code using iSWAP gates instead of the traditional CNOT, extending the set of viable gates for error correction without additional overhead.
  arXiv  Detail & Related papers  (2024-12-18T21:56:50Z)
• Code switching revisited: Low-overhead magic state preparation using color codes [0.0]
  We propose a protocol to prepare a high-fidelity magic state on a two-dimensional (2D) color code using a three-dimensional (3D) color code. We numerically demonstrate that these modifications lead to a significant improvement in the fidelity of the magic state.
  arXiv  Detail & Related papers  (2024-10-09T18:00:02Z)
• Flag Proxy Networks: Tackling the Architectural, Scheduling, and Decoding Obstacles of Quantum LDPC codes [1.870400753080051]
  In this paper, we consider two under-studied families of QLDPC codes: hyperbolic surface codes and hyperbolic color codes. degree-4 FPNs of the hyperbolic surface and color codes are respectively $2.9times$ and $5.5times$ more space-efficient than the $d = 5$ planar surface code. The hyperbolic codes also have error rates comparable to their planar counterparts.
  arXiv  Detail & Related papers  (2024-09-22T01:08:58Z)
• SCALAR-NeRF: SCAlable LARge-scale Neural Radiance Fields for Scene Reconstruction [66.69049158826677]
  We introduce SCALAR-NeRF, a novel framework tailored for scalable large-scale neural scene reconstruction. We structure the neural representation as an encoder-decoder architecture, where the encoder processes 3D point coordinates to produce encoded features. We propose an effective and efficient methodology to fuse the outputs from these local models to attain the final reconstruction.
  arXiv  Detail & Related papers  (2023-11-28T10:18:16Z)
• Improved Pairwise Measurement-Based Surface Code [0.0]
  We devise a new realization of the surface code on a rectangular lattice of qubits utilizing single-qubit and nearest-neighbor two-qubit Pauli measurements. This realization gains substantial advantages over prior pairwise measurement-based realizations of the surface code.
  arXiv  Detail & Related papers  (2023-10-19T17:59:55Z)
• Facilitating Practical Fault-tolerant Quantum Computing Based on Color Codes [0.6963971634605797]
  In this work, we address several key issues to facilitate practical fault-tolerant quantum computing based on color codes. First, by introducing decoding graphs with error-rate-related weights, we obtained the threshold of $0.57%$ of the triangular color code. Second, our work firstly investigates the circuit-level decoding of color code lattice surgery, and gives an efficient decoding algorithm. Third, a new state injection protocol of the triangular color code is proposed, reducing the output magic state error rate in one round of 15 to 1 distillation by two orders of magnitude compared to a previous rough protocol.
  arXiv  Detail & Related papers  (2023-09-11T03:56:18Z)
• Graphical CSS Code Transformation Using ZX Calculus [0.6734802552703861]
  We present a generic approach to transform CSS codes by building upon their equivalence to phase-free ZX diagrams. We show how ZX and graphical encoder maps relate several equivalent perspectives on these code-transforming operations.
  arXiv  Detail & Related papers  (2023-07-05T17:04:49Z)
• Towards Accurate Image Coding: Improved Autoregressive Image Generation with Dynamic Vector Quantization [73.52943587514386]
  Existing vector quantization (VQ) based autoregressive models follow a two-stage generation paradigm. We propose a novel two-stage framework: (1) Dynamic-Quantization VAE (DQ-VAE) which encodes image regions into variable-length codes based their information densities for accurate representation.
  arXiv  Detail & Related papers  (2023-05-19T14:56:05Z)
• CSS code surgery as a universal construction [51.63482609748332]
  We define code maps between Calderbank-Shor-Steane (CSS) codes using maps between chain complexes. We describe code surgery between such codes using a specific colimit in the category of chain complexes.
  arXiv  Detail & Related papers  (2023-01-31T16:17:25Z)
• The X-Cube Floquet Code [2.191505742658975]
  We introduce the X-Cube Floquet code, a dynamical quantum error-correcting code where the number of encoded logical qubits grows with system size. Within a single Floquet cycle, the codespace between that of the X-Cube switches fracton order and layers of entangled, two-dimensional toric codes. The encoded logical qubits' dynamics are analyzed, and we argue that the new code has a non-zero error threshold.
  arXiv  Detail & Related papers  (2022-11-10T18:59:55Z)
• Improved decoding of circuit noise and fragile boundaries of tailored surface codes [61.411482146110984]
  We introduce decoders that are both fast and accurate, and can be used with a wide class of quantum error correction codes. Our decoders, named belief-matching and belief-find, exploit all noise information and thereby unlock higher accuracy demonstrations of QEC. We find that the decoders led to a much higher threshold and lower qubit overhead in the tailored surface code with respect to the standard, square surface code.
  arXiv  Detail & Related papers  (2022-03-09T18:48:54Z)
• Morphing quantum codes [77.34726150561087]
  We morph the 15-qubit Reed-Muller code to obtain the smallest known stabilizer code with a fault-tolerant logical $T$ gate. We construct a family of hybrid color-toric codes by morphing the color code.
  arXiv  Detail & Related papers  (2021-12-02T17:43:00Z)
• Subpixel Heatmap Regression for Facial Landmark Localization [65.41270740933656]
  Heatmap regression approaches suffer from discretization-induced errors related to both the heatmap encoding and decoding process. We propose a new approach for the heatmap encoding and decoding process by leveraging the underlying continuous distribution. Our approach offers noticeable gains across multiple datasets setting a new state-of-the-art result in facial landmark localization.
  arXiv  Detail & Related papers  (2021-11-03T17:21:28Z)
• Spatial-Separated Curve Rendering Network for Efficient and High-Resolution Image Harmonization [59.19214040221055]
  We propose a novel spatial-separated curve rendering network (S$2$CRNet) for efficient and high-resolution image harmonization. The proposed method reduces more than 90% parameters compared with previous methods. Our method can work smoothly on higher resolution images in real-time which is more than 10$times$ faster than the existing methods.
  arXiv  Detail & Related papers  (2021-09-13T07:20:16Z)
• Numerical Implementation of Just-In-Time Decoding in Novel Lattice Slices Through the Three-Dimensional Surface Code [0.0]
  We develop and simulate an explicit recipe for a just-in-time decoding scheme in three 3D surface codes. We find evidence for a threshold $p_c sim 0.1%$ in all three codes.
  arXiv  Detail & Related papers  (2020-12-15T19:00:04Z)
• 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)
• Geo-PIFu: Geometry and Pixel Aligned Implicit Functions for Single-view Human Reconstruction [97.3274868990133]
  Geo-PIFu is a method to recover a 3D mesh from a monocular color image of a clothed person. We show that, by both encoding query points and constraining global shape using latent voxel features, the reconstruction we obtain for clothed human meshes exhibits less shape distortion and improved surface details compared to competing methods.
  arXiv  Detail & Related papers  (2020-06-15T01:11:48Z)
• L$^2$-GCN: Layer-Wise and Learned Efficient Training of Graph Convolutional Networks [118.37805042816784]
  Graph convolution networks (GCN) are increasingly popular in many applications, yet remain notoriously hard to train over large graph datasets. We propose a novel efficient layer-wise training framework for GCN (L-GCN), that disentangles feature aggregation and feature transformation during training. Experiments show that L-GCN is faster than state-of-the-arts by at least an order of magnitude, with a consistent of memory usage not dependent on dataset size.
  arXiv  Detail & Related papers  (2020-03-30T16:37:56Z)
• Sparse Graphical Memory for Robust Planning [93.39298821537197]
  We introduce Sparse Graphical Memory (SGM), a new data structure that stores states and feasible transitions in a sparse memory. SGM aggregates states according to a novel two-way consistency objective, adapting classic state aggregation criteria to goal-conditioned RL. We show that SGM significantly outperforms current state of the art methods on long horizon, sparse-reward visual navigation tasks.
  arXiv  Detail & Related papers  (2020-03-13T17:59:32Z)
• Image Fine-grained Inpainting [89.17316318927621]
  We present a one-stage model that utilizes dense combinations of dilated convolutions to obtain larger and more effective receptive fields. To better train this efficient generator, except for frequently-used VGG feature matching loss, we design a novel self-guided regression loss. We also employ a discriminator with local and global branches to ensure local-global contents consistency.
  arXiv  Detail & Related papers  (2020-02-07T03:45:25Z)

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.