Scaling and logic in the color code on a superconducting quantum processor

• URL: http://arxiv.org/abs/2412.14256v1
• Date: Wed, 18 Dec 2024 19:00:05 GMT
• Title: Scaling and logic in the color code on a superconducting quantum processor
• Abstract summary: We present a demonstration of the color code on a superconducting processor, achieving logical error suppression and performing logical operations.<n>We inject magic states, a key resource for universal computation, achieving fidelities exceeding 99% with post-selection.<n>This work establishes the color code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors.
• Score: 109.61104855764401
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum error correction is essential for bridging the gap between the error rates of physical devices and the extremely low logical error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting processors have focused primarily on the surface code, which offers a high error threshold but poses limitations for logical operations. In contrast, the color code enables much more efficient logic, although it requires more complex stabilizer measurements and decoding techniques. Measuring these stabilizers in planar architectures such as superconducting qubits is challenging, and so far, realizations of color codes have not addressed performance scaling with code size on any platform. Here, we present a comprehensive demonstration of the color code on a superconducting processor, achieving logical error suppression and performing logical operations. Scaling the code distance from three to five suppresses logical errors by a factor of $\Lambda_{3/5}$ = 1.56(4). Simulations indicate this performance is below the threshold of the color code, and furthermore that the color code may be more efficient than the surface code with modest device improvements. Using logical randomized benchmarking, we find that transversal Clifford gates add an error of only 0.0027(3), which is substantially less than the error of an idling error correction cycle. We inject magic states, a key resource for universal computation, achieving fidelities exceeding 99% with post-selection (retaining about 75% of the data). Finally, we successfully teleport logical states between distance-three color codes using lattice surgery, with teleported state fidelities between 86.5(1)% and 90.7(1)%. This work establishes the color code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors in the near future.

Related papers

• Surface code logical operations on a superconducting quantum processor [66.1042398805403]
  We experimentally realize key elements of patch-based surface-code logical processing on a 107-qubit superconducting quantum processor.<n>Our results advance superconducting surface-code experiments from protected logical memory to active, patch-based fault-tolerant logical operations.
  arXiv  Detail & Related papers  (2026-07-01T21:07:02Z)
• Experimental Demonstration of Logical Magic State Distillation [62.77974948443222]
  We present the experimental realization of magic state distillation with logical qubits on a neutral-atom quantum computer.<n>Our approach makes use of a dynamically reconfigurable architecture to encode and perform quantum operations on many logical qubits in parallel.
  arXiv  Detail & Related papers  (2024-12-19T18:38:46Z)
• Demonstrating dynamic surface codes [138.1740645504286]
  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)
• Quantum error correction below the surface code threshold [107.92016014248976]
  Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit. We present two surface code memories operating below a critical threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms.
  arXiv  Detail & Related papers  (2024-08-24T23:08:50Z)
• Improving threshold for fault-tolerant color code quantum computing by flagged weight optimization [0.9002260638342727]
  thresholds of color codes under circuit-level noise are relatively low because of their high-weight stabilizer generators. We propose a method to suppress the impact of such errors using conditional error probabilities conditioned on the measurement outcomes of flag qubits. This method can also be applied to other weight-based decoders, making the color codes more promising for the candidate of experimental implementation of QEC.
  arXiv  Detail & Related papers  (2024-02-21T17:40:51Z)
• Fault-Tolerant One-Bit Addition with the Smallest Interesting Colour Code [2.5553228515450765]
  We implement a small quantum algorithm, one-qubit addition, fault-tolerantly on the Quantinuum H1-1 quantum computer. We observe arithmetic errors with a rate of $sim 1.1 times 10-3$ for the fault-tolerant circuit and $sim 9.5 times 10-3$ for the unencoded circuit.
  arXiv  Detail & Related papers  (2023-09-18T15:56:14Z)
• 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)
• 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)
• Suppressing quantum errors by scaling a surface code logical qubit [147.2624260358795]
  We report the measurement of logical qubit performance scaling across multiple code sizes. Our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. Results mark the first experimental demonstration where quantum error correction begins to improve performance with increasing qubit number.
  arXiv  Detail & Related papers  (2022-07-13T18:00:02Z)
• Benchmarking quantum error-correcting codes on quasi-linear and central-spin processors [0.0]
  We evaluate the performance of small error-correcting codes on a superconducting processor based on transmon qubits and a spintronic quantum register consisting of a nitrogen-vacancy center in diamond. For codes involving multi-qubit controlled operations, the central-spin connectivity of the color centers enables lower error rates.
  arXiv  Detail & Related papers  (2022-07-12T14:41:08Z)
• The cost of universality: A comparative study of the overhead of state distillation and code switching with color codes [63.62764375279861]
  We compare two leading FT implementations of the T gate in 2D color codes under circuit noise. We find a circuit noise threshold of 0.07(1)% for the T gate via code switching, almost an order of magnitude below that achievable by state distillation in the same setting.
  arXiv  Detail & Related papers  (2021-01-06T19:00:01Z)

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.