Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits

• URL: http://arxiv.org/abs/2003.03049v1
• Date: Fri, 6 Mar 2020 06:24:02 GMT
• Title: Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits
• Authors: Christopher Chamberland and Kyungjoo Noh
• Abstract summary: We introduce a new concept which we call redundant ancilla encoding. We show that our scheme can produce magic states using an order of magnitude fewer qubits and space-time overhead.
• Score: 1.2891210250935146
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The overhead cost of performing universal fault-tolerant quantum computation for large scale quantum algorithms is very high. Despite several attempts at alternative schemes, magic state distillation remains one of the most efficient schemes for simulating non-Clifford gates in a fault-tolerant way. However, since magic state distillation circuits are not fault-tolerant, all Clifford operations must be encoded in a large distance code in order to have comparable failure rates with the magic states being distilled. In this work, we introduce a new concept which we call redundant ancilla encoding. The latter combined with flag qubits allows for circuits to both measure stabilizer generators of some code, while also being able to measure global operators to fault-tolerantly prepare magic states, all using nearest neighbor interactions. In particular, we apply such schemes to a planar architecture of the triangular color code family. In addition to our scheme being suitable for experimental implementations, we show that for physical error rates near $10^{-4}$ and under a full circuit-level noise model, our scheme can produce magic states using an order of magnitude fewer qubits and space-time overhead compared to the most competitive magic state distillation schemes. Further, we can take advantage of the fault-tolerance of our circuits to produce magic states with very low logical failure rates using encoded Clifford gates with noise rates comparable to the magic states being injected. Thus, stabilizer operations are not required to be encoded in a very large distance code. Consequently, we believe our scheme to be suitable for implementing fault-tolerant universal quantum computation with hardware currently under development.

Related papers

• 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. We introduce a measurement-free deformation protocol of the Bacon-Shor code to realize a logical $mathitCCZ$ gate. 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)
• 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. 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)
• Scaling and logic in the color code on a superconducting quantum processor [109.61104855764401]
  We present a demonstration of the color code on a superconducting processor, achieving logical error suppression and performing logical operations. We inject magic states, a key resource for universal computation, achieving fidelities exceeding 99% with post-selection. This work establishes the color code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors.
  arXiv  Detail & Related papers  (2024-12-18T19:00:05Z)
• Magic State Injection on IBM Quantum Processors Above the Distillation Threshold [1.7359033750147501]
  This work employs a qubit-efficient rotated heavy-hexagonal surface code for IBM quantum processors. We report error thresholds for both logical bit- and phase-flip errors, of $approx0.37%$ and $approx0.31%$, respectively. Our work demonstrates the potential for realising non-Clifford logical gates by producing high-fidelity logical magic states on IBM quantum devices.
  arXiv  Detail & Related papers  (2024-12-02T12:35:52Z)
• Demonstrating real-time and low-latency quantum error correction with superconducting qubits [52.08698178354922]
  We demonstrate low-latency feedback with a scalable FPGA decoder integrated into a superconducting quantum processor. We observe logical error suppression as the number of decoding rounds is increased. The decoder throughput and latency developed in this work, combined with continued device improvements, unlock the next generation of experiments.
  arXiv  Detail & Related papers  (2024-10-07T17:07:18Z)
• Even more efficient magic state distillation by zero-level distillation [0.8009842832476994]
  We propose zero-level distillation, which prepares a high fidelity logical magic state using physical qubits on a square lattice. The key idea behind is using the Steane code to distill a logical magic state by using noisy Clifford gates with error detection.
  arXiv  Detail & Related papers  (2024-03-06T19:01:28Z)
• Encoding a magic state with beyond break-even fidelity [1.449788466039287]
  We propose and implement a scheme to prepare a magic state on a superconducting qubit array using error correction. We find that our scheme produces better magic states than those we can prepare using the individual qubits of the device. Our prototype will be invaluable in the future as it can reduce the number of physical qubits needed to produce high-fidelity magic states.
  arXiv  Detail & Related papers  (2023-05-23T01:19:53Z)
• 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)
• 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)
• Error mitigation for universal gates on encoded qubits [5.774786149181392]
  We show how to implement Clifford+T circuits with a number of T-gates inversely proportional to the physical noise rate. We argue that such circuits can be out of reach for state-of-the-art classical simulation algorithms.
  arXiv  Detail & Related papers  (2021-03-08T17:27:04Z)

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.