Exploring the quantum capacity of a Gaussian random displacement channel using Gottesman-Kitaev-Preskill codes and maximum likelihood decoding

• URL: http://arxiv.org/abs/2411.04277v1
• Date: Wed, 06 Nov 2024 21:47:20 GMT
• Title: Exploring the quantum capacity of a Gaussian random displacement channel using Gottesman-Kitaev-Preskill codes and maximum likelihood decoding
• Authors: Mao Lin, Kyungjoo Noh,
• Abstract summary: We analyze the error-correction performance of several families of multi-mode Gottesman-Kitaev-Preskill codes. We find that the error threshold of the surface-square GKP code is remarkably close to $sigma=1/sqrtesimeq 0.6065$. By focusing on multi-mode GKP codes that encode just one logical qubit over multiple bosonic modes, we show that GKP codes can achieve non-zero quantum state transmission rates.
• Score: 0.9208007322096532
• License:
• Abstract: Determining the quantum capacity of a noisy quantum channel is an important problem in the field of quantum communication theory. In this work, we consider the Gaussian random displacement channel $N_{\sigma}$, a type of bosonic Gaussian channels relevant in various bosonic quantum information processing systems. In particular, we attempt to make progress on the problem of determining the quantum capacity of a Gaussian random displacement channel by analyzing the error-correction performance of several families of multi-mode Gottesman-Kitaev-Preskill (GKP) codes. In doing so we analyze the surface-square GKP codes using an efficient and exact maximum likelihood decoder (MLD) up to a large code distance of $d=39$. We find that the error threshold of the surface-square GKP code is remarkably close to $\sigma=1/\sqrt{e}\simeq 0.6065$ at which the best-known lower bound of the quantum capacity of $N_{\sigma}$ vanishes. We also analyze the performance of color-hexagonal GKP codes up to a code distance of $d=13$ using a tensor-network decoder serving as an approximate MLD. By focusing on multi-mode GKP codes that encode just one logical qubit over multiple bosonic modes, we show that GKP codes can achieve non-zero quantum state transmission rates for a Gaussian random displacement channel $N_{\sigma}$ at larger values of $\sigma$ than previously demonstrated. Thus our work reduces the gap between the quantum communication theoretic bounds and the performance of explicit bosonic quantum error-correcting codes in regards to the quantum capacity of a Gaussian random displacement channel.

Related papers

• The multimode conditional quantum Entropy Power Inequality and the squashed entanglement of the extreme multimode bosonic Gaussian channels [53.253900735220796]
  Inequality determines the minimum conditional von Neumann entropy of the output of the most general linear mixing of bosonic quantum modes. Bosonic quantum systems constitute the mathematical model for the electromagnetic radiation in the quantum regime.
  arXiv  Detail & Related papers  (2024-10-18T13:59:50Z)
• 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)
• Error-corrected quantum repeaters with GKP qudits [1.1279808969568252]
  The Gottesman-Kitaev-Preskill (GKP) code offers the possibility to encode higher-dimensional qudits into individual bosonic modes. The GKP code has found recent applications in theoretical investigations of quantum communication protocols.
  arXiv  Detail & Related papers  (2023-03-28T15:04:06Z)
• Closest lattice point decoding for multimode Gottesman-Kitaev-Preskill codes [0.8192907805418581]
  Quantum error correction (QEC) plays an essential role in fault-tolerantly realizing quantum algorithms of practical interest. We study multimode Gottesman-Kitaev-Preskill (GKP) codes, encoding a qubit in many oscillators. We implement a closest point decoding strategy for correcting random shift errors.
  arXiv  Detail & Related papers  (2023-03-08T16:42:42Z)
• 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)
• 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)
• Gaussian conversion protocol for heralded generation of qunaught states [66.81715281131143]
  bosonic codes map qubit-type quantum information onto the larger bosonic Hilbert space. We convert between two instances of these codes GKP qunaught states and four-foldsymmetric binomial states corresponding to a zero-logical encoded qubit. We obtain GKP qunaught states with a fidelity of over 98% and a probability of approximately 3.14%.
  arXiv  Detail & Related papers  (2023-01-24T14:17:07Z)
• Biased Gottesman-Kitaev-Preskill repetition code [0.0]
  Continuous-variable quantum computing architectures based upon the Gottesmann-Kitaev-Preskill (GKP) encoding have emerged as a promising candidate. We study the code-capacity behaviour of a rectangular-lattice GKP encoding with a repetition code under an isotropic Gaussian displacement channel.
  arXiv  Detail & Related papers  (2022-12-21T22:56:05Z)
• Low overhead fault-tolerant quantum error correction with the surface-GKP code [60.44022726730614]
  We propose a highly effective use of the surface-GKP code, i.e., the surface code consisting of bosonic GKP qubits instead of bare two-dimensional qubits. We show that a low logical failure rate $p_L 10-7$ can be achieved with moderate hardware requirements.
  arXiv  Detail & Related papers  (2021-03-11T23:07:52Z)
• 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)
• Describing quantum metrology with erasure errors using weight distributions of classical codes [9.391375268580806]
  We consider using quantum probe states with a structure that corresponds to classical $[n,k,d]$ binary block codes of minimum distance. We obtain bounds on the ultimate precision that these probe states can give for estimating the unknown magnitude of a classical field.
  arXiv  Detail & Related papers  (2020-07-06T16:22:40Z)

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.