High-threshold and low-overhead fault-tolerant quantum memory

• URL: http://arxiv.org/abs/2308.07915v2
• Date: Wed, 21 Feb 2024 00:30:47 GMT
• Title: High-threshold and low-overhead fault-tolerant quantum memory
• Authors: Sergey Bravyi, Andrew W. Cross, Jay M. Gambetta, Dmitri Maslov, Patrick Rall, and Theodore J. Yoder
• Abstract summary: We present an end-to-end quantum error correction protocol based on a family of LDPC codes with a high encoding rate. We show that 12 logical qubits can be preserved for nearly one million syndrome cycles using 288 physical qubits.
• Score: 4.91491092996493
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an end-to-end quantum error correction protocol that implements fault-tolerant memory based on a family of LDPC codes with a high encoding rate that achieves an error threshold of $0.8\%$ for the standard circuit-based noise model. This is on par with the surface code which has remained an uncontested leader in terms of its high error threshold for nearly 20 years. The full syndrome measurement cycle for a length-$n$ code in our family requires $n$ ancillary qubits and a depth-7 circuit composed of nearest-neighbor CNOT gates. The required qubit connectivity is a degree-6 graph that consists of two edge-disjoint planar subgraphs. As a concrete example, we show that 12 logical qubits can be preserved for nearly one million syndrome cycles using 288 physical qubits in total, assuming the physical error rate of $0.1\%$. We argue that achieving the same level of error suppression on 12 logical qubits with the surface code would require nearly 3000 physical qubits. Our findings bring demonstrations of a low-overhead fault-tolerant quantum memory within the reach of near-term quantum processors.

Related papers

• 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)
• Entangling four logical qubits beyond break-even in a nonlocal code [0.0]
  Quantum error correction protects logical quantum information against environmental decoherence. We encode the GHZ state in four logical qubits with fidelity $ 99.5 pm 0.15 % le F le 99.7 pm 0.1% $ (after postselecting on over 98% of outcomes) Our results are a first step towards realizing fault-tolerant quantum computation with logical qubits encoded in geometrically nonlocal quantum low-density parity check codes.
  arXiv  Detail & Related papers  (2024-06-04T18:00:00Z)
• Fault-tolerant hyperbolic Floquet quantum error correcting codes [0.0]
  We introduce a family of dynamically generated quantum error correcting codes that we call "hyperbolic Floquet codes" One of our hyperbolic Floquet codes uses 400 physical qubits to encode 52 logical qubits with a code distance of 8, i.e., it is a $[[400,52,8]]$ code. At small error rates, comparable logical error suppression to this code requires 5x as many physical qubits (1924) when using the honeycomb Floquet code with the same noise model and decoder.
  arXiv  Detail & Related papers  (2023-09-18T18:00:02Z)
• Quantum computation on a 19-qubit wide 2d nearest neighbour qubit array [59.24209911146749]
  This paper explores the relationship between the width of a qubit lattice constrained in one dimension and physical thresholds. We engineer an error bias at the lowest level of encoding using the surface code. We then address this bias at a higher level of encoding using a lattice-surgery surface code bus.
  arXiv  Detail & Related papers  (2022-12-03T06:16:07Z)
• Protecting Expressive Circuits with a Quantum Error Detection Code [0.0]
  We develop a quantum error detection code for implementations on existing trapped-ion computers. By encoding $k$ logical qubits into $k+2$ physical qubits, this code presents fault-tolerant state initialisation and syndrome measurement circuits.
  arXiv  Detail & Related papers  (2022-11-12T16:46:35Z)
• Overcoming leakage in scalable quantum error correction [128.39402546769284]
  Leakage of quantum information out of computational states into higher energy states represents a major challenge in the pursuit of quantum error correction (QEC) Here, we demonstrate the execution of a distance-3 surface code and distance-21 bit-flip code on a Sycamore quantum processor where leakage is removed from all qubits in each cycle. We report a ten-fold reduction in steady-state leakage population on the data qubits encoding the logical state and an average leakage population of less than $1 times 10-3$ throughout the entire device.
  arXiv  Detail & Related papers  (2022-11-09T07:54:35Z)
• 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)
• Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays [3.575043595126111]
  We propose a qubit encoding and gate protocol for $171$Yb neutral atom qubits that converts the dominant physical errors into erasures. We estimate that 98% of errors can be converted into erasures.
  arXiv  Detail & Related papers  (2022-01-10T18:56:31Z)
• Exponential suppression of bit or phase flip errors with repetitive error correction [56.362599585843085]
  State-of-the-art quantum platforms typically have physical error rates near $10-3$. Quantum error correction (QEC) promises to bridge this divide by distributing quantum logical information across many physical qubits. We implement 1D repetition codes embedded in a 2D grid of superconducting qubits which demonstrate exponential suppression of bit or phase-flip errors.
  arXiv  Detail & Related papers  (2021-02-11T17:11:20Z)
• 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.