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Experimental demonstration of a graph state quantum error-correction code

B. A. Bell, D. A. Herrera-Martí, M. S. Tame, D. Markham, W. J. Wadsworth, J. G. Rarity

arXiv:1404.5498v1quant-ph

TL;DR

A four-qubit graph-state code had previously been realized only in the circuit model, leaving its implementation within measurement-based quantum computation unshown. This work uses an all-optical setup to encode quantum information in the graph state and demonstrates error detection and correction, with results close to theory and limited by the initial resource-state quality.

  • Problem

    The four-qubit code had been realized only in the circuit model, leaving its graph-state implementation within measurement-based quantum computation unshown.

    Source: Introduction · p. 3

  • Method

    The experiment generated a four-qubit graph-state code and teleported quantum information into it, then tested encoding, error detection, and correction.

    Source: Introduction · pp. 3–4

  • Results

    The graph-state code detected general errors at unknown locations and corrected known-location errors or loss, with results close to theory and limited only by initial resource-state quality.

    Source: Discussion · p. 13, Results · p. 13

  • Takeaways & Limitations

    The authors describe compact quantum error-correction demonstrations as necessary first steps toward large-scale quantum computers and note potential applications including lossy-channel communication, lossy interferometry, and secret sharing.

    Source: Introduction · pp. 3–4

    The code detects but cannot correct general single-qubit errors when their location is unknown.

    Source: Results · p. 12

Abstract

from arXiv · show

Scalable quantum computing and communication requires the protection of quantum information from the detrimental effects of decoherence and noise. Previous work tackling this problem has relied on the original circuit model for quantum computing. However, recently a family of entangled resources known as graph states has emerged as a versatile alternative for protecting quantum information. Depending on the graph's structure, errors can be detected and corrected in an efficient way using measurement-based techniques. In this article we report an experimental demonstration of error correction using a graph state code. We have used an all-optical setup to encode quantum information into photons representing a four-qubit graph state. We are able to reliably detect errors and correct against qubit loss. The graph we have realized is setup independent, thus it could be employed in other physical settings. Our results show that graph state codes are a promising approach for achieving scalable quantum information processing.

graph state code. We have used an all-optical setup to encode quantum

An all-optical setup encoded quantum information in photons representing a four-qubit graph state, enabling reliable error detection and correction against qubit loss. The realized graph is setup independent and could be employed in other physical settings; the results suggest graph-state codes may support scalable quantum information processing.

graph state code. We have used an all-optical setup to encode quantum

  • The all-optical experiment encoded quantum information into photons representing a four-qubit graph state and reliably detected errors and corrected qubit loss.The realized graph is setup independent and could be employed in other physical settings.Source: graph state code. We have used an… · p. 2
  • The realized graph is setup independent and could be employed in other physical settings.Source: graph state code. We have used an… · p. 2

results show that graph state codes are a promising approach for achieving

Introduction

Quantum error-correcting codes protect information from decoherence and noise, while graph codes offer a compact alternative to resource-intensive topological codes in measurement-based quantum computation. This work experimentally demonstrates a four-qubit graph-state code, including encoding, error detection, and correction.

Introduction

  • Quantum error-correcting codes counter decoherence and noise, and the threshold theorem permits reliable computation when component noise stays below a given threshold.The resulting coherence-time enhancement is described as crucial for enabling speedups in quantum algorithms.Source: Introduction · p. 2
  • Topological code embeddings have large thresholds, but their resource size and complexity remain largely beyond current technologies; graph codes offer a more compact alternative [36-47].Graph codes use the stabilizer formalism and are relevant to both measurement-based and circuit-model computation.Source: Introduction · p. 3
  • The four-qubit code demonstrates graph-state error correction in measurement-based quantum computation, extending an earlier realization restricted to the circuit model.The experiment also characterizes the code’s performance.Source: Introduction · p. 3
  • The experiment uses the smallest graph code capable of detecting one quantum error, the four-qubit code [[4,1,2]], which corrects a known-location loss or error and detects an unknown-location error.The paper notes applications including lossy-channel communication, lossy interferometry, and secret sharing [54-57].Source: Introduction · p. 3
  • The code is generated before quantum information is teleported into it, and the experiment demonstrates encoding, error detection, and correction in sequence.The authors report protection against arbitrary general errors and known-location loss, plus detection of general errors at unknown locations.Source: Introduction · p. 4

Results

The experiment demonstrates a four-qubit graph code that encodes quantum information and recovers it after qubit loss. It also tests the code’s ability to detect unknown single-qubit errors and correct errors whose locations are known.

Results

  • The initial graph resource showed genuine multipartite entanglement, with a lower-bound fidelity of 0.58 ± 0.03 to the ideal state.Genuine multipartite entanglement also persisted after the ancilla was removed, with a reported lower-bound fidelity of 0.58 ± 0.03.Source: Results · pp. 7–8
  • The reconstructed encoding channel closely resembled the input Bloch sphere rotated by a Hadamard operation.Encoding transfers the ancilla input into the graph code, up to a logical byproduct determined by the measurement result.Source: Results · pp. 8, 10
  • The encoded-and-recovered qubit had average fidelity 0.82 ± 0.01 in the first reported case; after qubit 1 was lost, average fidelity was 0.81 ± 0.01 and process fidelity 0.73 ± 0.01.Source: Results · p. 11
  • The code detected unknown single-qubit errors and corrected known single-qubit errors, with measured stabilizer expectations consistent with theory across probe states.Unknown single-qubit errors cannot generally be corrected by this code; detected states are discarded and the protocol restarted.Source: Results · pp. 12–13

Discussion

The experiment demonstrates a four-qubit graph code in photons, with error correction and detection close to theory but limited by the initial resource state's quality. The authors identify possible photonic applications and propose larger graph states and concatenation as next steps.

Discussion

  • The smallest graph code demonstrated corrects one general quantum error or a loss at a known location, and detects a general error at an unknown location.The results were in close agreement with theory and were limited by the quality of the initial resource state.Source: Discussion · p. 13
  • The graph code and measurement-based techniques could transfer to ion traps, cavity-QED, and superconducting qubits.Suggested photonic applications include communication over lossy channels, lossy interferometry, and secret sharing.Source: Discussion · p. 13
  • Larger graph states with enhanced error-correction capabilities and concatenation against loss are identified as next steps.Source: Discussion · p. 13
  • The authors present the four-qubit code's characterization as an initial step toward full-scale fault-tolerant quantum information processing.Source: Discussion · p. 13

Methods

The methods combine photonic sources and path interferometers to build the graph-code resource, use state-specific entanglement witnesses, and analyze encoding and loss recovery through stabilizers and logical operators.

Experimental setup

  • A birefringent photonic crystal fibre source generates nearly spectrally uncorrelated signal-idler pairs, avoiding the need for tight filtering for quantum interference.A second source supplies photons fused with the entangled pair; displaced Sagnac interferometers provide phase-stable path qubits.Source: Experimental setup · pp. 14–15

Entanglement witnesses

  • The entanglement witnesses are locally rotated versions of established witnesses, adapted to the five-qubit resource, box cluster, and rotated GHZ state.The witness constructions account for local complementation operations where needed.Source: Entanglement witnesses · pp. 15–16

Stabilizer picture of the graph code

  • The four-qubit code is a common eigenspace of three stabilizers, and its logical operators omit qubit 4, so that qubit can be lost without decoding it.Measuring the ancilla in the X basis teleports information into the code; measuring qubits 2 and 5 then leaves qubit 1 with the state up to known Pauli corrections.Source: Stabilizer picture of the graph code · pp. 17–18
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