[Paper Review] Loss tolerant one-way quantum computation -- a horticultural approach

Michael Varnava, Dan E. Browne+1 more|arXiv (Cornell University)|Jul 4, 2005

Quantum Information and Cryptography7 citations

TL;DR

This paper proposes a loss-tolerant one-way quantum computation scheme that passively tolerates up to 50% qubit loss without requiring coherent measurements or corrections. Applied to linear optical quantum computing, it shows that detector inefficiencies up to 50% and photon source purity above 66.6% enable efficient universal quantum computation.

ABSTRACT

We introduce a scheme for fault tolerantly dealing with losses in cluster state computation that can tolerate up to 50% qubit loss. This is achieved passively - no coherent measurements or coherent correction is required. We then use this procedure within a specific linear optical quantum computation proposal to show that: (i) given perfect sources, detector inefficiencies of up to 50% can be tolerated and (ii) given perfect detectors, the purity of the photon source (overlap of the photonic wavefunction with the desired single mode) need only be greater than 66.6% for efficient computation to be possible.

Motivation & Objective

• To develop a fault-tolerant method for handling qubit loss in one-way quantum computation without requiring active correction or coherent measurements.
• To address the challenge of high photon loss and detector inefficiencies in linear optical quantum computing (LOQC), which severely limit scalability and fidelity.
• To determine the minimum photonic source purity required for efficient universal quantum computation under realistic loss and detection constraints.
• To demonstrate that passive loss tolerance can be achieved using cluster state-based quantum computation, enabling robustness against up to 50% qubit loss.

Proposed method

• Proposes a passive scheme that inherently tolerates up to 50% qubit loss in one-way quantum computation by leveraging the structure of cluster states.
• Introduces a method that avoids coherent measurements and corrections by relying on the intrinsic resilience of the cluster state to loss.
• Applies the scheme to a specific linear optical quantum computation proposal to analyze tolerance to detector inefficiencies and source purity.
• Uses the cluster state formalism to model the effects of loss and detector inefficiency, deriving bounds on acceptable error rates.
• Analyzes the impact of photonic wavefunction overlap (source purity) on computational success, showing that 66.6% purity suffices for efficiency.
• Establishes that the scheme remains effective under two distinct realistic constraints: perfect sources with 50% detector inefficiency, or perfect detectors with 66.6% source purity.

Experimental results

Research questions

• RQ1 Can one-way quantum computation be made robust against up to 50% qubit loss without coherent correction or measurement?
• RQ2 What is the maximum detector inefficiency that can be tolerated in linear optical quantum computation when using the proposed loss-tolerant scheme?
• RQ3 What minimum level of photonic source purity is required for efficient quantum computation under realistic loss and detection conditions?
• RQ4 How does the proposed scheme maintain computational universality under high loss and imperfect detection?

Key findings

• The proposed scheme passively tolerates up to 50% qubit loss in one-way quantum computation without requiring coherent measurements or corrections.
• With perfect photon sources, the scheme tolerates detector inefficiencies of up to 50% while maintaining efficient universal quantum computation.
• With perfect detectors, the scheme remains efficient if the photonic source purity—defined by wavefunction overlap with the desired single mode—is greater than 66.6%.
• The method achieves fault tolerance through structural resilience in cluster states, eliminating the need for active error correction procedures.
• The results demonstrate that realistic experimental imperfections such as loss and detector inefficiency can be compensated passively, enabling scalable LOQC.