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arXiv:2308.04192 · Physical Review Letters

High-Photon-Loss Threshold Quantum Computing Using GHZ-State Measurements

Brendan Pankovich, Angus Kan, Kwok Ho Wan, Maike Ostmann, Alex Neville, S. Omkar, Adel Sohbi, Kamil Brádler

Published Aug 1, 2024• 30 citations
arXivHTMLPDF

Abstract

We propose fault-tolerant architectures based on performing projective measurements in the Greenberger-Horne-Zeilinger (GHZ) basis on constant-sized, entangled resource states. We present linear-optical constructions of the architectures, where the GHZ-state measurements are encoded to suppress the errors induced by photon loss and the probabilistic nature of linear optics. Simulations of our constructions demonstrate high single-photon-loss thresholds compared to the state-of-the-art linear-optical architecture realized with encoded two-qubit fusion measurements performed on constant-sized resource states. We believe this result shows a resource-efficient path to achieving photonic fault-tolerant quantum computing.

DOI
10.1103/physrevlett.133.050604

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Physical Review Letters•Mar 28, 2024•47 citations
We propose fault-tolerant architectures based on performing projective measurements in the Greenberger-Horne-Zeilinger (GHZ) basis on constant-sized, entangled resource states. We present linear-optical constructions of the architectures, where the GHZ-state measurements are encoded to suppress the errors induced by photon loss and the probabilistic nature of linear optics. Simulations of our constructions demonstrate high single-photon-loss thresholds compared to the state-of-the-art linear-optical architecture realized with encoded two-qubit fusion measurements performed on constant-sized resource states. We believe this result shows a resource-efficient path to achieving photonic fault-tolerant quantum computing.
Linear optical quantum computing is beset by the lack of deterministic entangling operations besides photon loss.Motivated by advancements at the experimental front in deterministic generation of various kinds of multiphoton entangled states, we propose an architecture for linear-optical quantum computing that harnesses the availability of three-photon Greenberger-Horne-Zeilinger (GHZ) states.Our architecture and its subvariants use polarized photons in GHZ states, polarization beam splitters, delay lines, optical switches, and on-off detectors.We concatenate the topological quantum error-correction code with three-qubit repetition codes and estimate that our architecture can tolerate a remarkably high photon-loss rate of 11.5%; this makes a drastic change that is at least an order higher than those of known proposals.Furthermore, considering three-photon GHZ states as resources, we estimate the resource overheads to perform gate operations with an accuracy of 10 -6 (10 -15 ) to be 2.07 × 10 6 (5.03 × 10 7 ).Compared to other all-photonic schemes, our architecture is also resource efficient.In addition, the resource overhead can be even further improved if larger GHZ states are available.Given its striking enhancement in the photon-loss threshold and the recent progress in generating multiphoton entanglement, our scheme moves scalable photonic quantum computing a step closer to reality.
Bell state measurements (BSMs) play a significant role in quantum information and quantum computing, in particular in fusion-based quantum computing (FBQC). The FBQC model is a framework for universal quantum computing, provided that we are able to perform entangling measurements, called fusions, on qubits within small entangled resource states. Here, we analyze the usage of different linear-optical BSM circuits as fusions in the FBQC schemes and numerically evaluate hardware requirements for fault-tolerance in this framework. We examine and compare the performance of several BSM circuits with varying additional resources and estimate the requirements on losses for every component of the linear-optical realization of fusions under which errors in fusion networks caused by these losses can be corrected. Our results show that fault-tolerant quantum computing in the FBQC model is possible with currently achievable levels of optical losses in an integrated photonic implementation, provided that we can create and detect single photons of the resource states with a total marginal efficiency higher than 0.973.
We propose a fault-tolerant quantum computation scheme in a measurement-based manner with finite-sized entangled resource states and encoded-fusion scheme with linear optics. The encoded fusion is an entangled measurement devised to enhance the fusion success probability in the presence of losses and errors based on a quantum error-correcting code. We apply an encoded-fusion scheme, which can be performed with linear optics and active feedforwards to implement the generalized Shor code, to construct a fault-tolerant network configuration in a three-dimensional Raussendorf-Harrington-Goyal lattice based on the surface code. Numerical simulations show that our scheme allows us to achieve up to 10 times higher loss thresholds than nonencoded fusion approaches with limited numbers of photons used in fusion. Our scheme paves an efficient route toward fault-tolerant quantum computing with finite-sized entangled resource states and linear optics.
In the quest to build general-purpose photonic quantum computers, fusion-based quantum computation has risen to prominence as a promising strategy. This model allows a ballistic construction of large cluster states which are universal for quantum computation, in a scalable and loss-tolerant way without feed-forward, by fusing many small n-photon entangled resource states. However, a key obstacle to this architecture lies in efficiently generating the required essential resource states on photonic chips. One such critical seed state that has not yet been achieved is the heralded three-photon Greenberger-Horne-Zeilinger (3-GHZ) state. Here, we address this elementary resource gap, by reporting the first experimental realization of a heralded dual-rail encoded 3-GHZ state. Our implementation employs a low-loss and fully programmable photonic chip that manipulates six indistinguishable single photons of wavelengths in the telecommunication regime. Conditional on the heralding detection, we obtain the desired 3-GHZ state with a fidelity 0.573+-0.024. Our work marks an important step for the future fault-tolerant photonic quantum computing, leading to the acceleration of building a large-scale optical quantum computer.
We propose a novel architecture for fault-tolerant quantum computing that incorporates strong single-photon nonlinearities into a photonic GHZ-measurement-based architecture. The nonlinearities substantially reduce resource overheads compared to conventional linear-optics-based architectures, which require significant redundancy to accommodate probabilistic photon generation and probabilistic entangling operations. By removing linear-optical failure modes, our nonlinear architecture can also tolerate much higher optical losses than linear approaches, with a baseline loss tolerance of $\sim$12\% using a 32-photon resource state and a foliated surface code. Nonlinear photonic architectures provide a route to dramatically improving practical implementations of fault-tolerant quantum computing.
In the quest to build general-purpose photonic quantum computers, fusion-based quantum computation has risen to prominence as a promising strategy. This model allows a ballistic construction of large cluster states which are universal for quantum computation, in a scalable and loss-tolerant way without feed forward, by fusing many small n-photon entangled resource states. However, a key obstacle to this architecture lies in efficiently generating the required essential resource states on photonic chips. One such critical seed state that has not yet been achieved is the heralded three-photon Greenberger-Horne-Zeilinger (3-GHZ) state. Here, we address this elementary resource gap, by reporting the first experimental realization of a heralded 3-GHZ state. Our implementation employs a low-loss and fully programmable photonic chip that manipulates six indistinguishable single photons of wavelengths in the telecommunication regime. Conditional on the heralding detection, we obtain the desired 3-GHZ state with a fidelity 0.573±0.024. Our Letter marks an important step for the future fault-tolerant photonic quantum computing, leading to the acceleration of building a large-scale optical quantum computer.