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arXiv:2209.09774 · npj Quantum Information

Long-range data transmission in a fault-tolerant quantum bus architecture

Shin Ho Choe, Robert König

Published Dec 26, 2024• 1 citation
arXivHTMLPDF

Abstract

Abstract We propose a fault-tolerant scheme for generating long-range entanglement at the ends of a rectangular array of qubits of length R with a square cross-section of $$m=O({\log }^{2}R)$$ m = O ( log 2 R ) qubits. It is realized by a constant-depth circuit producing a constant-fidelity Bell-pair (independent of R) for local stochastic noise of strength below an experimentally realistic threshold. The scheme can be viewed as a quantum bus in a quantum computing architecture where qubits are arranged on a rectangular 3D grid, and all operations are between neighboring qubits. Alternatively, it can be seen as a quantum repeater protocol along a line, with neighboring repeaters placed at a short distance to allow constant-fidelity nearest-neighbor operations. To show our protocol uses a number of qubits close to optimal, we show that any noise-resilient distance-R entanglement generation scheme realized by a constant-depth circuit needs at least $$m=\Omega (\log R)$$ m = Ω ( log R ) qubits per repeater.

DOI
10.1038/s41534-024-00928-4

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Abstract We propose a fault-tolerant scheme for generating long-range entanglement at the ends of a rectangular array of qubits of length R with a square cross-section of m=O(log⁡2R)m=O({\log }^{2}R)m=O(log2R) m = O ( log 2 R ) qubits. It is realized by a constant-depth circuit producing a constant-fidelity Bell-pair (independent of R) for local stochastic noise of strength below an experimentally realistic threshold. The scheme can be viewed as a quantum bus in a quantum computing architecture where qubits are arranged on a rectangular 3D grid, and all operations are between neighboring qubits. Alternatively, it can be seen as a quantum repeater protocol along a line, with neighboring repeaters placed at a short distance to allow constant-fidelity nearest-neighbor operations. To show our protocol uses a number of qubits close to optimal, we show that any noise-resilient distance-R entanglement generation scheme realized by a constant-depth circuit needs at least m=Ω(log⁡R)m=\Omega (\log R)m=Ω(logR) m = Ω ( log R ) qubits per repeater.
Consider a rectangular grid of qubits in 2D with single-qubit and nearest-neighbor two-qubit operations subject to local stochastic Pauli noise. At different length scales, this setup describes both a single quantum computing device with geometrically limited connectivity between qubits arranged on a disc, and planar networks composed of quantum repeater stations of constant size. We give a protocol which robustly generates entanglement between distant qubits in this setup. For noise below a constant threshold error strength, it generates a constant-fidelity Bell pair between qubits separated by an arbitrarily large distance RRR. To generate distance-RRR entanglement, a rectangular grid of qubits of dimensions Θ(R)×Θ(poly(log⁡R))Θ(R)\times Θ(\mathsf{poly}(\log R))Θ(R)×Θ(poly(logR)) suffices. Our protocol applies quantum operations in one shot, establishing a Bell state in a constant time up to a known Pauli correction. In contrast, existing entanglement generation protocols either require local quantum devices controlling a number of qubits growing with the targeted distance, or are not single-shot, i.e., have a distance-dependent execution time. The protocol leverages many-body entanglement in networks and provides the first example of a short-range entangled state in 2D with long-range localizable entanglement robust to local stochastic Pauli noise. As an immediate corollary, we construct a 2D-local stabilizer Hamiltonian whose Gibbs states possess long-range localizable entanglement at constant positive temperature.
To realize long-distance quantum communication, it is crucial to design quantum repeater architectures that can deal with transmission losses and operational errors. Code concatenation of photonic graph codes is a promising way to achieve this; however, existing concatenated codes that can correct both transmission losses and operational errors are extremely hardware-demanding. We propose a one-way quantum repeater architecture based on concatenated ring graph codes and linear optical Bell-state measurements. We construct a scheme to generate the concatenated ring graph codes using quantum emitters, where the number of matter qubits scales linearly with concatenation depth. Furthermore, we devise a measurement strategy at each repeater station with a simple experimental setup where photons are measured in the order that they are created and show that entanglement swapping is fault-tolerant to both transmission losses and operational errors. This allows for long-distance quantum communication (>104> 10^4>104 km) at a kHZ rate even in the presence of single qubit error rates ε>10−3ε> 10^{-3}ε>10−3.
We prove a fault-tolerance theorem for quantum computation against adversarial noise. For every quantum circuit on Nˉ\bar{N}Nˉ logical qudits of depth Tˉ\bar{T}Tˉ, we construct a fault-tolerant circuit on N=poly(Nˉ)N=\text{poly}(\bar{N})N=poly(Nˉ) physical qudits of depth Tˉ⋅Nˉo(1)\bar{T}\cdot\bar{N}^{o(1)}Tˉ⋅Nˉo(1), which is robust against an adversary who may arbitrarily choose and corrupt an almost-linear number N1−o(1)N^{1-o(1)}N1−o(1) of physical qudits at each time step. This robustness significantly improves upon prior fault-tolerance theorems, which assumed corruptions were either local and stochastic, or else only act on a polynomially vanishing fraction of qudits. Our fault-tolerance scheme addresses a key bottleneck towards constructing quantum PCPs via the circuit-to-Hamiltonian mapping of Anshu, Breuckmann, and Nguyen (STOC'24). More fundamentally, our result demonstrates that fault-tolerant quantum computation remains possible under noise models that are global, worst-case, and non-Markovian over the full duration of the computation, directly countering concerns that correlated noise could fundamentally undermine quantum fault tolerance. Our construction is based on a new family of subsystem product codes we develop, which have large dimension and distance along with low-weight parity-checks, and which support transversal non-Clifford gates. We show how to perform single-shot fault-tolerant error correction on these codes using a Floquet-like procedure based on the local testability of classical tensor codes. We then obtain a universal fault-tolerance scheme using repeated code switching in a hypercubic qudit architecture. Finally, we recursively compose our scheme with itself to reduce an initially exponential qudit dimension down to a constant.
We show how to realize a general quantum circuit involving gates between arbitrary pairs of qubits by means of geometrically local quantum operations and efficient classical computation. We prove that circuit-level local stochastic noise modeling an imperfect implementation of our derived schemes is equivalent to local stochastic noise in the original circuit. Our constructions incur a constant-factor increase in the quantum circuit depth and a polynomial overhead in the number of qubits. To execute an arbitrary quantum circuit on n qubits, we give a three-dimensional quantum fault-tolerance architecture involving O ( n 3 / 2 log 3  n ) qubits and a quasi-two-dimensional architecture using O ( n 2 log 3  n ) qubits. Applied to recent fault-tolerance constructions, this gives a fault-tolerance-threshold theorem for universal quantum computations with local operations, a polynomial qubit overhead, and a quasipolylogarithmic depth overhead. More generally, our transformation dispenses with the need for considering the locality of operations when designing schemes for fault-tolerant quantum information processing.
Distribution of quantum resources such as entanglement over distances beyond a few fiber attenuation lengths requires realization of quantum repeaters that utilize entanglement swapping to extend the distance between the entangled qubit pairs [1]. A quantum repeater is a small quantum computer capable of generating entangled qubit pairs with its neighboring repeaters and storing them in stable quantum memories. Once the entangled pairs are generated, it will perform Bell basis measurements, classical communication with appropriate repeaters, and single qubit gates necessary for entanglement swapping. For high fidelity operation, it might perform local operations and classical communications (LOCC) such as entanglement distillation [2] and/or quantum error correction [3,4]. Generation of remote entangled ion pairs mediated by photonic qubits has been demonstrated [5] but their reach is limited since the photons used in the experiment are in the UV part of the spectrum. Coherent conversion of the photons emitted by Yb ion at 369.5nm to a photon at 1310 nm would enable entanglement generation over long distances [6].
We introduce an alternative type of quantum repeater for long-range quantum communication with improved scaling with the distance. We show that by employing hashing, a deterministic entanglement distillation protocol with one-way communication, one obtains a scalable scheme that allows one to reach arbitrary distances, with constant overhead in resources per repeater station, and ultrahigh rates. In practical terms, we show that, also with moderate resources of a few hundred qubits at each repeater station, one can reach intercontinental distances. At the same time, a measurement-based implementation allows one to tolerate high loss but also operational and memory errors of the order of several percent per qubit. This opens the way for long-distance communication of big quantum data.