Any-To-Any Connected Cavity-Mediated Architecture for Quantum Computing with Trapped Ions or Rydberg Arrays

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Any-To-Any Connected Cavity-Mediated Architecture for Quantum Computing with Trapped Ions or Rydberg Arrays

Joshua Ramette, Josiah Sinclair, Zachary Vendeiro, Alyssa Rudelis, Marko Cetina, and Vladan Vuletić

PRX Quantum 3, 010344 – Published 17 March 2022

Abstract

We propose a hardware architecture and protocol for connecting many local quantum processors contained within an optical cavity. The scheme is compatible with trapped ions or Rydberg arrays, and realizes teleported gates between any two qubits by distributing entanglement via single-photon transfers through a cavity. Heralding enables high-fidelity entanglement even for a cavity of moderate quality. For processors composed of trapped ions in a linear chain, a single cavity with realistic parameters successfully transfers photons every few $μ s$ , increasing the interchain entanglement rate over 2 orders of magnitude beyond current methods and eliminating a major bottleneck for scaling trapped-ion systems. For one realistic scenario, we outline how to achieve the any-to-any entanglement of 20 ion chains containing a total of 500 qubits in $200 μ s$ , with both fidelities and rates limited only by local operations and ion readout. For processors composed of Rydberg atoms, our method fully connects a large array of thousands of neutral atoms. The connectivity afforded by our architecture is extendable to tens of thousands of qubits using multiple overlapping cavities, expanding capabilities for noisy intermediate-scale quantum era algorithms and Hamiltonian simulations, as well as enabling more robust high-dimensional error-correcting schemes.

Received 21 September 2021
Accepted 18 January 2022

DOI:https://doi.org/10.1103/PRXQuantum.3.010344

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum gates Quantum information architectures & platforms Quantum information processing Quantum simulation

Atoms

Atom & ion cooling Cavity resonators Jaynes-Cummings model

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Joshua Ramette ^1,*, Josiah Sinclair ¹, Zachary Vendeiro ¹, Alyssa Rudelis¹, Marko Cetina², and Vladan Vuletić ¹

¹Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
²Duke Quantum Center and Department of Physics, Duke University, Durham, North Carolina 27708, USA

^*jramette@mit.edu; joshuaramette@gmail.com

Popular Summary

Building a quantum computer requires exquisite control over a large number of interacting qubits. This is hard. In particular, having every qubit interact with every other qubit inherently conflicts with having a large number of qubits, since having both requires either infinite-range (yet targeted) interactions, a high-dimensional topology (packing every qubit "close" to all other qubits), or the ability to shuffle qubits around at high speed. Despite the challenges associated with engineering a high degree of connectivity, it is expected that qubit connectivity will be an essential ingredient for extracting a computational advantage from a quantum computer. In fact, the most powerful quantum computers built to date outshine the competition not by having the most qubits, but by being fully connected! In this work we propose a new architecture for quantum computing which will enable hundreds of times larger all-connected systems than previously possible. Our approach places trapped ions or Rydberg atoms inside an optical cavity and relies on heralded single-photon transfers through the cavity to connect distant qubits. We show that it is possible to connect many trapped ion chains in a single cavity with speeds 100-1000 times faster than what is possible with current methods, eliminating the major inter-chain connection bottleneck that currently limits trapped ion systems to a single chain and tens of qubits. Our methods also endow large Rydberg arrays with microsecond-fast any-to-any gates, along with enabling non-destructive read-out that is hundreds of times faster than previously possible.

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Vol. 3, Iss. 1 — March - May 2022

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Figure 1
Architecture for cavity-mediated quantum gate between any two qubits applied to (a) Rydberg atoms or (b) multiple chains of trapped ions. Photon transfers via the cavity produce heralded entanglement of communication qubits. Local interactions between communication and memory qubits enable teleported gates between any two memory qubits. Different atomic species can be used for the communication and memory qubits so that the latter remain unaffected during the entanglement process for communication qubits.
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Figure 2
Heralded photon transfers create entanglement between distant communication qubits. Subsequent high-fidelity local operations enable teleported quantum gates between distant memory qubits.
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Figure 3
Atomic level scheme for the communication qubits. The communication qubits are coupled to the cavity with strength $g_{i}$ and addressed individually with Rabi frequency $Ω_{i}$ . The excited state $| e ⟩$ decays at $Γ$ , and the level and addressing schemes are chosen to suppress the probability of decay into the operation states $| r_{0} ⟩$ and $| r_{1} ⟩$ . Raman transitions or microwaves enable site selective rotations between the qubit states $| 0 ⟩$ and $| 1 ⟩$ and between the operation states $| r_{0} ⟩$ and $| r_{1} ⟩$ . For trapped ions, long-lived shelving levels can be used as part of the heralding process. For Rydberg atoms, Rydberg levels conveniently act as operation states.
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Figure 4
Comparison of the average rates for distributing entanglement to $M$ any-to-any-connected local processors comprising $N$ total qubits for different modalities (a)–(c). (a) Red line: intracavity entanglement method proposed here with 25 ions per chain using the parameters outlined in this section, with the entanglement time given by $(τ_{parallel} + \frac{1}{2} M τ_{serial}) / p$ , and where $p = 0.40$ , $τ_{serial} = 5.3 μ s$ (see the Supplemental Material [49]), and $τ_{parallel} = 28 μ s$ [52]. The red line changes from solid to dashed at $N = 500$ , representing the number of ions that could be fit comfortably in a single rf trap along the cavity axis. (b) Blue lines: photonic interconnects with 25 ions per chain using the method of Refs. [29, 31, 53] can entangle many pairs of ion chains in parallel if the photons are routed through an optical cross-connect switch. The dashed blue line shows the current state of the art for entangling two ions (5 ms) [32], and the solid blue line shows the same with additional realistic overheads necessary for achieving high-fidelity full connectivity, including a factor of 2 overhead for entanglement purification [32, 54], cross-connect switch insertion losses (1.3 dB per photon), and switching time (10 ms overhead) [55, 56]. (c) Yellow line: ion shuttling architectures [57, 58], where ions are physically transported between different ion traps, require milliseconds of sympathetic re-cooling after each split/merge operation. Demonstrated geometries (two ions per local processor, see [25]) lead to linearly increasing transport time for fully connected circuits.
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Figure 5
With nearest-neighbor Rydberg gate errors of $ϵ_{R} = 10^{- 3}$ [62], the nonlocal teleported cnot gate error is limited to $ϵ_{CNOT} \sim 2 ϵ_{R} = 2 \times 10^{- 3}$ (a) Error probabilities due to local two-qubit gate errors for gates between qubits $d$ sites apart, when implemented directly via teleportation (constant error $ϵ_{CNOT}$ , solid blue) or via local swap gates [red, three local cnot gates per swap gate for an error $ϵ_{R} + 3 (d - 1) ϵ_{R}$ ]. (b) Comparing storage and gate errors for implementing serial any-to-any gates. The serial system can be scaled until $N T / τ \sim ϵ_{CNOT}$ before storage errors would dominate gate errors.
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Figure 6
Extension to larger systems. The methods outlined here could be extended using several overlapping cavity modes, creating systems with potentially $10^{4}$ all-connected qubits. Several vertical cavity modes (shaded) provide parallelization, such that many photon transfers can be accomplished simultaneously. Any two communication ions can be entangled in two steps, by photon-mediated communication along a horizontal and a vertical cavity mode.
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