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Distributed Quantum Computing across an Optical Network Link

D. Main, P. Drmota, D. P. Nadlinger, E. M. Ainley, A. Agrawal, B. C. Nichol, R. Srinivas, G. Araneda, D. M. Lucas

arXiv:2407.00835v1quant-ph

TL;DR

Scaling quantum computers requires more qubits without sacrificing precise control and inter-connectivity, but deterministic and repeatable QGT across separate modules had not been demonstrated. The paper distributes computation between photonically interconnected trapped-ion modules using heralded remote entanglement, deterministically teleports non-local gates, and demonstrates multi-gate circuits and Grover’s algorithm. The results establish distributed quantum computation across modules and motivate photonic networking across multiple quantum platforms.

  • Problem

    DQC needs scalable interconnectivity across quantum modules, but deterministic and repeatable quantum gate teleportation across separate photonically linked modules had not been demonstrated.

  • Method

    The experiment uses heralded remote entanglement between network qubits to teleport gates between circuit qubits in two trapped-ion modules separated by about 2 m.

  • Results

    The teleported CZ gate achieved 86.1(9) % average gate fidelity, while distributed iSWAP and SWAP circuits used 2 and 3 QGT instances, respectively.

  • Takeaways & Limitations

    Photonic interconnects provide a route to scalable DQC across trapped-ion and other quantum-computing platforms, including hybrid networks.

  • Takeaways & Limitations

    The measured distributed-circuit performance is limited primarily by errors in local operations, while remote entanglement fidelity was 97.15(9) %.

Abstract

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Distributed quantum computing (DQC) combines the computing power of multiple networked quantum processing modules, enabling the execution of large quantum circuits without compromising on performance and connectivity. Photonic networks are well-suited as a versatile and reconfigurable interconnect layer for DQC; remote entanglement shared between matter qubits across the network enables all-to-all logical connectivity via quantum gate teleportation (QGT). For a scalable DQC architecture, the QGT implementation must be deterministic and repeatable; until now, there has been no demonstration satisfying these requirements. We experimentally demonstrate the distribution of quantum computations between two photonically interconnected trapped-ion modules. The modules are separated by $\sim$ 2 m, and each contains dedicated network and circuit qubits. By using heralded remote entanglement between the network qubits, we deterministically teleport a controlled-Z gate between two circuit qubits in separate modules, achieving 86% fidelity. We then execute Grover's search algorithm - the first implementation of a distributed quantum algorithm comprising multiple non-local two-qubit gates - and measure a 71% success rate. Furthermore, we implement distributed iSWAP and SWAP circuits, compiled with 2 and 3 instances of QGT, respectively, demonstrating the ability to distribute arbitrary two-qubit operations. As photons can be interfaced with a variety of systems, this technique has applications extending beyond trapped-ion quantum computers, providing a viable pathway towards large-scale quantum computing for a range of physical platforms.

INTRODUCTION

Distributed quantum computing uses photonically interconnected modules to scale quantum processors while preserving local module complexity and enabling non-local gates through quantum gate teleportation. This work demonstrates a deterministic, repeatable implementation between trapped-ion modules using heralded remote entanglement and dedicated network, circuit, and auxiliary qubits.

  • INTRODUCTION: DQC executes large quantum computations across networked modules, transforming qubit-scaling complexity into building modules and connecting them.The architecture combines classical and quantum information channels while preserving the reduced complexity of individual modules.
  • INTRODUCTION: Quantum gate teleportation replaces direct quantum-information transfer with shared entanglement, local operations, and classical communication.QGT uses one Bell pair and two classical bits for non-local entangling gates, while channel losses can be overcome through repeated entanglement generation.
  • INTRODUCTION: Photonic interconnects provide all-to-all connectivity with a dynamically reconfigurable network topology for distributed modules.The architecture separates network qubits, which interface with photons, from circuit qubits, which interact locally and store computation states.
  • INTRODUCTION: Prior demonstrations lacked deterministic, repeatable non-local gate operation across photonically interconnected modules because photon loss or circuit-qubit decoherence caused non-determinism.Photonic implementations required post-selection, while a trapped-ion demonstration generated entanglement locally and transported it only about 840 µm within one trap.
  • INTRODUCTION: The experiment distributes computation between two trapped-ion modules about 2 m apart, using network qubits for heralded entanglement and circuit qubits for computation.Each module contains 88Sr+ and 43Ca+ ions; an auxiliary Ca+ qubit temporarily mediates local entangling operations before feed-forward completes the teleported CZ gate.
  • INTRODUCTION: 86.1(9) % average gate fidelity was measured for the teleported CZ process using quantum process tomography.The protocol starts from arbitrary circuit-qubit states and produces output states available for further computation.

DISTRIBUTED QUANTUM COMPUTING

The paper demonstrates distributed quantum computations using sequential quantum gate teleportation, including arbitrary two-qubit gates and Grover’s search algorithm. The distributed Grover implementation achieves an average success rate of 71(1) %.

  • At most three CZ gates suffice to decompose any arbitrary two-qubit unitary operation.
  • 70(2) % and 64(2) % average gate fidelities are measured for distributed iSWAP and SWAP gates, compiled from two and three QGT instances, respectively.
  • Grover’s two-qubit search uses one QGT instance for the oracle and another for diffusion, marking and decoding the target state.
  • 71(1) % is the average success rate for identifying marked states across the four-item search space.
  • The distributed processor executes Grover’s algorithm deterministically, described as the first deterministic execution of any algorithm on a distributed quantum computer.

DISCUSSION

The discussion attributes circuit performance primarily to teleported-CZ errors, especially remote-entanglement quality, while identifying hardware and networking extensions. It also reports photonic-network applicability beyond trapped-ion modules.

  • Error sources: The distributed-circuit performance is consistent with errors from the teleported CZ gates, with most identified sources arising during local operations.The measured fidelity is slightly below the error-budget prediction, attributed to calibration drifts during data acquisition.
  • Error sources: 97.15(9) % fidelity is measured for remotely entangled network qubits in the desired |Ψ+⟩ state.
  • Error sources: Entanglement purification is proposed to distribute higher-fidelity entangled states from multiple lower-fidelity states.The paper links this improvement to higher-fidelity entangling gates between modules.
  • Scaling modules: The implementation has one circuit qubit per module, whereas three circuit qubits and one network qubit per module would enable purification of arbitrary quantum channels.
  • Platform scope: Photonic interconnects integrated into a single device could mitigate computational bottlenecks from ion-transport overheads in QCCD architectures.
  • Platform scope: Photonic interconnects could connect trapped-ion modules with diamond colour centres, neutral atoms, qudits, and continuous-variable quantum computing platforms.Wavelength conversion could connect modules based on different physical platforms.

METHODS

The apparatus uses two-species trapped-ion modules with separate network, circuit, and auxiliary qubits. Quantum process tomography reconstructs processes from tomographically complete preparations and measurements while modelling SPAM errors.

  • Dual-species ion-trap modules: The circuit qubit has approximately two orders of magnitude lower magnetic-field sensitivity than the network qubit, supporting quantum-memory operation.The reported circuit-qubit transition sensitivity is 122 kHz mT−1 at approximately 0.5 mT.
  • Dual-species ion-trap modules: An auxiliary Ca+ qubit supports local entangling operations, state preparation, and readout, while circuit information can be transferred to it.The species are spectrally isolated, allowing one species to be addressed without decohering the other.
  • Quantum process tomography: Quantum process tomography reconstructs a process matrix by applying a process to tomographically complete input states and measuring the outputs.The reconstruction uses diluted maximum-likelihood estimation.
  • Quantum process tomography: SPAM errors are modelled by replacing ideal σz measurements with positive-operator-valued measures parameterized by state-dependent errors.The parameters ϵ_|0⟩ and ϵ_|1⟩ represent SPAM errors for the corresponding qubit states.
  • Quantum process tomography: Resampling measurement outcomes yields fidelity error bars given by the standard deviation across resampled data sets.The resampling also tests sensitivity to statistical fluctuations in the input data.

Remote entanglement generation

Remote entanglement is generated by interfering photons from separate trapped-ion modules and heralding detector patterns, while circuit-qubit decoupling preserves stored information during attempts. The resulting network link is characterized before QGT use.

  • Remote entanglement generation: Photon interference at a central Bell-state analyser projects the two network ions into a maximally entangled state, with detector clicks heralding successful generation.A 674 nm π-pulse maps the entanglement to optical network qubits.
  • Remote entanglement generation: 9.7 s−1 is the average entanglement generation rate, equivalent to 103 ms per successful network-qubit entanglement.Each attempt takes 1168 ns, and successful heralding requires 7084 attempts on average; sympathetic recooling is interleaved to mitigate heating.
  • Remote entanglement generation: The reconstructed remote state has 97.15(9) % fidelity to the desired Ψ+ Bell state.The fidelity is obtained from quantum state tomography with corrections for imperfect tomographic measurements.
  • Circuit-qubit memory during entanglement: Circuit qubits preserve encoded information during entanglement generation through long coherence times and dynamical decoupling.The circuit qubits exhibit approximately 100 ms coherence times and have been shown robust to network activity.
  • Circuit-qubit memory during entanglement: The QGT sequence begins immediately after entanglement heralding, then completes the decoupling sequence and applies propagated Z corrections.This timing suppresses dephasing while accounting for dynamical-decoupling pulses propagated through the teleported CZ gate.
  • Circuit-qubit memory during entanglement: The storage process during entanglement generation has fidelities of 98.1(4) % for Alice and 98.2(5) % for Bob relative to the ideal operation.Quantum process tomography evaluates whether the circuit-qubit information changes during network-entanglement generation.

Local mixed-species entangling gates

The experiment uses deterministic mixed-species geometric phase gates to entangle the optical network qubit with a Ca+ auxiliary qubit, enabling separate network and circuit roles within each module.

  • Local mixed-species entangling gates: A single pair of 402 nm Raman beams implements deterministic geometric phase gates between the Sr+ network qubit and Ca+ auxiliary qubit.The gate is applied directly to the optical network qubit rather than the ground-state Zeeman qubit.

Hyperfine qubit transfer

Circuit-qubit states are coherently transferred to an auxiliary Ca+ qubit for local mixed-species gates and transferred back afterward. Composite pulses suppress off-resonant excitation caused by near-degenerate transitions, and benchmarking quantifies the transfer error.

  • Transfer mechanism: Circuit information must be coherently mapped to the auxiliary qubit before local mixed-species gates and mapped back afterward.The circuit qubit does not participate directly in the mixed-species gate.
  • Transfer mechanism: A three-pulse composite sequence suppresses off-resonant excitation from the unwanted transition.The pulses are resonant with T0, have durations equal to the T1 2π-time, and use optimized phases.
  • Transfer characterization: The transfer benchmark models survival probability using the number of hyperfine transfers, SPAM offsets, and a depolarising probability.The analysis assumes negligible single-qubit gate errors relative to transfer infidelity and similar forward and reverse transfer fidelities.
  • Transfer characterization: 3.8(2) × 10−3 and 2.6(1) × 10−3 are the measured errors per transfer for Alice and Bob, respectively.These values come from the modified randomized-benchmarking measurement.

Conditional Operations

After measuring the network qubits, the modules exchange outcomes and apply conditional local rotations to complete quantum gate teleportation. Measurement errors can induce an effective joint phase-flip and contribute to the teleported CZ gate error.

  • Conditional Operations: The modules exchange mid-circuit measurement outcomes mA and mB, then apply conditional rotations UA and UB to their circuit qubits.The outcomes are exchanged in real time through a classical communication link.
  • Conditional Operations: The rotations depend on the parity mA ⊕ mB, selecting S or S† for each module.Here, S = diag(1, i).
  • Conditional Operations: Measurement errors apply the wrong conditional rotation, appearing as a joint phase-flip on the circuit qubits after teleportation.The relevant errors arise from imperfect basis-mapping rotations and fluorescence detection.
  • Conditional Operations: 0.091(3) % and 0.122(2) % are the estimated Alice and Bob contributions, respectively, to teleported CZ gate error.The estimates combine single-qubit rotation and fluorescence-detection error mechanisms.

AUTHOR INFORMATION

The listed authors built and operated the experimental apparatus, analyzed the data, prepared the manuscript, and supervised or discussed the work.

  • AUTHOR INFORMATION: DM, PD, DPN, EMA, AA, BCN, RS, and GA built and operated the experimental apparatus.DM led the experimental work with assistance from PD and DPN.
  • AUTHOR INFORMATION: DM performed the data analysis and prepared the manuscript with input from all authors.DML secured funding and supervised the work.
  • AUTHOR INFORMATION: All authors contributed to discussion and interpretation of the results.

Competing Interests

RS is partially employed by Oxford Ionics Ltd.; the remaining authors declare no competing interests.

  • Competing Interests: RS is partially employed by Oxford Ionics Ltd.
  • Competing Interests: The remaining authors declare no competing interests.

Corresponding Authors

The supplied material identifies correspondence contacts and describes the trapped-ion module, qubit roles, measurement performance, and supporting experimental procedures.

  • Corresponding Authors: Correspondence should be addressed to DM or DML.
  • Module and Qubit Configuration: Each module co-traps one 88Sr+ ion and one 43Ca+ ion in a micro-fabricated surface Paul trap.The Sr+ ion provides the optical network qubit, while Ca+ supplies circuit and auxiliary qubits.
  • Measurement Performance: The average state-preparation and measurement error is 5.0(2) × 10^-3.
  • Experimental Procedures: Remote entanglement uses 200 µs attempts interleaved with 2.254 ms sympathetic re-cooling until heralded.Knill dynamical decoupling pulses preserve the circuit-qubit state during attempts.
  • Experimental Procedures: The supporting procedures include mixed-species local CZ gates and coherent transfer between circuit and auxiliary qubits.
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