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Co-Designing a Scalable Quantum Computer with Trapped Atomic Ions

K. R. Brown, J. Kim, C. Monroe

arXiv:1602.02840v1quant-ph

TL;DR

Practical trapped-ion quantum processors require new integration technologies and system-engineering approaches, while their connectivity and reconfigurability motivate scalable architectures. This paper presents modular ion-crystal units linked by Coulomb interactions and photonic channels, showing how dynamic, reconfigurable wiring can extend connectivity across very large numbers of modules and support multiple quantum codes and applications.

  • Problem

    Practical implementation of trapped-ion quantum processors requires new integration technologies and system-engineering approaches beyond those available for classical solid-state circuits.

  • Method

    The paper develops a modular architecture combining Coulomb-based links within elementary logic units with photonic connections between modules and a non-blocking optical crossconnect.

  • Results

    The architecture can extend connectivity across potentially thousands or millions of qubits and supports dynamic higher-level graphs, while allowing different quantum error-correction codes without constructing new hardware.

  • Takeaways & Limitations

    Reconfigurable modular wiring allows the same ion-trap hardware to support a variety of quantum applications, protocols, and error-correction codes.

  • Takeaways & Limitations

    Large ion crystals face motional-mode crosstalk, heating, and fluctuating-field errors that limit faithful gates, although control techniques may support crystals of N = 10–100 qubits.

Abstract

from arXiv · show

The first generation of quantum computers are on the horizon, fabricated from quantum hardware platforms that may soon be able to tackle certain tasks that cannot be performed or modelled with conventional computers. These quantum devices will not likely be universal or fully programmable, but special-purpose processors whose hardware will be tightly co-designed with particular target applications. Trapped atomic ions are a leading platform for first generation quantum computers, but are also fundamentally scalable to more powerful general purpose devices in future generations. This is because trapped ion qubits are atomic clock standards that can be made identical to a part in 10^15, and their quantum circuit connectivity can be reconfigured through the use of external fields, without modifying the arrangement or architecture of the qubits themselves. In this article we show how a modular quantum computer of any size can be engineered from ion crystals, and how the wiring between ion trap qubits can be tailored to a variety of applications and quantum computing protocols.

ION TRAP QUBITS AND WIRES

Trapped-ion qubits use stable electronic levels in laser-cooled ion crystals, combining accurate state control with long coherence and frequency-standard properties.

  • Trapping and crystals: Ions are confined by electromagnetic fields in linear radiofrequency traps, where Coulomb repulsion and external confinement form a linear crystal.Rare background-gas collisions can temporarily disrupt the crystal; cryogenic vacuum can reduce collision rates by orders of magnitude.
  • Qubit encoding: Each qubit is encoded in two stable electronic levels, |↓⟩ and |↑⟩, corresponding to bit values 0 and 1.Optical pumping and state-dependent fluorescence enable nearly perfect initialization and detection.
  • Qubit properties: The 171Yb+ hyperfine qubit levels are separated by νHF = 12.642812 GHz and provide an excellent frequency standard.Observed coherence times exceed 1000 s.
  • Cooling: Laser cooling confines ions near the bottom of the trap, while more sophisticated cooling can bring them nearly to rest.Cooling supports the motional control used in trapped-ion operations.

Wiring atomic qubits with the Coulomb interaction

Coulomb-coupled ion motion provides a reconfigurable data bus: state-dependent optical or microwave forces map qubit states onto collective motion to mediate entangling gates.

  • Wiring atomic qubits with the Coulomb interaction: State-dependent optical or microwave dipole forces couple internal qubit states to collective ion motion through Coulomb repulsion.The force depends on the qubit state through the Pauli operator σz and a field gradient.
  • Wiring atomic qubits with the Coulomb interaction: Mapping multiple ions onto collective motion enables entangling gates between separated ions, including controlled-NOT operations.Experiments with a few ions have achieved entangled-state fidelities greater than 99.9%.
  • Wiring atomic qubits with the Coulomb interaction: Rgate/2π ∼10–100 kHz is demonstrated for current experiments, while ultrafast high-intensity optical fields may enable gates in the GHz range.The gate-rate expression depends on recoil and collective-motion frequencies.
  • Scaling limits: Gate speed decreases approximately as 1/N as the number of ions N grows.Larger crystals also introduce crosstalk among collective-motion modes and greater sensitivity to motional heating and fluctuating fields.
  • Scaling limits: Individual optical addressing and pulse shaping should permit faithful control of single crystals ranging from N = 10–100 qubits despite these errors.Beyond roughly 50 qubits, multiplexed QCCD architectures shuttle ions between zones to couple separated chains.

Wiring atomic qubits with photons

Photonic interfaces connect separate trapped-ion modules, extending local Coulomb links into a modular architecture whose connectivity can scale and be reconfigured optically.

  • Wiring atomic qubits with photons: Photonic interfaces link separate trapped-ion chains, allowing gates between qubits regardless of their relative locations.They can support fault-tolerant error correction even when individual photonic interconnect attempts succeed with small probability.
  • Wiring atomic qubits with photons: Communication qubits emit photons whose interference at a 50/50 beamsplitter heralds entanglement between memory qubits through entanglement-swapping.The interface uses fast laser excitation and detectors to identify successful Bell-state projections.
  • Wiring atomic qubits with photons: Typical photonic connection rates are approximately 100 Hz for γ/2π ∼10 MHz, F ∼1–10%, and ηD ∼20%.The mean rate is R(FηD)^2/2 and is limited by the emission rate, collection fraction, and detector efficiency.
  • Implementation constraints: Communication qubits must be isolated from memory qubits to prevent scattered excitation light and emitted photons from disturbing spectator memories.Physical shuttling or separate atomic species can reduce this crosstalk.
  • Modular architecture: ELU modules combine Coulomb-based internal links with photonic intermodule connections, and optical crossconnects can extend connectivity to thousands or millions of qubits.The architecture supports modular distributed quantum computing.

INTEGRATION TECHNOLOGIES FOR TRAPPED ION QUANTUM COMPUTERS

Practical trapped-ion processors require new integration technologies and system-engineering approaches beyond those used for large-scale classical solid-state circuits.

  • INTEGRATION TECHNOLOGIES FOR TRAPPED ION QUANTUM COMPUTERS: Unlike classical solid-state circuits, practical trapped-ion quantum processors require new integration technologies and system-engineering approaches.The paper presents current efforts toward developing these technologies.

Chip Traps and Optical Control of Qubits

Microfabricated ion traps and integrated optical-control technologies provide a path toward compact, reproducible trapped-ion processors. The architecture combines semiconductor-fabricated traps, reconfigurable laser control, compact lasers, and cryogenic vacuum systems.

  • Fabricated ion traps: Lithographic fabrication defines ion-trap electrodes with sub-micrometer precision for reproducible ELU modules.The electrodes must sustain high static and rf potentials with insulating barriers in ultra-high vacuum.
  • Fabricated ion traps: Silicon microfabrication has matured into complex surface traps, including Sandia’s high-optical-access and GTRI/Honeywell’s ball-grid-array designs.Recent experiments demonstrated high-performance qubit measurement and quantum gates in microfabricated surface traps.
  • Optical control: Programmable, reconfigurable local gates require fixed-frequency off-resonant lasers and beam-distribution technology to drive selected interactions.For ^171Yb^+ systems, 355 nm lasers are described as suitable for gate operations, while micromirrors and multichannel AOMs support optical delivery.
  • Optical control: Large-scale systems require tunable lasers with optical frequencies stable and accurate to better than 10 kHz, corresponding to fractional precision of ∼10^-10.Traditional stabilization uses individual optical components on an optical table, creating a large footprint susceptible to environmental drift.
  • Compact vacuum systems: Closed-cycle cryogenic technology can reduce the volume and operational burden of the ultra-high-vacuum environment while improving vacuum conditions.The compact enclosure integrates the surface trap with the vacuum package and supports operation at temperatures below 10 K.

Photonic Technology

Scalable trapped-ion processors require integrated photonics for fluorescence readout and optical links, alongside compact cryogenic packaging and controller hardware. Optical switches can dynamically connect multiple ELUs in parallel.

  • Integrated photonics: High-numerical-aperture optics can collect ∼10% of emitted photons, while an integrated optical cavity could extract ∼50%.These efficiencies are relevant to measuring many qubits and linking ELU modules through single photons.
  • Optical networking: Multiplexed photonic elements require non-blocking, transparent optical cross-connect switches with many input/output ports.Such switches establish optical paths between selected ports using passive optical elements.
  • Cryogenic packaging: The compact cryogenic enclosure integrates the ion trap, getter pumps, and atomic source in a sealed ultra-high-vacuum package.Cooling the package establishes the UHV environment, while optical components can be arranged around the cryostat.
  • Optical networking: Optical devices can be reconfigured in real time to form parallel connections between multiple ELUs.The connections support quantum links formed by devices entangled with trapped-ion qubits.
  • Optical networking: Visible- and blue-spectrum integrated photonics, or noiseless conversion to infrared and telecom bands, would support trapped-ion optical networks.These technologies are especially relevant to long-distance quantum communication applications.
  • Controllers: A scalable controller must stabilize lasers, control rf and static voltages, process detected photons, and apply digital laser pulses.These functions support qubit preparation, measurement, and manipulation.

APPLICATIONS AND OPPORTUNITIES FOR THE TRAPPED ION QUANTUM PROCESSOR

The modular ion-trap architecture addresses the mismatch between hardware-independent algorithms and the physical geometry of quantum processors. Its flexible, reconfigurable connectivity can realize arbitrary geometries with few swaps or teleportation steps.

  • Motivation: Hardware-independent algorithms, applications, and error-correcting codes often do not respect the physical geometry of the underlying quantum system.The modular ion-trap architecture is presented as a way to accommodate these designs through flexible connectivity.
  • Architectural opportunity: Reconfigurable connectivity allows arbitrary interaction geometries with a minimal number of swaps and/or teleportation steps.The section examines opportunities enabled by this hardware beyond conventional gate-model computing.

Topology of Interactions

Trapped-ion modules provide dense local connectivity through long-range Coulomb interactions, while photonic links create a dynamic, reconfigurable graph between modules. This hierarchy supports varied interaction patterns and parallel operations.

  • Topology of Interactions: A one-dimensional ion crystal can implement a fully connected, high- or undefined-dimensional interaction graph within one ELU.Long-range Coulomb interactions enable direct gates between distant qubit pairs, alongside parallel two-qubit and multiqubit operations.
  • Topology of Interactions: 20-ion ELU chains can use four remote-entangling ions, local fast gates over four ion spaces, and complete-graph couplings mediated by crystal normal modes.The figure also indicates that 50-ion chains with a local gate distance of nine ions should be possible.
  • Topology of Interactions: Additional single-qubit gates can remove links from long-range global Ising interactions to generate arbitrary circuits.This provides circuit-level control over the otherwise highly connected interaction graph.
  • Inter-module topology: Photonic channels connect highly connected ELUs into a higher-level graph determined by photon-coupled-ion density.That graph is dynamic and reconfigurable, potentially supporting diverse applications and suggesting new algorithm structures.

Quantum Simulation

Trapped-ion architectures support quantum simulation and error-correction schemes whose interaction structures range from local to fully connected. Their reconfigurability enables testing multiple codes and implementing Ising-based simulation and machine-learning protocols.

  • Global entangling operations in trapped ions can simulate nonlocal graph Hamiltonians, quantum magnetic Ising models, and many-body spin systems.
  • NP-hard Ising ground-state problems motivate quantum adiabatic algorithms, which begin in a strong transverse field and slowly switch it off.
  • Trapped atomic ions are well-suited to generic quantum adiabatic algorithms despite engineering challenges in fabricating large-scale ion-trap chips.
  • Machine Learning and the Boltzmann Machine: Boltzmann machines classify data using thermal Ising-model distributions, with quantum annealing or adiabatic methods proposed to determine classifications and tune couplings.
  • Quantum Error Correction: QEC graphs encode interactions between data qubits and syndrome ancillas, allowing code structures to be compared with physical qubit-connectivity graphs.
  • Quantum Error Correction: Surface codes have an error threshold around 1% but are zero-rate and require magic-state-based gate teleportation for universal computation.
  • Quantum Error Correction: The modular, reconfigurable ion-trap architecture can implement surface and concatenated CSS codes without constructing new hardware for each code.

OUTLOOK

Trapped atomic ion qubits combine coherence, high-performance logic gates, and extensive connectivity with reconfigurability, making the platform a leading candidate for large-scale quantum computing.

  • Trapped atomic ion qubits offer exquisite quantum coherence, high-performance quantum logic gates, and unmatched connectivity and reconfigurability.
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