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Perspective: Toward large-scale fault-tolerant universal photonic quantum computing

Shuntaro Takeda, Akira Furusawa

arXiv:1904.07390v1quant-ph

TL;DR

Large-scale photonic quantum computing is limited by probabilistic entangling gates and optical circuits that are difficult to scale and reconfigure. The perspective combines hybrid qubit-CV processing with time-domain multiplexing to address these limitations. It identifies deterministic universal gates, arbitrarily large-scale computation without circuit reconfiguration, hardware-efficient error correction, and ultra-high bandwidth as supported prospects.

  • Problem

    Photonic quantum computing faces probabilistic entangling gates and optical circuits whose size and programmability hinder large-scale implementation.

  • Method

    The perspective develops a hybrid qubit-CV approach together with time-domain multiplexing and loop-based or one-way photonic computing schemes.

  • Results

    The hybrid approach can provide deterministic photonic-qubit teleportation and deterministic controlled-phase gates in principle, while time-domain multiplexing enables arbitrarily large-scale computation without changing optical-circuit configuration.

  • Takeaways & Limitations

    These schemes support linear-optical scaling, compatibility with hardware-efficient error correction, and all-optical operation with bandwidth beyond THz in principle.

Abstract

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Photonic quantum computing is one of the leading approaches to universal quantum computation. However, large-scale implementation of photonic quantum computing has been hindered by its intrinsic difficulties, such as probabilistic entangling gates for photonic qubits and lack of scalable ways to build photonic circuits. Here we discuss how to overcome these limitations by taking advantage of two key ideas which have recently emerged. One is a hybrid qubit-continuous variable approach for realizing a deterministic universal gate set for photonic qubits. The other is time-domain multiplexing technique to perform arbitrarily large-scale quantum computing without changing the configuration of photonic circuits. These ideas together will enable scalable implementation of universal photonic quantum computers in which hardware-efficient error correcting codes can be incorporated. Furthermore, all-optical implementation of such systems can increase the operational bandwidth beyond THz in principle, utimately enabling large-scale fault-tolerant universal quantum computers with ultra-high operation frequency.

I. INTRODUCTION

Photonic quantum computing offers room-temperature operation and high bandwidth, but scaling is hindered by weak photon interactions and circuit-size constraints. The perspective focuses on hybrid qubit-CV processing and time-domain multiplexing as routes toward scalable systems.

  • I. INTRODUCTION: Photonic systems can preserve quantum states at room temperature and provide high-bandwidth communication because photons interact weakly with their environment and propagate at light speed.These properties make photons advantageous information carriers for quantum communication.
  • I. INTRODUCTION: Photons’ lack of mutual interaction makes two-qubit entangling gates difficult, while their propagation requires many sequential optical components and large circuits.These intrinsic constraints directly complicate large-scale photonic quantum computing.
  • I. INTRODUCTION: The hybrid qubit-CV approach combines complementary representations to seek deterministic and robust quantum computing.The perspective presents this as one of two key ideas for overcoming photonic-scaling limitations.
  • I. INTRODUCTION: Time-domain multiplexing encodes many information units in optical pulses sharing one path and can support arbitrarily large-scale computation without changing circuit configuration.The perspective discusses time-domain-multiplexed one-way computation and loop-based architectures.
  • I. INTRODUCTION: The perspective reviews the hybrid approach, time-domain multiplexing schemes, experimental progress, and remaining technical challenges.Sections II and III develop the two ideas, while Section IV summarizes the perspective.

II. HYBRID QUANTUM COMPUTING

Photonic quantum information processing has two major approaches: discrete-variable qubits and continuous variables, each exploiting a different aspect of light’s wave-particle duality.

  • II. HYBRID QUANTUM COMPUTING: Photonic quantum information processing has two major approaches, qubits and continuous variables, which exploit different aspects of light’s wave-particle duality.The paper introduces the hybrid approach after reviewing and comparing these two approaches.

A. Qubit approach

Photonic qubits encode information in single-photon degrees of freedom and require one-qubit rotations plus two-qubit entangling gates for universal computation. Linear-optical methods avoid strong nonlinearities but remain difficult to scale because entangling gates are probabilistic.

  • A. Qubit approach: A classical bit takes one of two values, whereas a qubit is a superposition of two logical states with information encoded in complex coefficients.The paper introduces qubits as the quantum analogue of classical bits.
  • A. Qubit approach: Universal qubit computation requires one-qubit rotation gates and two-qubit entangling gates.The former change qubit coefficients, while the latter create interactions between qubits.
  • A. Qubit approach: Photonic qubits can encode information in a single photon’s polarization, propagation direction, or arrival time.In polarization encoding, one-qubit gates correspond to rotating the photon’s polarization.
  • A. Qubit approach: A controlled-NOT gate would require a photon-conditioned π phase shift, but no known nonlinear optical material provides sufficient single-photon nonlinearity.The required conditional phase can arise through an optical Kerr effect in principle, but its strength is inadequate.
  • A. Qubit approach: KLM showed that scalable photonic quantum computation can use single-photon sources, detectors, and linear optics without a nonlinear medium.Its controlled-NOT gate is probabilistic and uses ancillary photons and linear-optical elements.
  • A. Qubit approach: Probabilistic two-qubit gates make larger-scale computation almost impractical because task-success probability decreases exponentially with the number of such gates.Alternative atom-cavity approaches introduce additional coupling, conversion-efficiency, and spectral-distortion difficulties.

B. CV approach

Continuous-variable (CV) quantum computing encodes information in continuous optical quadratures and can implement deterministic teleportation-based gates. Universal CV computation requires Gaussian operations together with at least one non-Gaussian gate, while one-way schemes apply gates through measurement choices.

  • CV encoding: CV quantum information is encoded in continuous real values using optical amplitude and phase quadratures x̂ and p̂.The state can also be expanded in the photon-number basis, with qubit computing occupying the zero- and one-photon subspace.
  • Universal gates: Universal CV quantum computation requires arbitrary Gaussian gates and at least one non-Gaussian gate involving a higher-order Hamiltonian.Gaussian gates use Hamiltonians linear or quadratic in x̂ and p̂, whereas non-Gaussian gates involve higher-order terms.
  • Universal gates: Photonic CV systems easily implement displacement, phase-shift, and beam-splitter operations, but squeezing and cubic-phase gates require nonlinear effects.The cubic-phase gate requires third-order nonlinearity, which is difficult to achieve for weak quantum light.
  • Teleportation: CV quantum teleportation can be deterministic because squeezed ancillary beams, joint quadrature measurements, and feedforward operations are deterministic.Its transfer fidelity is limited because perfect fidelity requires infinite squeezing and therefore infinite energy.
  • Teleportation: Changing ancillary states or measurement and feedforward configurations transforms CV teleportation into gates such as squeezing and cubic-phase operations.Teleportation-based gates replace direct nonlinear interactions on arbitrary input states with preparation of specific ancillary states.
  • One-way computation: One-way CV computation cascades teleportation circuits and applies different gates by changing measurement bases, while cluster-state preparation remains unchanged.Cluster states are prepared from squeezed light, then computation proceeds through repeated measurement and feedforward operations.

C. Hybrid qubit-CV approach

The hybrid qubit-CV approach combines robust qubit encoding with deterministic CV gates, enabling deterministic photonic-qubit teleportation and, in principle, fault-tolerant computation with finite squeezing.

  • Hybrid qubit-CV approach: One-qubit gates use beam splitters and phase shifts, while controlled-phase gates can be implemented deterministically by decomposing them into deterministic CV gates.The decomposition uses cubic phase gates and other Gaussian gates.
  • Hybrid qubit-CV approach: Broadband CV teleportation and narrowband photonic-qubit technologies enabled the first deterministic quantum teleportation of photonic qubits.Subsequent experiments included teleportation of two-mode photonic-qubit entanglement and deterministic squeezing gates on single photons.
  • Hybrid qubit-CV approach: CV gates also apply to higher-photon-number states, enabling teleportation of two-photon two-mode qutrits and quantum information beyond qubits.This exploits the infinite-dimensional Hilbert space of continuous variables.
  • Hybrid qubit-CV approach: GKP, cat, and binomial codes encode one logical qubit in a single optical mode, simplifying logical operations and error correction.The GKP code is reported to significantly outperform the other codes under photon loss in most cases.
  • Hybrid qubit-CV approach: CV teleportation enables deterministic quantum logic gates, unlike probabilistic qubit teleportation, but finite squeezing limits gate fidelity.The GKP approach provides a fault-tolerant squeezing threshold, with a conservative upper bound of 20.5 dB.
  • Hybrid qubit-CV approach: Producing GKP states and implementing error correction remain key technologies for the hybrid approach, despite reported optical squeezing up to 15 dB.Several optical methods for generating approximate GKP states await experimental demonstration.

III. STRATEGY FOR LARGE-SCALE QUANTUM COMPUTING

The paper examines architectures for large-scale photonic quantum computing that perform sequential CV gates on many qubits, focusing on time-domain multiplexed one-way and loop-based designs.

  • III. STRATEGY FOR LARGE-SCALE QUANTUM COMPUTING: The proposed strategy introduces time-domain multiplexed one-way quantum computation and loop-based architectures for sequential CV gates.The section also discusses the technical challenges associated with these architectures.

A. Typical architecture for photonic quantum computing

The conventional one-beam-per-qubit architecture is convenient at small scale but becomes impractical because circuits grow with computation size and lack programmability.

  • A. Typical architecture for photonic quantum computing: The standard architecture operates arrays of light sources in parallel, with gate components arranged sequentially along each optical path.This configuration is the most established way to build photonic circuits.
  • A. Typical architecture for photonic quantum computing: More than 500 mirrors and beam splitters were required for a single-step CV teleportation experiment, illustrating the construction difficulty of larger circuits.Circuit size increases with the number of qubits and gates.
  • A. Typical architecture for photonic quantum computing: Integrated photonic chips can miniaturize and scale photonic circuits while allowing parameters such as phase shifts and beam-splitter transmissivities to be adjusted.The paper describes integration of components including nonlinear materials, beam splitters, EOMs, and detectors.

B. Time-domain multiplexed one-way quantum computation

Time-domain multiplexing encodes many qubits in optical pulse trains sharing an optical path, enabling large-scale programmable computation with a constant number of components. It also supports deterministic generation of ultra-large-scale cluster states suitable for fault-tolerant one-way computation.

  • B. Time-domain multiplexed one-way quantum computation: Time-domain multiplexing encodes arbitrarily many qubits in optical pulses propagating through a single or few optical paths.This approach exploits light’s degrees of freedom to increase the number of encoded qubits efficiently.
  • B. Time-domain multiplexed one-way quantum computation: A constant number of optical components can support arbitrarily large-scale quantum computation using time-domain multiplexing.
  • B. Time-domain multiplexed one-way quantum computation: One-way quantum computation is programmable because different tasks use different measurement bases without changing the cluster-state preparation setup.
  • B. Time-domain multiplexed one-way quantum computation: Time-domain multiplexing deterministically generates ultra-large-scale continuous-variable cluster states by dividing continuous squeezed beams into time bins and coupling them with delays and beam splitters.
  • B. Time-domain multiplexed one-way quantum computation: With squeezing above a threshold, time-domain multiplexed one-way computation is presented as a route to scalable, universal, fault-tolerant photonic quantum computing using GKP qubits.

C. Loop-based architecture for photonic quantum computing

Loop-based architectures store pulse-encoded quantum information in an outer loop and process it sequentially in an inner loop. Dynamic control provides deterministic, programmable gates, while losses in long delays and switches remain a scalability constraint.

  • C. Loop-based architecture for photonic quantum computing: A nested-loop circuit stores n input pulses in an outer loop and uses an inner loop to sequentially perform teleportation-based gates.The outer loop acts as quantum memory, while the inner loop acts as the processor.
  • C. Loop-based architecture for photonic quantum computing: Dynamic control of beam splitter transmissivity, phase shift, feedforward gain, and measurement basis enables different gates for individual pulses.
  • C. Loop-based architecture for photonic quantum computing: Once required ancillary states are prepared, the architecture can deterministically perform all gates needed for universal continuous-variable quantum computation.
  • C. Loop-based architecture for photonic quantum computing: The architecture is programmable and can process many modes and steps without changing the photonic circuit, but optical losses from long delays and switches can limit performance.
  • C. Loop-based architecture for photonic quantum computing: An experiment using one squeezed-light source, one optical loop, variable optical components, and a tunable homodyne detector demonstrated programmable generation of various entangled states.

D. Technical challenges

Scaling time-domain photonic quantum computing requires shorter pulses, broader component bandwidth, and longer low-loss, stable delay lines. Current constraints imply practical trade-offs between qubit count, pulse duration, bandwidth, loss, and stability.

  • D. Technical challenges: The number of processable qubits is limited by delay-line length divided by optical-pulse width.This ratio determines both the input modes of two-dimensional cluster states and the pulses stored in loop-based architectures.
  • D. Technical challenges: Shortening pulses increases the number of qubits but broadens their frequency spectrum, requiring optical and electrical components with sufficient operational bandwidth.
  • D. Technical challenges: 100 MHz is the reported bandwidth for recent CV teleportation-based gates, with limitations mainly from homodyne detectors and squeezed-light sources.
  • D. Technical challenges: All-optical replacement of electronics can in principle increase system bandwidth beyond THz and reduce pulse width by several orders of magnitude.
  • D. Technical challenges: At 0.2 dB/km fiber loss, 100-m and 1-km fibers provide 99.5% and 95.5% transmission, corresponding to approximately 10 and 100 qubits for 50-ns pulses.

IV. CONCLUSION

The perspective identifies hybrid qubit-CV processing and time-domain multiplexing as routes toward scalable photonic quantum computing. Together with hardware-efficient error correction and all-optical bandwidth expansion, these ideas support large-scale fault-tolerant operation in principle.

  • IV. CONCLUSION: Hybrid qubit-CV processing combines deterministic continuous-variable operations with robust qubit encoding and can incorporate hardware-efficient error-correcting codes such as GKP qubits.
  • IV. CONCLUSION: Linear optical circuits with externally supplied nonlinearity can implement universal gates while avoiding pulse distortion and crosstalk associated with nonlinear optical systems.
  • IV. CONCLUSION: Time-domain multiplexed one-way and loop-based architectures increase the number of processable modes and support scalable photonic quantum computation.
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