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Optical hybrid approaches to quantum information

Peter van Loock

arXiv:1002.4788v1quant-ph

TL;DR

Optical quantum information schemes face limits when restricted to practical linear operations and resources. This review surveys hybrid approaches that combine discrete and continuous degrees of freedom, including weak and measurement-induced nonlinearities. It describes deterministic weakly nonlinear gates that may support efficient growth of some simple graph states.

  • Problem

    Practical linear optical resources alone do not provide CV or DV universality, while nonlinear interactions at the single-photon level are difficult to obtain.

    Source: §1.1 · p. 2, §2.3.2 · p. 8

  • Method

    The review surveys optical hybrid approaches combining DV and CV resources with weak or measurement-induced nonlinearities.

    Source: §3.1 · p. 17, §3.3.3 · p. 23

  • Results

    Deterministic, measurement-free weakly nonlinear gates may support efficient growth of simple linear or star graph states, with the qumode interacting as little as twice with each qubit.

    Source: §3.3.5 · p. 28

  • Takeaways & Limitations

    These gates may offer an alternative to nondeterministic standard linear-optics approaches for growing certain graph states.

    Source: §3.3.5 · p. 28

    Realizing more advanced or ultimately universal optical protocols depends substantially on experimentally implementing nonlinear measurements such as photon-number-resolving detections.

    Source: §3.3.4 · p. 27

Abstract

from arXiv · show

This article reviews recent hybrid approaches to optical quantum information processing, in which both discrete and continuous degrees of freedom are exploited. There are well-known limitations to optical single-photon-based qubit and multi-photon-based qumode implementations of quantum communication and quantum computation, when the toolbox is restricted to the most practical set of linear operations and resources such as linear optics and Gaussian operations and states. The recent hybrid approaches aim at pushing the feasibility, the efficiencies, and the fidelities of the linear schemes to the limits, potentially adding weak or measurement-induced nonlinearities to the toolbox.

1. Introduction

Optical quantum information draws on mature state-preparation techniques and linear optical elements, but discrete- and continuous-variable approaches face different practical trade-offs and limits. The review describes hybrid approaches that combine DV and CV resources and may add weak or measurement-induced nonlinearities.

1. Introduction

  • Discrete-variable schemes can achieve fairly high fidelities but typically rely on heralding, whereas continuous-variable schemes offer unconditional operations and high efficiencies at lower fidelities.The approaches use, respectively, photonic qubits and continuous-variable states in infinite-dimensional Hilbert spaces.Source: §1 · p. 2
  • Hybrid protocols combine DV and CV states, encodings, gates, measurements, and techniques to address limitations of schemes based on either type alone.Optical demonstrations draw on mature state-preparation techniques such as parametric down conversion and accessible linear elements such as beam splitters.Source: §1 · pp. 1–2

1.1. CV versus DV

  • Gaussian transformations alone cannot provide CV universality, and linear optical elements cannot provide DV universality or complete photonic two-qubit Bell measurements.Single-photon nonlinear interactions are difficult to obtain.Source: §1.1 · p. 2

1.2. Going hybrid

  • Weak nonlinearities can be enhanced with intense light fields and mediated between DV components by a bright CV qubus, supporting tasks from Bell-basis projections to entangling gates.Measurement-induced nonlinearities are another ingredient; KLM is fully DV-based, while GKP uses DV measurements with CV resources and encodes logical DV states in physical CV states.Source: §1.2 · pp. 2–3
  • The review identifies hybrid states and operations, qubus systems, weak nonlinearities, and measurement-induced nonlinearities as ingredients for pursuing feasibility, efficiency, and quantum advantage.The article covers optical encoding and processing before surveying hybrid protocols for computation and communication.Source: §1.2 · p. 3

2. Optical quantum information

This section frames optical quantum information around how information is encoded in optical states and processed efficiently. It distinguishes levels of efficiency according to encoding, scalability, and the feasibility of required resources.

2. Optical quantum information

  • Optical quantum information can encode information, including a qubit, into optical states using different types of encoding.The section raises how quantum information can be encoded into optical states and whether those states naturally permit different encodings.Source: §2 · p. 3
  • Processing optical quantum information efficiently depends on the encoding and on the scalability and feasibility of the required optical resources.The section distinguishes qualitatively different levels of efficiency.Source: §2 · p. 3
  • The section addresses both optical-state encoding and the efficient processing of information encoded in those states.Source: §2 · p. 3

2.1. Linear versus nonlinear operations

The section distinguishes linear optical transformations from nonlinear interactions and describes how practical optical resources implement the former. It also discusses offline non-Gaussian resources as an alternative to online nonlinear transformations.

2.1. Linear versus nonlinear operations

  • Linear transformations generated by quadratic Hamiltonians act linearly on mode operators and include passive elements and squeezers.The general LUBO also includes phase-space displacements; its active and passive components can be implemented using single-mode squeezers, phase shifters, and two-mode beam splitters.Source: §2.1 · pp. 3–4
  • In the hybrid context, the linear resources include offline-prepared optical Gaussian states and general LUBOs, with coherent states and homodyne detection identified as practical resources.The section also includes deterministic online squeezing in this toolbox.Source: §2.1 · p. 4
  • Cubic or higher-order interactions produce nonlinear transformations that can map Gaussian states to non-Gaussian states, but weak interactions may require long times during which photon losses dominate.An extremely weak Kerr effect in an optical fiber is given as an example.Source: §2.1 · p. 4
  • Offline nonlinear resources such as Fock and cat states can replace online nonlinear transformations, but their preparation is typically probabilistic and conditional on measurement outcomes.The section points to examples of highly nonlinear interactions in Fig. 2.1.2.Source: §2.1 · p. 4

2.2. Qubits versus qumodes

This section contrasts digital-style two-level qubits with infinite-dimensional qumodes represented by optical phase-space variables, then compares their encodings, tools, and tradeoffs.

2.2.2. Photonic qumodes

  • Qumodes encode optical states in an infinite-dimensional space using phase-space variables; position and momentum eigenstates can serve as a continuous-variable basis.Source: §2.2 · pp. 4–5, §2.2.2 · p. 6

2.2.1. Photonic qubits

  • Single-rail encoding uses one optical mode, but even single-qubit rotations require nonlinear interactions because they transform vacuum into a non-Gaussian superposition.The Hadamard gate is given as an example.Source: §2.2.1 · p. 5
  • Dual-rail qubits allow simple single-qubit rotations, but entangling two such qubits requires an interaction between two photons and therefore some form of nonlinearity.Polarization encoding is a specific dual-rail encoding, with rotations corresponding to polarization rotations.Source: §2.2.1 · p. 5
  • Practical photonic-qubit processing uses single-photon resources and passive linear optics; on/off detectors distinguish vacuum from non-vacuum but do not resolve photon number.Creating many-photon Fock states and counting large photon numbers are described as difficult.Source: §2.2.1 · p. 5
  • Single-photon encoding is fairly noise-robust and typically supports high-fidelity processing, though operations are often conditional and can have very low success probabilities.Source: §2.2.1 · p. 5

2.2.2. Photonic qumodes

  • Qumodes can use approximate quadrature eigenstates or coherent states as a basis; two coherent states can also be discriminated without error using a probabilistic linear-optical scheme.The described scheme uses a beam splitter, an ancilla coherent state, and on/off detectors.Source: §2.2.2 · p. 6
  • Gaussian qumode processing includes displacements, passive optics, and squeezers, while homodyne detection is near-unit efficiency; finite squeezing, loss, and noise constrain state quality.Gaussian entangled states can be produced efficiently and unconditionally from squeezed light through beam splitters, but their quality is limited by finite squeezing.Source: §2.2.2 · p. 7

2.3. Implementing efficient quantum computation efficiently?

The section frames efficiency as polynomial rather than exponential physical-resource scaling, then compares optical gate and computation strategies against that criterion. It describes distinct DV and CV trade-offs in probability, resources, and fidelity.

2.3. Implementing efficient quantum computation efficiently?

  • Efficient quantum computation requires physical resources to scale as N or a polynomial of N, rather than exponentially with the 2^N-dimensional logical space.The section distinguishes this in-principle criterion from experimental efficiency, which depends on current technology.Source: §2.3 · p. 7

2.3.1. Universal sets

  • Universal processing of the discussed optical encodings requires at least one gate unavailable from linear transformations alone.The section notes that even a single-rail Hadamard or a dual-rail entangling gate requires nonlinearity.Source: §2.3.1 · pp. 7–8

2.3.2. Nonlinear versus linear optics

  • A self/cross-Kerr coupling of approximately π is infeasible at the single-photon level, motivating linear-optics alternatives.Multiple-rail encoding implements any unitary on a d-level system using one photon in d optical modes, but scales poorly as the number of qubits grows.Source: §2.3.2 · pp. 8–9

2.3.3. Teleportation-based approaches

  • KLM uses photon-counting-induced probabilistic gates and auxiliary photonic states; feedforward and teleportation can make operations asymptotically near-deterministic.Near-deterministic KLM operations remain impractical because the required ancilla states are too complicated to engineer with current experimental capabilities.Source: §2.3.3 · p. 9

2.3.4. Cluster-based approaches

  • Cluster computation encodes gates in an offline entangled state and applies them through local measurements, reducing linear-optics resource costs and making online computation deterministic.Scalability and resource costs depend on how efficiently cluster states can be grown using probabilistic entangling gates.Source: §2.3.4 · p. 10
  • CV cluster computation approaches full CV universality by combining linear Gaussian and nonlinear non-Gaussian measurements on an approximate Gaussian cluster state.The section also notes that Gaussian operations on Gaussian states are efficiently classically simulable.Source: §2.3.1 · p. 8, §2.3.4 · p. 10
  • DV schemes are probabilistic but can reach near-unit fidelities with extra resources, whereas CV schemes are typically deterministic but have fidelities below unity.Source: §2.3.4 · p. 11
  • Even efficient and reliable long-distance quantum communication with linear operations may require resources comparable to optical quantum computation.Source: §2.3.4 · p. 11

2.4. Implementing efficient quantum communication efficiently?

Direct optical transmission is vulnerable to losses, while quantum repeaters can extend communication over arbitrary distances with subexponential resource growth if sufficient memories and quantum error detection are available. The section reviews repeater mechanisms and their practical constraints, including the fidelity–rate trade-off in DLCZ.

Direct transmission

  • Direct transmission suffers exponentially decreasing photon arrival probability, and unknown photon states cannot be copied along the channel.Loss and excess noise also degrade quantum-state transfer over distance.Source: §2.4 · p. 11

Quantum repeaters

  • Repeaters distribute entangled pairs between nearby stations, then use swapping to extend their range and purification to distill high-fidelity pairs.Purification addresses the low-fidelity pairs that can result from imperfect initial generation and swapping.Source: §2.4 · pp. 11–12
  • With sufficient local quantum memories and quantum error detection, repeaters support communication over arbitrary distances with resources scaling subexponentially with distance.Without that scaling, direct transmission would be no less efficient in resource terms.Source: §2.4 · p. 12

Practical constraints

  • A naive chain of teleportation segments without error detection or memories does not provide efficient resource scaling, though it may help resolve single-photon signals against detector dark counts.Experimental quantum communication had reached about 250 km in the section’s account.Source: §2.4 · p. 12
  • Repeater operation requires memory during classical confirmation waits; available memories of about 1 s do not meet the needs of a fully nested protocol.Local error-detection logic can increase those memory requirements further.Source: §2.4 · p. 12

Trade-offs

  • Heralded schemes can yield high initial entanglement fidelity but small pair-generation rates, and also face phase-stabilization and purification complications.Fully CV approaches avoid heralding but Gaussian states and operations alone cannot perform entanglement distillation.Source: §2.4 · pp. 12–13

DLCZ

  • DLCZ combines weakly excited CV Gaussian resources with DV photon detection to conditionally prepare DV entangled states.Collective enhancement in sufficiently large atomic ensembles suppresses spontaneous-emission effects.Source: §2.4 · p. 13
  • As the squeezing parameter r decreases, DLCZ pair fidelity approaches 1 as F ≈ 1 − r^2, while average creation time grows as T ≈ T0/r^2.Here T0 ≡ tint + L0/c.Source: §2.4 · p. 13

3. Hybrid approaches

Hybrid quantum information schemes exploit discrete and continuous degrees of freedom together, motivated by the limitations of approaches restricted to either one. Their motivation includes tasks that Gaussian resources and operations alone cannot accomplish.

Hybrid protocols

  • A hybrid protocol uses both discrete- and continuous-variable degrees of freedom to manipulate and measure quantum subsystems.Optical qumodes naturally represent continuous variables, while atomic spins and other two-level systems provide qubits.Source: §3 · p. 13

Motivation

  • Combining CV and DV approaches is motivated in part by Gaussian resources being insufficient for several advanced tasks.The cited examples include qumode error detection and correction and universal quantum computation on qumodes.Source: §3 · p. 13

3.1. Overview

The overview surveys hybrid optical protocols that combine discrete and continuous resources or operations to address constraints of linear approaches. It ranges from state engineering and measurement to hybrid entanglement, weak nonlinearities, and implementation requirements.

Motivation

  • Even ideal-efficiency linear elements and photon detectors do not remove the fundamental restrictions and no-go results of the linear approaches.Improved experimental performance alone, including increased squeezing, cannot resolve them.Source: §3.1 · p. 14

Hybrid strategies

  • Hybrid schemes combine nonlinear resources with linear operations, or linear resources with nonlinear operations, and may also use weak or measurement-induced nonlinearities.The review considers such approaches for hybrid computation and communication.Source: §3.1 · p. 14

Applications

  • The overview spans coherent-state discrimination, cat-state engineering, entanglement distillation, and quantum computational resources.Examples include photon-counting and homodyne-based methods, as well as conditional non-Gaussian state preparation.Source: §3.1 · pp. 14–15

Implementation

  • Hybrid implementations require time-resolved homodyning synchronized with photon-counting events and bandwidths of at least ∼100 MHz, rather than the ∼30 kHz used in standard continuous-wave experiments.The stated bandwidth corresponds to timescales of about 100 ns.Source: §3.1 · p. 15

Quantum state engineering

  • Offline squeezing of a Fock state with CV homodyne detection and postselection can produce an approximate cat state while preserving input non-Gaussianity [110].An experiment produced a cat state squeezed by 3.5 dB.Source: §3.1 · p. 15

State discrimination

  • Displacing, squeezing, or applying a nonlinear transformation before an on/off detector progressively improves binary coherent-state discrimination, with the nonlinear transformation attaining minimum error.The approaches beat the optimal receiver based only on homodyne detection.Source: §3.1 · pp. 15–16

Online squeezing

  • Online squeezing can benefit tasks beyond state engineering, including near-minimum-error coherent-state discrimination and measurement-based nonlinear gate corrections.It could also unsqueeze the cat state produced in the cited experiment.Source: §3.1 · p. 16

Hybrid entanglement

  • A weak dispersive interaction makes a qumode’s phase rotation depend on the qubit state, creating hybrid entanglement that qubit measurement can convert into a cat state.The phase angle can be small, around θ ∼ 10^-2, while a sufficiently large coherent amplitude can yield a large cat state.Source: §3.1 · pp. 16–17

3.2. Hybrid entanglement

Hybrid entanglement can be quantified by representing relevant states in effective two-dimensional spaces, while moment-based partial-transposition tests extend detection when that representation is unavailable. The section also considers transferring continuous-variable entanglement to remote discrete-variable qubits, with loss and coupling conditions constraining the transfer.

3.2.1. Qubit-qumode entangled states

  • Qumode-qumode quasi-Bell states can be maximally entangled two-qubit states regardless of mode-state overlap, with the relative phase determining the state.For coherent-state examples, amplitude damping leaves the states expressible as two-qubit density operators, but decoherence is faster for larger α.Source: §3.2.1 · pp. 17–18
  • |Ψ−⟩ has exactly 1 ebit for every α≠0, whereas |Ψ+⟩ reaches Bell-state form only as α→∞; these hybrid states are bounded by one ebit, unlike squeezed Gaussian states.The cited comparison notes that about 10 dB of squeezing corresponds to about 3 ebits.Source: §3.2.1 · p. 18
  • Partial-transposition moment hierarchies unify continuous-variable inseparability criteria; higher moments can detect non-Gaussian entanglement missed by second moments, and fourth-order-moment entanglement has been detected experimentally.A sufficiently high-order moment subdeterminant for |Ψ−⟩ is negative for every nonzero α, proving that state is entangled.Source: §3.2.1 · pp. 18–19

3.2. Hybrid entanglement

  • Entanglement quantification is straightforward when hybrid or non-Gaussian states can be represented in two-dimensional subspaces; otherwise, moment-matrix partial-transposition criteria can test inseparability.The section also asks whether potentially unbounded continuous-variable entanglement can be transferred to discrete-variable qubit systems.Source: §3.2 · p. 17, §3.2.1 · p. 19

3.2.2. Qubit-qumode entanglement transfer

  • Entangled two-mode squeezed fields can drive remote cavities containing two-level systems, with cavity-qubit interactions transferring continuous-variable entanglement to the atomic qubits.In the weak-coupling regime, the cavity steady state becomes a two-mode squeezed state; the transfer scheme is considered with ideal channel transmission in the section’s analysis.Source: §3.2.2 · pp. 19–20
  • A nearly pure atomic steady state requires sufficiently large cooperativity; channel losses degrade shared continuous-variable entanglement, though it remains nonzero unless thermal noise is also present.Cooperativity is given as proportional to 1/(Γκ).Source: §3.2.2 · pp. 19–20

3.3. Hybrid quantum computing

This section surveys hybrid optical quantum computing approaches involving qubit–qumode encodings and interactions, alongside offline nonlinear resources and linear online processing. It covers these and related routes, including Gaussian cluster resources with nonlinear measurements, to hybrid optical gates and computation.

3.3.1. Encoding qubits into qumodes

  • Dual-rail and fixed-photon multi-rail encodings embed DV states in qumodes; dual rail detects errors, while photon-loss-affected multiphoton states can retain high entanglement.Linear optics can universally process single-photon multi-rail states, but not scalably without complicated ancillas and feedforward.Source: §3.3.1 · pp. 20–21
  • GKP encoding protects logical qubits against sufficiently small phase-space shifts, but Gaussian operations yield only Clifford gates, so universality needs physical non-Gaussian operations.The required non-Gaussian operations or resources make fault-tolerant, universal qubit-in-qumode processing difficult to implement.Source: §3.3.1 · p. 21

3.3.2. Hybrid Hamiltonians

  • Elementary hybrid Hamiltonians including controlled rotations and displacements can generate universal computation; a qumode bus can mediate an exact finite-time two-qubit entangling gate without direct qubit interaction.The exact qubus construction matters because switching Hamiltonians over arbitrarily short intervals is unrealistic; the alternative uses a controlled geometric phase gate.Source: §3.3.2 · p. 22

3.3.3. Nonlinear resources and linear operations

  • GKP prepares approximate cubic phase states offline from Gaussian squeezed resources and photon-number measurements, then uses linear Gaussian operations and homodyne detection to enact cubic gates.The measurement-dependent state preparation requires phase-free squeezing corrections.Source: §3.3.3 · p. 23
  • With nonlinear offline CV resources and homodyne Bell measurements, correction degree is one below gate order; cubic gates alone need only Gaussian online operations.Quartic gates instead require cubic corrections.Source: §3.3.3 · pp. 23–24
  • A teleported quartic self-Kerr gate with beam splitters yields an approximate, unconditional, deterministic two-qubit CZ, but its intervening corrections remain cubic.Those cubic corrections require further nonlinear processing.Source: §3.3.3 · p. 24
  • For the NSS gate, Ref. obtains fidelities F > 0.9 only at success probabilities < 10−4, while offline nonlinear ancillas could leave online operations linear.The proposal’s postselection makes it fairly inefficient; the passage presents offline preparation of reasonably faithful nonlinear resource states as promising for universal processing.Source: §3.3.3 · p. 25

3.3.4. Linear resources and nonlinear operations

  • Cubic gates can use offline cubic states with linear online operations, or Gaussian cluster resources with online photon-number measurements and cluster-implemented squeezing corrections.In the latter implementation, the photon-number measurement must precede the other measurements because the desired cubic gate is non-Gaussian.Source: §3.3.4 · pp. 25–26
  • CV cluster computation can implement gates through measurement choices, with Fourier transforms switching between x and p gates and vertical CZ links completing the universal set.The cluster is prepared offline; computation is universal in the approximate, asymptotic sense, and the CZ links require a cluster at least two-dimensional.Source: §3.3.4 · p. 25
  • A linear four-mode CV cluster supports arbitrary single-mode LUBOs, while a finite two-dimensional cluster of ∼N^2 qumodes supports arbitrary N-mode LUBOs.The approach performs squeezing offline, avoiding online squeezing of fragile non-Gaussian states; the single-mode scheme was experimentally implemented [208].Source: §3.3.4 · p. 26
  • Universal cluster protocols depend on experimentally available nonlinear measurements, while finite-squeezing imperfections may require nonlinear elements for error correction.An alternative is to use Gaussian ancillas with nonlinear measurements for difficult gates such as the NSS gate, while implementing simpler dual-rail qubit gates directly.Source: §3.3.4 · p. 27

3.3.5. Weakly nonlinear operations

  • Weak interactions with θ ∼ 10−2 require displacements corresponding to about 10^4 mean photons, making gates more sensitive to photon loss; ideal protocols reach unit fidelity and efficiency only with perfect interactions.The large displacements increase loss sensitivity, so each gate protocol requires careful loss analysis.Source: §3.3.5 · p. 28
  • Deterministic, measurement-free gates using weak qubit–qumode interactions can generate two-qubit entanglement and may efficiently grow linear or star qubit graph states.For these simple graph states, the qumode may interact only twice with each qubit.Source: §3.3.5 · pp. 27–28

3.4. Hybrid quantum communication

Hybrid quantum communication uses optical qumodes to distribute entanglement and transfers it to qubit memories, with measurement and postselection shaping the fidelity–efficiency trade-off. Repeater proposals combine weak, loss-sensitive traveling qumodes with local operations and identify unresolved implementation challenges.

Repeater architecture

  • A hybrid repeater can use measurement-free entangling sequences locally and measurement-based preparation for nonlocal entanglement, with postselection of favorable results after channel losses.Its distillation and swapping stages require local entangling gates, qubit measurements, and classical communication.Source: §3.4 · pp. 29–30

Entanglement transfer

  • The hybrid qubit–qumode entanglement after fiber loss can be transferred to two qubits, with its quality trading off against initial qumode photon number.The plotted entanglement of formation reflects competing effects: large photon numbers increase loss-induced decoherence, while small numbers yield little initial entanglement.Source: §3.4 · p. 29

Measurement choices

  • Homodyne detection along the x-axis requires very large qumode amplitudes to suppress overlap errors when interactions are weak, worsening loss-induced decoherence.For θ ∼10^-2, the cited example requires photon numbers of ∼10^8.Source: §3.4 · p. 30
  • Homodyne detection along p has peak distances scaling as ∼αθ, but requires postselection and cannot completely transfer entanglement at optimal transmission.Discarding outcomes reduces pair-creation efficiency, while retaining only selected outcomes trades efficiency against fidelity.Source: §3.4 · p. 30
  • Non-Gaussian unambiguous state discrimination can eliminate bit-flip errors, while related measurement variations allow fidelity to be tuned against success probability, including near-unit fidelities at reasonable probabilities.The review also identifies photon-number-resolving detection with two probe pulses, CSS-state projections, and homodyne detection using squeezed-state ancillae as possible variations.Source: §3.4 · p. 30

Repeater architecture

  • Local qumode ancillae may use large amplitudes because their losses do not depend on channel distance, whereas traveling qumodes must remain sufficiently weak to resist loss.Local homodyne detection can support two-qubit operations; nonlocal qumodes may instead use non-Gaussian photon measurements.Source: §3.4 · pp. 30–31
  • Hybrid flying-qumode repeaters use 10–30 km station spacing and avoid the long-distance interferometry required by flying-qubit approaches.Open issues include efficient memory transfers, error-resistant distillation and connections, and full optimization against non-hybrid repeaters.Source: §3.4 · pp. 30–31

4. Summary and outlook

The review surveys hybrid optical approaches that combine discrete and continuous variables to address limitations of schemes restricted to Gaussian resources and operations. It presents hybrid protocols as a promising route, while noting that finite squeezing creates computation errors and that error correction itself requires a nonlinear element.

Summary and outlook

  • Gaussian-only continuous-variable states and operations cannot provide universal quantum computation, entanglement distillation, or more general quantum error correction.The review also notes that fully Gaussian qumode computing can be efficiently simulated classically.Source: §4 · p. 31
  • Hybrid protocols combine discrete and continuous variables, using non-Gaussian measurement or nonlinear interactions to work around restrictions of Gaussian approaches.Examples include Gaussian cluster states paired with non-Gaussian measurement and intense Gaussian pulses acting as a quantum bus for qubit interactions.Source: §4 · p. 31
  • The review presents hybrid schemes combining linear resources with measurement-induced or weak nonlinearities as a promising route to optical quantum computation and communication.It frames these schemes as part of efforts to combine stable matter systems for storage and processing with photonic systems for communication.Source: §4 · p. 31
  • Finite squeezing in Gaussian cluster states causes computation errors, and suppressing them requires efficient quantum error correction that itself needs a nonlinear element.Thus, unconditional preparation of the linear resource states does not remove the need for nonlinear resources elsewhere in the computation.Source: §4 · p. 31
  • The review identifies photonic qubits processed with polarization dual-rail encoding and coupled through nonlinearly transformed or measured Gaussian qumode ancillae as a promising hybrid approach.Source: §4 · p. 32
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