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Why I am optimistic about the silicon-photonic route to quantum computing

Terry Rudolph

arXiv:1607.08535v1quant-ph

TL;DR

The paper addresses how to build a large-scale silicon-photonic quantum computer despite source nondeterminism, optical loss, and device imperfections. It outlines an architecture based on multiplexed 3-photon entangled-state sources and ballistic interferometry, arguing that universal cluster-state computation can follow without quantum memory. The overview concludes that low environmental stochastic noise and tolerable known static imperfections make the route promising, while substantial photonics-specific theory remains.

  • Problem

    The central challenge is constructing a scalable photonic quantum computer whose sources, imperfections, and cluster-state use are sufficiently understood for large computations.

  • Method

    The paper presents a silicon-photonic architecture that multiplexes heralded single photons into small entangled states, then scatters them ballistically through an interferometer to produce a universal cluster state.

  • Results

    Optical-frequency photons in passive interferometers have presently unmeasurable and expectedly very small environmental stochastic noise, while known static imperfections can still permit universal computation in the discussed example.

  • Takeaways & Limitations

    The proposed architecture can use a constant number of photonic elements per photon, avoid proper quantum memory, and support arbitrary gates once a functional photonic qubit exists.

Abstract

from arXiv · show

This is a short overview explaining how building a large-scale, silicon-photonic quantum computer has been reduced to the creation of good sources of 3-photon entangled states (and may simplify further). Given such sources, each photon need pass through a small, constant, number of components, interfering with at most 2 other spatially nearby photons, and current photonics engineering has already demonstrated the manufacture of thousands of components on two-dimensional semiconductor chips with performance that allows the creation of tens of thousands of photons entangled in a state universal for quantum computation. At present the fully-integrated, silicon-photonic architecture we envisage involves creating the required entangled states by starting with single-photons produced non-determistically by pumping silicon waveguides (or cavities) combined with on-chip filters and nanowire superconducting detectors to herald that a photon has been produced. These sources are multiplexed into being near-deterministic, and the single photons then passed through an interferometer to non-deterministically produce small entangled states - necessarily multiplexed to near-determinism again. This is followed by a `ballistic' scattering of the small-scale entangled photons through an interferometer such that some photons are detected, leaving the remainder in a large-scale entangled state which is provably universal for quantum computing implemented by single-photon measurements. There are a large number of questions regarding the optimum ways to make and use the final cluster state, dealing with static imperfections, constructing the initial entangled photon sources and so on, that need to be investigated before we can aim for millions of qubits capable of billions of computational time-steps. The focus in this article is on the theoretical side of such questions.

I. INTRODUCTION

The overview argues that silicon photonics may offer exceptionally low stochastic noise, while its constant photon overhead can be absorbed by error correction. Its architecture reduces scaling to producing small entangled photon states, after which modular interferometry can generate universal cluster-state computation without quantum memory.

  • Motivation: PICs may reduce stochastic noise several orders of magnitude below optimistic estimates for matter-based approaches.The passage gives raw stochastic error rates of 10^-6 as a pessimistic estimate and expects at least 10^-8 with current devices.
  • Architecture: The architecture’s primary challenge is efficiently producing small 3-photon entangled states on a PIC, rather than scaling controlled matter-based qubits.Given such sources, the large-scale architecture is an interferometer built from high-precision fabricable components.
  • Architecture: Less than 20 physical photons per final cluster-state qubit are expected, with only two photons passing through potentially noisy active elements.This overhead is lower than the roughly 100 physical photons per raw computational photon described for nondeterministic linear-optical gates.
  • Architecture: All photons pass through a constant number of photonic elements regardless of computation size, and no proper quantum memory is required.The modular cluster-state architecture also supports arbitrary numbers of functional photonic qubits and arbitrary gates between them.
  • Open questions: The article emphasizes that substantial photonics-specific theory remains necessary because much existing matter-based theory does not address photonic construction challenges.It does not advocate abandoning matter-based approaches.

A. Photons need to be indistinguishable from their neighbors

The proposed architecture requires photons to interfere locally with nearby photons, making source quality and wavepacket matching central engineering requirements. Static trimming can improve interference by precisely adjusting PIC components without ongoing maintenance or power consumption.

  • A. Photons need to be indistinguishable from their neighbors: Each photon must interfere with at most 3 spatially nearby photons, ideally with the same wavepacket.The architecture therefore requires considerable improvement in photon sources and wavepacket indistinguishability.
  • A. Photons need to be indistinguishable from their neighbors: Laser trimming can enhance interference by precisely manipulating the final single-photon state.The adjustment is set-and-forget: it changes static device properties without maintenance or power consumption.

B. Static imperfection is not stochastic noise

The paper distinguishes static, characterizable imperfections from stochastic noise and argues that known imperfections may still support universal computation. It identifies modeling how manufacturing errors affect the large-scale cluster state as an open theoretical problem.

  • B. Static imperfection is not stochastic noise: PIC manufacturing imperfections are static rather than time-drifting, producing systematic error when their details are unknown.Known systematic imperfections are described as more benign and potentially correctable algorithmically or through measurement choices.
  • B. Static imperfection is not stochastic noise: A vague possibility is that systematic imperfection produces a state in the same symmetry-protected universality class as the cluster state.The passage presents this as uncertain and notes that further theory is needed.
  • B. Static imperfection is not stochastic noise: Near-unit fidelity to the ideal cluster state is unnecessary because local imperfections can drive overlap toward zero while computation remains viable.The relevant requirement is precise knowledge of the actual state, not necessarily high overlap with the ideal state.
  • B. Static imperfection is not stochastic noise: For a bond-percolated lattice, |⟨+|˜+⟩i|2 approximately 0.96 would suffice for infinite localizable entanglement and computational universality in the example discussed.The example uses ideal controlled-Z operations with known, varying single-qubit states and individual filtering or removal.
  • B. Static imperfection is not stochastic noise: The paper asks whether manufacturing imperfections can be modeled simply enough to apply existing measurement-based quantum-computation theory.This is identified as a largely unexplored theoretical question.

III. LOGICAL OVERVIEW OF THE ARCHITECTURE

The logical architecture generates a bond-percolated three-dimensional cluster state from small entangled states, then uses single-photon measurements to implement computation. Its scalability relies on efficient percolation, limited computational windows, and a two-dimensional chip capable of producing arbitrarily large logical clusters with at most one crossing.

  • Logical cluster state: The proposed logical state is a bond-percolated 3D lattice whose measurement bases are selected by an efficient classical side-computation.The architecture is modular apart from phase shifts applied before measurement.
  • Logical cluster state: The cluster’s z-direction represents time, and only a computational window of nearby photons must remain alive during measurement.Measurement choices can depend on lattice features behind the leading layer, requiring a finite window.
  • Computational methods: Method 1 carves paths encoding single qubits, whereas Method 2 uses the originating surface code and offers likely stochastic-noise tolerance.For Method 1, preliminary simulations indicate paths can continue essentially indefinitely with a computational window of about 10–15.
  • Computational methods: Photon loss can be handled by computational-basis measurements that logically remove lost photons, although the described recovery is probably not optimal.The method relies on the lattice being percolated well above threshold.
  • Computational methods: Once the cluster exists, one- and two-qubit gates differ only in their patterns of single-photon measurements.This makes the photonic progression from single-qubit to two-qubit operations unlike the conventional hardware progression.
  • Scaling and geometry: A y-depth of 6 can yield paths extending O(10^4) qubits in the x and z directions, demonstrating efficient large-scale entanglement from 3-photon GHZ resources.The proposed 2D chip architecture can generate arbitrarily large 3D logical clusters with at most one photon crossing.
  • Scaling and geometry: A 1+1-dimensional architecture becomes problematic for Method 2 because maintaining surface-code fault tolerance would require interaction nonlocality to grow with computation size.The alternative 2+1-dimensional design avoids this issue while retaining bounded photon crossings.

IV. PHYSICAL OVERVIEW OF THE ARCHITECTURE

The physical architecture places photon sources, interferometers, delays, phase shifters, and detectors on a two-dimensional semiconductor wafer. Its design concentrates active control on computational photons while using boosted fusion gates to connect unit cells into the logical cluster.

  • Wafer architecture: The wafer’s x and y dimensions correspond to the logical cluster lattice, forming a 2+1-dimensional architecture.Sources occupy one region, interferometers the middle, and detectors the far end.
  • Sources and computation: Each unit cell contains 6 sources producing 3-photon GHZ states, with 18 emitted photons and 2 computational photons in the final logical lattice.The computational photons are separated by a delay of about 10–15 clock cycles before basis selection.
  • Sources and computation: Only the 2 computational photons pass through active phase shifters; the remaining photons support fusion, measurement, or inter-cell connections.The unit-cell layout has only one photon crossing, at the center.
  • Inter-cell fusion: Boosted Type-II fusion raises the cluster-joining success probability from 1/2 to 3/4 by consuming four single photons or a Bell pair.The fusion interferometers connect neighboring unit cells.
  • Physical resources: Each photon has an optical depth of about 10 and interferes with at most 3 other photons.This short world line is a central physical simplification of the architecture.
  • Physical resources: If CMOS-compatible, highly pure 3-photon sources exist, the architecture requires 16 physical photons per final cluster-state qubit and only 2 photons through potentially noisy active elements.The remainder is an interferometer built from components already fabricable to suitable tolerances.
  • Open questions: The proposal leaves open whether 3-photon GHZ states are necessary and whether fusion probabilities can be improved with no more-entangled ancillas.The authors also report no current method for verifying optimality of existing interferometer designs.

V. DETECTORS

Integrated superconducting detectors have removed much of the detector bottleneck for photonic quantum computing, with high efficiency, low jitter, rapid reset, and negligible dark counts considered achievable. Small detector improvements may substantially reduce the scale required when sources are multiplexed.

  • Detector capabilities: Number-resolving, fully integrable superconducting detectors have substantially addressed detectors as a primary obstacle to photonic quantum computing.The paper presents detector development as nearing a complete solution to this bottleneck.
  • Detector capabilities: High-90s efficiency, low-10s-picoseconds jitter, reset times of tens of nanoseconds, and vanishing dark counts are achievable.These performance characteristics are especially valuable for multiplexed photon sources.
  • Scaling implications: Small detector-efficiency improvements can produce large downstream savings in the overall computer’s scale, particularly with multiplexed sources.The leverage arises because source multiplexing compounds detector-performance requirements.

VI. SWITCHES/PHASE SHIFTERS

Switches and phase shifters are the architecture’s main sources of stochastic noise, so the design seeks to minimize active components and characterize static imperfections separately. Current devices trade speed against loss, while the relevant measurement error may be predominantly Pauli-Z type.

  • Device tradeoffs: Mach–Zehnder phase shifters can implement switches, with electro-optical devices favored for speed and electro-mechanical devices offering low loss but slower operation.Thermo-electric phase shifters are described as slow.
  • Device tradeoffs: Silicon switches currently trade speed for loss: gigahertz devices are lossy, whereas megahertz devices can have very low loss.Intermediate performance characteristics are also possible.
  • Noise sources: Static imperfections can be characterized and corrected more readily than stochastic noise from active-element imprecision.The relevant static effects include fabrication tolerances, voltage accuracy, and photon-wavepacket properties.
  • Measurement control: High-quality GHZ sources would limit each photon to at most one switch or phase shifter before measurement.Surface-code plus magic-state operation requires computational photons to be measured in Pauli-X or Z bases.
  • Measurement control: A set-and-forget design can route photons to either direct detectors or a static 50:50 beamsplitter, enabling precise characterization and tuning of effective X and Z measurements.Only the routing switch remains dynamically controlled.
  • Noise estimates: Switch noise probably affects mainly the relative phase between paths entering the 50:50 beamsplitter for X measurement, producing predominantly Pauli-Z-type error.The paper calls for better direct measurements of achievable stochastic-noise levels.
  • Noise estimates: 10^-5 Pauli-Z error is currently associated with phase fluctuations in the X measurement, while approximately 10^-8 is expected to be achievable.The lower estimate is linked to shot-noise considerations, with possible sub-shot-noise improvements left open.
  • Open questions: The remaining design questions include switch-speed specialization, set-and-forget advantages, and whether lower-performance switches could reduce noise with algorithmic correction.These questions remain unresolved within the proposed architecture.

VII. DELAYS

The architecture uses fixed passive waveguide delays and multiplexing to convert probabilistic photon production into a near-deterministic stream. Further multiplexing is required because producing 3-photon GHZ states or Bell pairs remains probabilistic, while source indistinguishability and loss constrain performance.

  • VII. DELAYS: 27 meters of on-chip spiral waveguide has already been constructed for fixed photon delays.Fixed delays require only passive waveguides; bend losses remain an engineering concern.
  • VII. DELAYS: Producing a 3-photon GHZ state from six single photons succeeds with probability 1/32, requiring another multiplexing stage afterward.The desired entangled states are produced probabilistically, including 3-photon GHZ states and Bell pairs.
  • VII. DELAYS: S + 1 switches with cascading delays can provide any delay from 0 to 2S −1 clock units.The delays are implemented as waveguide spirals rather than fiber.
  • VII. DELAYS: Heralded photons require filtering for purity, while photons from different sources may not achieve the high interference visibility of photons from one nonlinear process.Source design must balance indistinguishability, filtering, repetition rate, coupling, and noise transferred from matter-based emitters.
  • VII. DELAYS: Temporal multiplexing groups random photons into blocks and moves one available photon to the block’s final time bin.Extra photons in a block are discarded, and the resulting stream has a longer time-bin period.
  • VII. DELAYS: Lossless switches would make the nondeterministic photon source effectively deterministic, but switches introduce loss and stochastic noise.The architecture therefore seeks to minimize active components.

A. Asynchronous computation and relative-time multiplexing

Relative-time multiplexing relaxes the need for global synchrony by matching photons according to their relative arrival times. The approach can improve photon-pair production and reduce switching and delay demands when assembling large cluster states, while leaving optimization questions open.

  • Relative-time multiplexing: Relative-time multiplexing matches photons by adjusting their relative time separation rather than forcing them into a particular clock cycle.A sliding-window implementation delays an incoming photon to meet a photon from another stream when their separation is within the available delay range.
  • Relative-time multiplexing: Four photon streams can produce Bell pairs, while six streams can directly produce the desired 3-GHZ states.At higher photon densities, more sophisticated graph-theoretic matching algorithms can use photons more efficiently, although collisions within delay networks must be considered.
  • Asynchronous cluster-state construction: RMUX allows non-computational photons in fused 3-GHZ streams to synchronize only with photons involved in their own fusion.The architecture can operate asynchronously, and switching requirements can be reduced further by routing different photons through different numbers of switches.
  • Open questions: The central open questions concern collision-avoiding delay networks, matching and multiplexing combinations, finite delays, and the best allocation of switching asymmetry.These questions remain largely unexplored for asynchronous GHZ-state generation and fusion.

B. Dump the Pump?

Dump-the-pump multiplexing moves active control from photonic qubits to the pump, potentially improving heralded single-photon production. Its benefits must be weighed against loss through cascaded crystals and linear-depth implementation, while related optimization questions remain open.

  • Operating principle: Dump-the-pump avoids switching photonic qubits by extinguishing the pump when heralding indicates that a photon has been produced.The proposal cascades nonlinear downconversion processes and uses idler photons to herald production.
  • Operating principle: The active element operates on a pump with a different frequency from the photonic qubits and need only be extinguished, not coherently switched.This permits consideration of switching devices different from those used for direct photonic-qubit multiplexing.
  • Trade-offs: The main disadvantages are potential loss as produced photons pass through all crystals and the linear depth of the procedure.This lacks the compactness of a logarithmic-depth switching network.
  • Expected performance: A strongly pumped SPDC source offers at most about 1/5 single-photon emission probability, while dump-the-pump may raise it to around 2/3–3/4 with 5 or 6 cascaded downconversions.The proposed improvement is intended to make subsequent single-photon multiplexing more effective.
  • Open questions: Open questions include applying dump-the-pump to heralded Bell pairs and GHZ states and optimizing its combination with relative-time multiplexing.The relevant engineering questions include how efficiently and quickly the pump can be extinguished.

IX. LOSS TOLERANCE

The section develops loss-tolerant cluster-state methods for photonic computation, while emphasizing that explicit loss tolerance in ballistic architectures remains an open problem.

  • Loss mechanisms: Photon loss is detectable when a detector fails to register a photon, enabling architectures that condition computation on photon-click events.The approach uses variations of Type-II fusion gates designed to rely only on events that trigger detector clicks.
  • Open problems: The architecture still lacks a demonstrated mechanism for very high loss tolerance within a ballistic design without quantum memory or extremely long delays.The section identifies explicit loss tolerance in ballistic architectures as ongoing work and lists integration with loss-tolerant codes as an open question.
  • Graph construction: Highly connected graphs need not require many CZ gates, because graph operations such as local complementation can generate crazy-graph building blocks from bounded-degree graphs.Figure 7 illustrates this construction by measuring two qubits in X on a low-degree graph.
  • Loss-tolerant wires: Replacing each wire qubit with L completely connected qubits makes teleportation succeed when at least one qubit survives in every column.The construction protects teleportation against loss by using redundant columns rather than a single linear-cluster wire.
  • Loss-tolerant wires: For any per-qubit loss probability ϵ < 1, choosing polynomially large L can make the wire-success expression 1 − ϵ^L approximately 1, but graph size grows polynomially.The resulting ‘crazy graph’ increases the number of bonds, creating pressure for extremely low stochastic error during state construction.
  • Noise handling: Majority voting over surviving qubits can correct flipped X-measurement outcomes caused by Y or Z Pauli errors within a column.In the absence of noise, all qubits in a column yield the same X-measurement outcome, providing the reference for the vote.
  • Circuit extension: Loss tolerance for Clifford circuits can be extended by attaching pre-built cluster-state chunks as computation advances, with Hadamard and S gates implemented through graph-state choices.The S-gate resource is prepared in advance and retained only when its central Y-measured qubit was not lost.

X. CONCLUSIONS

The conclusion presents substantial experimental and theoretical progress toward all-photonic quantum computing, while stressing that important architectural simplifications remain for theorists to resolve.

  • Progress: Integrated photonics and advanced detectors have made major experimental progress toward an all-photonic quantum computer.The conclusion contrasts this progress with earlier schemes requiring inefficient gates and giant ancillary resource states prepared with large quantum memories.
  • Progress: The field has moved beyond circuit models and resource states that required approximately unit-efficiency gates or huge offline-prepared ancillas.These changes are presented as developments following the seminal Knill–Laflamme–Milburn work.
  • Open directions: Despite this progress, many potentially significant simplifications to the photonic architecture remain for theorists to investigate.The conclusion frames unresolved architectural simplification as the main remaining theoretical opportunity.
  • Future directions: The overview focuses on a purely photonic implementation, but hybrid light/matter systems and PIC networks with lossy interconnects also merit further investigation.These alternatives are identified as extensions of the architecture rather than as results established by the paper.

Appendix A: Sociological musings

The appendix argues that research choices are shaped by finite resources, expertise, and historical circumstances, while advocating broad support for serious quantum-computing approaches.

  • Research trajectories: Early photonic demonstrations often used inherently unscalable schemes because spontaneous parametric downconversion provided quick, low-volume entanglement sources.The appendix contrasts these demonstrations with the harder task of engineering good non-random photon sources.
  • Resource allocation: Different quantum-computing routes should not yet be forced into resource competition given the technology’s potential applications and related spin-offs.The argument includes communication, high-precision measurement, and unforeseen applications within its scope.
  • Research value: Serious quantum-computing approaches advance both understanding of physical systems and engineering boundaries while pursuing large-scale entanglement.The appendix presents these benefits as applying across a wide variety of physical platforms.
  • Historical motivation: The first quantum revolution linked quantum phenomena to technologies including transistors, electron microscopes, atomic clocks, lasers, computers, GPS, and the internet.The appendix uses this history to motivate continued investment in controlled quantum dynamics.
  • Research choices: Individual scientists nevertheless face finite resources and typically choose systems aligned with their expertise, funding opportunities, and early research background.The appendix characterizes geography as an important accidental influence on these research trajectories.
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