Photonic cluster state generation in three experiments and proposals

Short answer: Cluster states are entangled photonic resource states for measurement-based quantum computing and communication. A 2024 Nature Physics paper reports a microwave-domain experiment that generated a two-dimensional cluster state of four photons with 70% fidelity, a 2022 Nature Photonics paper reports a quantum-dot spin source with an entanglement length of about ten photons, and a 2019 Physical Review Letters paper proposes a scheme using coupled solid-state emitters. These are laboratory results and a proposal.

Mechanisms for Deterministic Generation

The generation of multidimensional photonic cluster states has historically relied on probabilistic methods, which limit the scalability of typical optical generation approaches. The 2024 authors report an experimental deterministic scheme. One approach utilizes a single flux-tunable transmon qubit as a quantum emitter within the microwave domain. This setup uses a coupled resonator array as a slow-light waveguide and a second auxiliary transmon as a switchable mirror. These components enable rapid, shaped emission of entangled photon wavepackets and selective time-delayed feedback of photon wavepackets to the emitter qubit.

Another mechanism involves the periodic excitation of a semiconductor quantum-dot-confined spin. In this scheme, a single QD-confined electron spin precesses in a magnetic field while driven by a temporal sequence of laser pulses. Following excitation, a single photon is deterministically emitted, and its polarization is entangled with the state of the QD-confined spin. This method allows for the continuous generation of a string of photons at deterministic gigahertz generation rates.

Experimental Realization and Fidelity

The experiments report specific fidelity and state sizes. In the microwave domain, the authors report generating a two-dimensional cluster state of four photons with 70% fidelity. This result was verified through the tomographic reconstruction of the quantum state. The system achieved rapid, shaped emission and selective time-delayed feedback, which are critical for the deterministic generation of these states.

In the semiconductor quantum dot approach, the authors report demonstrating a multi-indistinguishable photon cluster. This implementation featured an optimized entanglement length of about ten photons. The photons were generated at deterministic gigahertz rates. The indistinguishability of these photons is a key feature, as it allows for measurements and fusion of clusters by interfering photons. The authors say this opens possibilities for scaling up the cluster’s dimensionality by fusion, building graph states suited for measurement-based photonic quantum computers and all-photonic quantum repeaters.

Solid-State Interacting Emitters

The 2019 paper proposes a general method for controlled entanglement creation using coupled solid-state quantum emitters. This approach creates deterministic multiphoton entanglement without the need for any two-qubit gates. It functions regardless of whether the emitters are identical. The method makes direct use of the always-on exchange interaction in combination with single-qubit operations.

This technique provides a recipe for the generation of two-dimensional, cluster-state entangled photons. By leveraging the exchange interaction, the system avoids the complexity of direct two-qubit gate operations while maintaining the ability to generate large-scale entangled states.

Scalability and Resource Efficiency

Multidimensional photonic graph states, such as cluster states, possess a special entanglement structure that makes them valuable resources for quantum metrology, secure quantum communication, and measurement-based quantum computation. The inbuilt redundancy of cluster photons allows for repeated local measurements, which can compensate for losses and probabilistic Bell measurements. For feasible applications, cluster generation must be fast, deterministic, and produce indistinguishable photons.

The 2024 authors say probabilistic methods limit the scalability of typical optical generation. The 2022 authors say the ability to produce entangled particles in a controllable manner is essential for any quantum technology, and that entanglement between light particles is particularly crucial for quantum communication due to light’s non-interactive nature and long-lasting coherence. They say resources producing entangled multiphoton cluster states will enable communication between remote quantum nodes by allowing for the compensation of losses through the redundancy of the cluster photons.

FAQ

What fidelity was achieved in the microwave domain experiment?

The microwave domain experiment generated a two-dimensional cluster state of four photons with 70% fidelity. This result was verified by the tomographic reconstruction of the quantum state, as the authors report.

How does the semiconductor quantum dot method generate photons?

The method uses periodic excitation of a semiconductor quantum-dot-confined spin. A single photon is deterministically emitted following excitation, with its polarization entangled with the spin state. This allows for continuous generation at deterministic gigahertz rates.

Are two-qubit gates required for solid-state emitter schemes?

No, the proposed method for coupled solid-state quantum emitters does not require any two-qubit gates. It utilizes the always-on exchange interaction in combination with single-qubit operations to create deterministic multiphoton entanglement.

Why is photon indistinguishability important for cluster states?

Indistinguishability allows for the measurements and fusion of clusters by interfering photons. This capability enables the scaling up of the cluster’s dimensionality by fusion, which the authors say would help build graph states suited for measurement-based photonic quantum computers.

What limits the scalability of typical optical generation methods?

Typical optical generation methods rely on probabilistic approaches, which limit scalability. The 2024 paper presents a deterministic scheme as an alternative.