Deterministic generation of a two-dimensional cluster state (1906.08709v2)

Abstract: Measurement-based quantum computation offers exponential computational speed-up via simple measurements on a large entangled cluster state. We propose and demonstrate a scalable scheme for the generation of photonic cluster states suitable for universal measurement-based quantum computation. We exploit temporal multiplexing of squeezed light modes, delay loops, and beam-splitter transformations to deterministically generate a cylindrical cluster state with a two-dimensional (2D) topological structure as required for universal quantum information processing. The generated state consists of more than 30000 entangled modes arranged in a cylindrical lattice with 24 modes on the circumference, defining the input register, and a length of 1250 modes, defining the computation depth. Our demonstrated source of 2D cluster states can be combined with quantum error correction to enable fault-tolerant quantum computation.

• The paper demonstrates a deterministic, scalable method for generating 2D photonic cluster states essential for measurement-based quantum computing.
• It employs temporal multiplexing of squeezed light and delay loops to convert 1D EPR-entangled chains into a 2D cylindrical lattice with over 30,000 modes.
• The work confirms complete inseparability with variance below -3 dB, establishing a robust pathway toward universal, fault-tolerant quantum computation.

Deterministic Generation of a Two-Dimensional Cluster State

The paper "Deterministic generation of a two-dimensional cluster state" presents a method for generating photonic cluster states, which are essential for implementing measurement-based quantum computing (MBQC). The research addresses a significant challenge in MBQC: the reliable, deterministic, and scalable creation of large entangled states necessary for quantum information processing.

Overview of Methodology

The authors propose and demonstrate a scalable scheme to generate photonic cluster states using quantum continuous variables (CV). Specifically, the work involves the creation of a two-dimensional (2D) cylindrical cluster state comprising over 30,000 entangled modes. This state is generated through temporal multiplexing of squeezed light modes, delay loops, and beam-splitter transformations. The scheme demonstrates the feasibility of a universal and fault-tolerant quantum computing resource, addressing previous limitations associated with one-dimensional modalities.

Key Experimental Approach

1. Squeezed Vacuum States: The experimental setup uses two optical parametric oscillators (OPOs) to produce pairs of squeezed vacuum states at a telecom-compatible wavelength of 1550 nm.
2. EPR-State Generation: These squeezed states are then interfered on beam splitters to produce Einstein-Podolsky-Rosen (EPR) pairs, leading to a train of EPR-entangled modes.
3. 1D to 2D Cluster State Transition: The EPR states form an indefinitely long 1D cluster when entangled along a temporal chain. Further processing through additional delays and beam-splitter operations transforms this into a 2D cylindrical lattice.

Results and Verification

The experimental system demonstrates complete inseparability, vital for quantum computing applications, by ensuring all measured nullifiers (linear combinations of position and momentum operators) exhibit variance below the -3 dB inseparability bound. The reported cluster state comprises 24 modes in circumference and a computation depth of 1,250 modes. Notably, all operations can be conducted under ambient conditions, enhancing the practical applicability of the system.

Implications and Future Directions

The implications of this research are profound, particularly towards achieving scalable and universal quantum computation. The temporal multiplexing technique employed here simplifies the experimental requirements compared to previous methods. However, to achieve truly universal quantum computation, the incorporation of non-Gaussian elements is essential. Potential applications include algorithmic sub-routines such as boson sampling and other non-universal operations.

Further advancements are anticipated in enhancing the bandwidth and resolving phase stabilization challenges to increase the number of addressable modes. This robust platform sets the stage for more complex quantum information processes and may facilitate the creation of three-dimensional cluster states, opening new avenues for topologically protected MBQC.

Conclusion

The work outlined in this paper captures a significant stride in advancing quantum computing technology through innovative 2D cluster state generation. By overcoming the scalability limitations of previous implementations, it positions photon-based quantum computing closer to realistic applications and paves the way for groundbreaking developments in universal quantum computation with continuous variables.