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A Flexible GKP-State-Embedded Fault-Tolerant Quantum Computation Configuration Based on a Three-Dimensional Cluster State

Peilin Du, Jing Zhang, Tiancai Zhang, Rongguo Yang, Kui Liu, Jiangrui Gao

Abstract

The integration of diverse quantum resources and the exploitation of more degrees of freedom provide key operational flexibility for universal fault-tolerant quantum computation. In this work, we propose a flexible Gottesman-Kitaev-Preskill-state-embedded fault-tolerant quantum computation architecture based on a three-dimensional cluster state constructed in polarization, frequency, and orbital angular momentum domains. Specifically, we design optical entanglement generators to produce three diverse entangled pairs, and subsequently construct a three-dimensional cluster state via a beam-splitter network with several time delays. Furthermore, we present a partially squeezed surface-GKP code to achieve fault-tolerant quantum computation and ultimately find the optimal choice of implementing the squeezing gate to give the best fault-tolerant performance (the fault-tolerant squeezing threshold is 11.5 dB). Our scheme is flexible, scalable, and experimentally feasible, providing versatile options for future optical fault-tolerant quantum computation architecture.

A Flexible GKP-State-Embedded Fault-Tolerant Quantum Computation Configuration Based on a Three-Dimensional Cluster State

Abstract

The integration of diverse quantum resources and the exploitation of more degrees of freedom provide key operational flexibility for universal fault-tolerant quantum computation. In this work, we propose a flexible Gottesman-Kitaev-Preskill-state-embedded fault-tolerant quantum computation architecture based on a three-dimensional cluster state constructed in polarization, frequency, and orbital angular momentum domains. Specifically, we design optical entanglement generators to produce three diverse entangled pairs, and subsequently construct a three-dimensional cluster state via a beam-splitter network with several time delays. Furthermore, we present a partially squeezed surface-GKP code to achieve fault-tolerant quantum computation and ultimately find the optimal choice of implementing the squeezing gate to give the best fault-tolerant performance (the fault-tolerant squeezing threshold is 11.5 dB). Our scheme is flexible, scalable, and experimentally feasible, providing versatile options for future optical fault-tolerant quantum computation architecture.
Paper Structure (8 sections, 8 equations, 6 figures)

This paper contains 8 sections, 8 equations, 6 figures.

Table of Contents

  1. introduction
  2. Generation of large-scale 3D cluster states embedded with GKP states
  3. Generation of various entangled pairs
  4. Construction of large-scale 3D hybrid cluster states
  5. Fault-tolerant quantum computation using the partially squeezed surface-GKP code
  6. The partially squeezed surface-GKP code
  7. The fault-tolerant performance of introducing squeezing gate implementations in different steps
  8. Conclusion

Figures (6)

  • Figure 1: The schematic of the optical entanglement generator. Symbols $s$ and $i$ denotes the signal and idler modes, respectively. GD: general-dyne detection; BHD: balanced homodyne detection.
  • Figure 2: Illustration of the entanglement structure evolution via the optical entanglement generator shown in Fig.1. The pink rectangular area represents the joint measurement for generating hexapartite cluster states, and the gray rectangular area represents the joint measurement for inputting GKP states. Solid circles represent the cluster modes, and black squares represent the GKP states.
  • Figure 3: The 3D cluster state construction. (a) Schematic diagram of our scheme. (b)–(d) Entanglement structures of 1D, 2D, and 3D cluster states in steps I–III, respectively. Red arrows: PBS1/PBS2; black arrows: BS5/BS6; green solid arrows: PBS3; green dotted arrows: PBS4. Filled (hollow) circles: modes from OEG1(OEG2). Black squares: GKP states; black stars: output ports.
  • Figure 4: Another 3D cluster state structure generated by our scheme -- the 3D macronode RHG cluster state. The gray circle areas represent the macronode modes and all colored arrows (denoting BSs) and circles (denoting output modes from OEGs) are identical to those in Fig.3.
  • Figure 5: The partially squeezed surface-GKP codes. (a) Code layout for distance $d=3$. (b) Single-round Z-type stabilizer measurement. (c) Single-round X-type stabilizer measurement. Black squares denote data GKP qubits, while green and blue squares correspond to Z-type and X-type syndrome GKP qubits, respectively. Dashed circles represent idler modes, which can be erased by measuring the quadrature amplitude without affecting the surface code. Black and red lines represent two-mode gates with weight 1 and $\chi$, respectively.
  • ...and 1 more figures