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Multi-Outcome Circuit Optimization for Enhanced Non-Gaussian State Generation

S. Ismailzadeh, B. Abedi Ravan

Abstract

Photonic quantum computing has gained significant interest in recent years due to its potential for scaling to large numbers of qubits. A critical requirement for fault-tolerant quantum computation is the reliable generation of non-Gaussian quantum states, typically achieved using Gaussian operations and photon-number-resolving detectors. However, the probabilistic nature of quantum measurement typically results in low success rates for state preparation. Conventionally, these circuits are optimized to herald a single specific target outcome, thereby disregarding the potential utility of alternative measurement patterns generated by the same physical setup. In this work, we propose and demonstrate a multi-outcome optimization strategy that increases the overall acceptance probability by allowing a single circuit to produce useful quantum states across several measurement patterns. To evaluate this approach, we apply the framework to the generation of Gottesman-Kitaev-Preskill core states, Schrodinger cat states, binomial codes, and cubic phase states using both two-mode and three-mode Gaussian circuits. We demonstrate that the success probability can be enhanced through two distinct mechanisms: first, by simultaneously targeting a diverse set of useful resource states, and second, by aggregating degenerate outcomes to maximize the production rate of a single target state.

Multi-Outcome Circuit Optimization for Enhanced Non-Gaussian State Generation

Abstract

Photonic quantum computing has gained significant interest in recent years due to its potential for scaling to large numbers of qubits. A critical requirement for fault-tolerant quantum computation is the reliable generation of non-Gaussian quantum states, typically achieved using Gaussian operations and photon-number-resolving detectors. However, the probabilistic nature of quantum measurement typically results in low success rates for state preparation. Conventionally, these circuits are optimized to herald a single specific target outcome, thereby disregarding the potential utility of alternative measurement patterns generated by the same physical setup. In this work, we propose and demonstrate a multi-outcome optimization strategy that increases the overall acceptance probability by allowing a single circuit to produce useful quantum states across several measurement patterns. To evaluate this approach, we apply the framework to the generation of Gottesman-Kitaev-Preskill core states, Schrodinger cat states, binomial codes, and cubic phase states using both two-mode and three-mode Gaussian circuits. We demonstrate that the success probability can be enhanced through two distinct mechanisms: first, by simultaneously targeting a diverse set of useful resource states, and second, by aggregating degenerate outcomes to maximize the production rate of a single target state.
Paper Structure (13 sections, 7 equations, 3 figures, 5 tables, 1 algorithm)

This paper contains 13 sections, 7 equations, 3 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methods
  3. Gaussian Boson Sampling-like Device
  4. Multi-Outcome Optimization Strategy
  5. Target States
  6. Results
  7. Pattern Discovery via Beam Search
  8. Fixed-pattern optimization
  9. Multiplexing Diverse Resources
  10. Maximizing Yield via Probability Harvesting
  11. Rotation Variance
  12. Effect of Photon Loss
  13. discussion and Conclusion

Figures (3)

  • Figure 1: Gaussian Boson Sampling-like device architecture. Independent single-mode squeezing ($S_i$) and displacement ($D_i$) operations are applied to $N$ initial vacuum states. The modes are subsequently mixed via a passive linear optical unitary transformation $U$. Finally, photon-number-resolving measurements on $N-1$ ancillary modes herald the non-Gaussian target state $|\psi\rangle$ in the unmeasured output mode.
  • Figure 2: Wigner function representations demonstrating probability harvesting for the GKP $\ket{0_{A4}}$ state in a three-mode circuit. (a) The ideal target state. (b) The state heralded by the $(1,3)$ measurement pattern and (c) the state heralded by the $(3,1)$ pattern.
  • Figure 3: Wigner function representations demonstrating probability harvesting for the $\ket{\text{cat}_+}$ state in a three-mode circuit. (a) The ideal target state. (b), (c), (d), (e) and, (f) indicate the states heralded by the measurement patterns $(0,4)$, $(1,3)$, $(2,2)$, $(3,1)$ and, $(4,0)$ respectively.