Classical Simulation of Circuits with Realistic Odd-Dimensional Gottesman-Kitaev-Preskill States

Area of Science:

• Quantum computing
• Quantum information science
• Computational physics

Background:

• Classical simulation of quantum circuits is computationally expensive, especially for bosonic codes with many energy levels.
• Simulating quantum systems with infinite energy levels presents a significant challenge.
• Gottesman-Kitaev-Preskill (GKP) states are crucial for encoding quantum information in bosonic systems.

Purpose of the Study:

• To propose an efficient algorithm for simulating quantum circuits with encoded GKP states.
• To specifically address the simulation of odd-dimensional encoded qudits.
• To optimize simulations in the practically relevant regime of high, finite squeezing in codeword states.

Main Methods:

• Leveraging the Zak-Gross Wigner function for representing infinitely squeezed encoded stabilizer states positively.
• Developing an algorithm where runtime scales with the negativity of the Wigner function.
• Focusing on circuits involving input stabilizer GKP states, generalized GKP-encoded Clifford operations, and modular measurement.

Main Results:

• The algorithm enables efficient simulation of large-scale circuits with highly squeezed GKP states.
• For 12 dB squeezing, circuits with up to 1000 modes can be simulated with minimal sample increase compared to single-mode simulations.
• This represents a significant improvement over existing quantum circuit simulators.

Conclusions:

• The proposed algorithm offers a computationally efficient method for simulating bosonic quantum codes.
• This approach has substantial potential for benchmarking early quantum computing architectures that utilize bosonic codes.
• The method is particularly effective for GKP states with high degrees of squeezing.