[Paper Review] Generating Gottesman-Kitaev-Preskill qubit using a cross-Kerr interaction between a squeezed light and Fock states in optics

Kosuke Fukui, Mamoru Endo+4 more|arXiv (Cornell University)|Sep 10, 2021

Quantum Information and Cryptography84 references28 citations

TL;DR

This paper proposes a novel method to generate Gottesman-Kitaev-Preskill (GKP) qubits in optical continuous-variable quantum computing using a cross-Kerr interaction between a squeezed light and a superposition of Fock states. The scheme achieves high-fidelity GKP states with 10 dB squeezing and fidelities of 99.99% and 99.9% at success probabilities of 2.7% and 4.8%, respectively, offering a promising route toward fault-tolerant quantum computation with optical CV systems.

ABSTRACT

Gottesman-Kitaev-Preskill (GKP) qubit is a promising ingredient for fault-tolerant quantum computation (FTQC) in optical continuous variables due to its advantage of noise tolerance and scalability. However, one of the main problems in the preparation of the optical GKP qubit is the difficulty in obtaining the nonlinearity. Cross-Kerr interaction is one of the promising candidates for this nonlinearity. There is no existing scheme to use the cross-Kerr interaction to generate the optical GKP qubit for FTQC. In this work, we propose a generation method of the GKP qubit by using a cross-Kerr interaction between a squeezed light and a superposition of Fock states. We numerically show that the GKP qubit with the 10 dB can be generated with a mean fidelities of 99.99 and 99.9% at the success probabilities of 2.7 and 4.8%, respectively. Therefore, our method has potential method to generate the optical GKP qubit with a quality required for FTQC when we obtain the sufficient technologies for the preparation of ancillary Fock states and a cross-Kerr interaction.

Motivation & Objective

• To address the challenge of generating non-Gaussian GKP qubits in optical continuous-variable quantum computing due to the lack of required nonlinearities.
• To overcome limitations of prior cross-Kerr-based GKP state generation, such as mismatched quadrature codewords and high logical bit error rates.
• To propose a new scheme using a cross-Kerr interaction between a squeezed light and a superposition of Fock states to enable high-fidelity, scalable GKP qubit preparation.
• To demonstrate numerically that the proposed method can achieve the squeezing levels and fidelities required for fault-tolerant quantum computation with continuous variables.

Proposed method

• The scheme employs a cross-Kerr interaction Hamiltonian between a squeezed vacuum state (as the control mode) and an ancillary superposition of Fock states (|0⟩ + |1⟩)/√2.
• The interaction induces a conditional phase shift on the Fock state based on the amplitude of the squeezed light, entangling the two modes.
• By applying a homodyne measurement on the Fock state ancilla, the GKP qubit is projected onto the target logical state with high fidelity.
• The method avoids the phase rotation issue of previous schemes by using symmetric positive and negative amplitudes in the cross-Kerr interaction.
• The squeezing level of the generated GKP qubit matches the initial squeezing of the input squeezed light, preserving the desired error tolerance.
• Numerical simulations evaluate the state fidelity and success probability using the overlap between the generated state and the ideal GKP state.

Experimental results

Research questions

• RQ1 Can a cross-Kerr interaction between a squeezed light and a Fock state superposition generate a GKP qubit with high fidelity and sufficient squeezing for fault-tolerant quantum computation?
• RQ2 How does the proposed scheme overcome the codeword mismatch and high logical error rate issues present in prior cross-Kerr-based GKP state generation?
• RQ3 What is the achievable fidelity and success probability of the generated GKP state under realistic conditions with finite squeezing and non-ideal ancilla preparation?
• RQ4 Does the scheme preserve the squeezing level of the input squeezed light in the output GKP state, ensuring compatibility with fault-tolerant protocols?
• RQ5 Can the method be scaled to higher squeezing levels and higher fidelities with improved ancilla state preparation and interaction strength?

Key findings

• The proposed scheme generates a GKP qubit with 10 dB squeezing and a fidelity of 99.99% at a success probability of 2.7%.
• At a higher success probability of 4.8%, the scheme achieves a fidelity of 99.9% with the target GKP state.
• The method preserves the initial squeezing level of the input squeezed light in the generated GKP qubit, ensuring compatibility with fault-tolerant error correction thresholds.
• The scheme avoids the codeword mismatch problem between position and momentum quadratures by using symmetric interaction amplitudes.
• Numerical results show that the method has the potential to produce GKP qubits of sufficient quality for fault-tolerant quantum computation if ancilla Fock states and cross-Kerr interactions can be sufficiently prepared.
• The work identifies a viable path toward scalable, fault-tolerant optical quantum computation using continuous-variable systems.