Cubic phase gates are not suitable for non-Clifford operations on GKP states

Abstract

With the Gottesman-Kitaev-Preskill (GKP) encoding, Clifford gates and error correction can be carried out using simple Gaussian operations. Still, non-Clifford gates, required for universality, require non-Gaussian elements. In their original proposal, GKP suggested a particularly simple method of using a single application of the cubic phase gate to perform the logical non-Clifford T-gate. Here we show that this cubic phase gate approach performs extraordinarily poorly, even for arbitrarily large amounts of squeezing in the GKP state. Thus, contrary to common belief, the cubic phase gate is not suitable for achieving universal fault-tolerant quantum computation with GKP states.

arXiv comment7 pages, 3 figures, corrected typos

References in corpus (20)

• Encoding a qubit in an oscillator
• Quantum computation over continuous variables
• Time-Domain Multiplexed 2-Dimensional Cluster State: Universal Quantum Computing Platform
• Quantum error correction of a qubit encoded in grid states of an oscillator
• Deterministic generation of a two-dimensional cluster state
• Encoding a qubit in a trapped-ion mechanical oscillator
• Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States
• Performance and structure of single-mode bosonic codes
• Fault-tolerant bosonic quantum error correction with the surface-GKP code
• All-Gaussian universality and fault tolerance with the Gottesman-Kitaev-Preskill code
• Fidelity of Single Qubit Maps
• High-threshold fault-tolerant quantum computation with analog quantum error correction
• Progress towards practical qubit computation using approximate Gottesman-Kitaev-Preskill codes
• Improved quantum capacity bounds of Gaussian loss channels and achievable rates with Gottesman-Kitaev-Preskill codes
• Towards Scalable Bosonic Quantum Error Correction
• Single-Mode Displacement Sensor
• Conversion of Gaussian states to non-Gaussian states using photon-number-resolving detectors
• Modular Bosonic Subsystem Codes
• Measurement-free preparation of grid states
• Polylog-overhead highly fault-tolerant measurement-based quantum computation: all-Gaussian implementation with Gottesman-Kitaev-Preskill code

Cited by in corpus (18)

• A fault-tolerant continuous-variable measurement-based quantum computation architecture
• Encoding a qubit in a spin
• Building a large-scale quantum computer with continuous-variable optical technologies
• Encoding qubits in multimode grid states
• Architecture and noise analysis of continuous-variable quantum gates using two-dimensional cluster states
• Non-Clifford gate on optical qubits by nonlinear feedforward
• All-optical quantum computing using cubic phase gates
• Performance of teleportation-based error correction circuits for bosonic codes with noisy measurements
• Stabilizer subsystem decompositions for single- and multi-mode Gottesman-Kitaev-Preskill codes
• Subsystem analysis of continuous-variable resource states
• Stroboscopic high-order nonlinearity for quantum optomechanics
• Switching-free time-domain optical quantum computation with quantum teleportation
• Synthetic high angular momentum spin dynamics in a microwave oscillator
• Deterministic multi-mode gates on a scalable photonic quantum computing platform
• Nonlinear Phase Gates as Airy Transforms of the Wigner Function
• Using a Kerr interaction for GKP magic state preparation
• Nonlinear squeezing of superpositions of quadrature eigenstates
• Fault-Tolerant Non-Clifford GKP Gates using Polynomial Phase Gates and On-Demand Noise Biasing