From the Bloch sphere to phase space representations with the Gottesman-Kitaev-Preskill encoding
arXiv:1911.12346 · doi:10.1007/978-981-15-5191-8_9
Abstract
In this work, we study the Wigner phase-space representation of qubit states encoded in continuous variables (CV) by using the Gottesman-Kitaev-Preskill (GKP) mapping. We explore a possible connection between resources for universal quantum computation in discrete-variable (DV) systems, i.e. non-stabilizer states, and negativity of the Wigner function in CV architectures, which is a necessary requirement for quantum advantage. In particular, we show that the lowest Wigner logarithmic negativity of qubit states encoded in CV with the GKP mapping corresponds to encoded stabilizer states, while the maximum negativity is associated with the most non-stabilizer states, H-type and T-type quantum states.
arXiv comment(v1) Accepted for publication in the Springer's "Mathematics for Industry" series. (v2) Typo in the abstract fixed; URL of the conference where the paper has been presented added: International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), held in September 2019 in Fukuoka, Japan (https://www.mqc2019.org/mqc2019/program)
References in corpus (23)
- Cavity Optomechanics
- Encoding a qubit in an oscillator
- Improved Simulation of Stabilizer Circuits
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Observation of the Dynamical Casimir Effect in a Superconducting Circuit
- Negativity of the Wigner function as an indicator of nonclassicality
- Gaussian Boson Sampling
- Instantaneous non-local computation of low T-depth quantum circuits
- The Heisenberg Representation of Quantum Computers
- Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb
- Positive Wigner functions render classical simulation of quantum computation efficient
- Efficient Classical Simulation of Continuous Variable Quantum Information Processes
- Discrete phase space based on finite fields
- Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States
- Resource theory of quantum non-Gaussianity and Wigner negativity
- Generation of one-million-mode continuous-variable cluster state by unlimited time-domain multiplexing
- All-Gaussian universality and fault tolerance with the Gottesman-Kitaev-Preskill code
- Sufficient Conditions for Efficient Classical Simulation of Quantum Optics
- Continuous-Variable Instantaneous Quantum Computing is hard to sample
- Boson sampling with Gaussian measurements
- Continuous-Variable Sampling from Photon-Added or Photon-Subtracted Squeezed States
- Probabilistic Fault-Tolerant Universal Quantum Computation and Sampling Problems in Continuous Variables
- Demonstrating Quantum Error Correction that Extends the Lifetime of Quantum Information