Continuous-variable designs and design-based shadow tomography from random lattices
arXiv:2412.17909 · doi:10.1103/dy4m-gq5c
Abstract
We investigate state designs for continuous-variable quantum systems using the aid of lattice-like quantum states. These are code states of Gottesman-Kitaev-Preskill (GKP) codes. We show that for an n-mode system, the set of all GKP states forms a rigged continuous-variable state 2-design. We use these lattice state designs to construct a continuous variable shadow tomography protocol, derive sample complexity bounds for both global- and local GKP shadows under reasonable physical assumptions, and provide the physical gadgets needed to implement this protocol.
5+31 pages, 3 figures, comments welcome! v2-v4 contain corrections of minor errors and further clarifications
References in corpus (22)
- Gaussian Quantum Information
- Predicting Many Properties of a Quantum System from Very Few Measurements
- Symmetric Informationally Complete Quantum Measurements
- Real-time quantum error correction beyond break-even
- Encoding a qubit in a trapped-ion mechanical oscillator
- Evenly distributed unitaries: on the structure of unitary designs
- The randomized measurement toolbox
- Performance and structure of single-mode bosonic codes
- Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer
- Linear growth of quantum circuit complexity
- Towards Scalable Bosonic Quantum Error Correction
- Single-Mode Displacement Sensor
- Encoding a Qubit into a Cavity Mode in Circuit-QED using Phase Estimation
- Stabilizer entropies are monotones for magic-state resource theory
- Catalysis and activation of magic states in fault tolerant architectures
- Quantum Error Correction of Qudits Beyond Break-even
- Hardware-Encoding Grid States in a Non-Reciprocal Superconducting Circuit
- Quantum spherical codes
- The curious nonexistence of Gaussian 2-designs
- Continuous-variable quantum state designs: theory and applications
- Good Gottesman-Kitaev-Preskill codes from the NTRU cryptosystem
- The second moment of the Siegel transform in the space of symplectic lattices