Chasing shadows with Gottesman-Kitaev-Preskill codes
arXiv:2411.00235 · doi:10.22331/q-2026-01-19-1973
Abstract
We consider the task of performing shadow tomography of a logical subsystem defined via the Gottesman-Kitaev-Preskill (GKP) error correcting code. Our protocol does not require the input state to be a code state but is implemented by appropriate twirling of the measurement channel, such that the encoded logical tomographic information becomes encoded in the classical shadow. We showcase this protocol for measurements natural in continuous variable (CV) quantum computing. For heterodyne measurement, the protocol yields a probabilistic decomposition of any input state into Gaussian states that simulate the encoded logical information of the input relative to a fixed GKP code where we prove bounds on the Gaussian compressibility of states in this setting. For photon parity measurements, our protocol is equivalent to a Wigner sampling protocol for which we develop the appropriate sampling strategies. Finally, by randomizing over the reference GKP code, we show how Wigner samples of any input state relative to a random GKP codes can be used to estimate any sufficiently bounded observable.
35+10 pages, comments welcome!
References in corpus (36)
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Gaussian Quantum Information
- Variational Quantum Algorithms
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Improved Simulation of Stabilizer Circuits
- Error mitigation for short-depth quantum circuits
- Predicting Many Properties of a Quantum System from Very Few Measurements
- Logical quantum processor based on reconfigurable atom arrays
- Exact and Approximate Unitary 2-Designs: Constructions and Applications
- Efficient variational quantum simulator incorporating active error minimisation
- Real-time quantum error correction beyond break-even
- New class of quantum error-correcting codes for a bosonic mode
- The randomized measurement toolbox
- Evenly distributed unitaries: on the structure of unitary designs
- Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States
- Quantum Data Hiding
- Quantum certification and benchmarking
- Hardware-efficient autonomous quantum error correction
- Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer
- Simulation of quantum circuits by low-rank stabilizer decompositions
- Quantum computing with rotation-symmetric bosonic codes
- Propagating Gottesman-Kitaev-Preskill states encoded in an optical oscillator
- Robust shadow estimation
- Towards Scalable Bosonic Quantum Error Correction
- Classical Shadows With Noise
- Error Analysis For Encoding A Qubit In An Oscillator
- Optimising shadow tomography with generalised measurements
- Encoding qubits in multimode grid states
- Twirling and Hamiltonian Engineering via Dynamical Decoupling for GKP Quantum Computing
- Shadow tomography on general measurement frames
- Quantum spherical codes
- Continuous-variable quantum state designs: theory and applications
- The second moment of the Siegel transform in the space of symplectic lattices
- Information transmission with continuous variable quantum erasure channels
- Continuous-variable designs and design-based shadow tomography from random lattices
- Fiber Bundle Fault Tolerance of GKP Codes