Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding

Abstract

Quantum resource theories are a powerful framework to characterize and quantify relevant quantum phenomena and identify processes that optimize their use for different tasks. Here, we define a resource measure for magic, the sought-after property in most fault-tolerant quantum computers. In contrast to previous literature, our formulation is based on bosonic codes, well-studied tools in continuous-variable quantum computation. Particularly, we use the Gottesman-Kitaev-Preskill code to represent multi-qubit states and consider the resource theory for the Wigner negativity. Our techniques are useful to find resource lower bounds for different applications as state conversion and general unitary synthesis, in which measurements, auxiliary states, and classical feed-forward are allowed. The analytical expression of our magic measure allows us to extend current analysis limited to small dimensions, easily addressing systems of up to 12 qubits.

References in corpus (50)

• Surface codes: Towards practical large-scale quantum computation
• Good Quantum Error-Correcting Codes Exist
• Quantum Teleportation is a Universal Computational Primitive
• Encoding a qubit in an oscillator
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• A Theory of Fault-Tolerant Quantum Computation
• Negativity of the Wigner function as an indicator of nonclassicality
• Robustness of entanglement
• Robustness of coherence: An operational and observable measure of quantum coherence
• The Resource Theory of Stabilizer Computation
• Instantaneous non-local computation of low T-depth quantum circuits
• The Heisenberg Representation of Quantum Computers
• Restrictions on Transversal Encoded Quantum Gate Sets
• Positive Wigner functions render classical simulation of quantum computation efficient
• Optimal Quantum Circuits for General Two-Qubit Gates
• Application of a resource theory for magic states to fault-tolerant quantum computing
• The general structure of quantum resource theories
• Methodology for quantum logic gate constructions
• Improved classical simulation of quantum circuits dominated by Clifford gates
• Trading classical and quantum computational resources
• A mathematical theory of resources
• Stabilizer Rényi entropy
• Simulation of quantum circuits by low-rank stabilizer decompositions
• (Quantumness in the context of) Resource Theories
• Resource theory of quantum non-Gaussianity and Wigner negativity
• Novel constructions for the fault-tolerant Toffoli gate
• Bosonic quantum error correction codes in superconducting quantum circuits
• Convex resource theory of non-Gaussianity
• Quantum information processing with bosonic qubits in circuit QED
• Towards Scalable Bosonic Quantum Error Correction
• Quantum Error Correction with the Gottesman-Kitaev-Preskill Code
• Wigner function negativity and contextuality in quantum computation on rebits
• Lower bounds on the non-Clifford resources for quantum computations
• Quantifying quantum speedups: improved classical simulation from tighter magic monotones
• Quantifying magic for multi-qubit operations
• Contextuality and Wigner function negativity in qubit quantum computation
• Robustness of Magic and Symmetries of the Stabiliser Polytope
• Quantifying Contextuality
• Catalysis and activation of magic states in fault tolerant architectures
• A fault-tolerant non-Clifford gate for the surface code in two dimensions
• Phase space simulation method for quantum computation with magic states on qubits
• Quantum interference as a resource for quantum speedup
• A State Distillation Protocol to Implement Arbitrary Single-qubit Rotations
• Cost-Reduced All-Gaussian Universality with the Gottesman-Kitaev-Preskill Code: Resource-Theoretic Approach to Cost Analysis
• Exact synthesis of single-qubit unitaries over Clifford-cyclotomic gate sets
• Discrete Wigner Formalism for Qubits and Non-Contextuality of Clifford Gates on Qubit Stabilizer States
• A polynomial time and space heuristic algorithm for T-count
• Tensor of coherences parameterization of multiqubit density operators for entanglement characterization
• Constraints on magic state protocols from the statistical mechanics of Wigner negativity
• From the Bloch sphere to phase space representations with the Gottesman-Kitaev-Preskill encoding

Cited by in corpus (23)

• Quantifying nonstabilizerness of matrix product states
• Stabilizer entropies and nonstabilizerness monotones
• Measuring magic on a quantum processor
• Scalable measures of magic resource for quantum computers
• Stabilizer entropies are monotones for magic-state resource theory
• Magic-state resource theory for the ground state of the transverse-field Ising model
• Nonstabilizerness determining the hardness of direct fidelity estimation
• Learning efficient decoders for quasi-chaotic quantum scramblers
• Quantifying non-stabilizerness via information scrambling
• Quantifying dynamical magic with completely stabilizer preserving operations as free
• Handbook for Quantifying Robustness of Magic
• Bridging magic and non-Gaussian resources via Gottesman-Kitaev-Preskill encoding
• Sufficient condition for universal quantum computation using bosonic circuits
• Limitations of Classically-Simulable Measurements for Quantum State Discrimination
• Maximal Magic for Two-qubit States
• Clifford operations and homological codes for rotors and oscillators
• Classical simulation and quantum resource theory of non-Gaussian optics
• A trace distance-based geometric analysis of the stabilizer polytope for few-qubit systems
• Faster computation of nonstabilizerness
• Invested and Potential Magic Resources in Measurement-Based Quantum Computation
• Grand Unification of All Discrete Wigner Functions on $d\times d$ Phase Space
• Tessellation codes: encoded quantum gates by geometric rotation
• High-expressibility Quantum Neural Networks using only classical resources