Nearly Optimal T-Count for Symmetry-Based Quantum State Purification

arXiv:2610.12098 · quant-ph · Submitted 2026-10-08 · Read on arXiv

quant-ph

Submitted: 2026-10-08

Updated: 2026-10-08

Terminology

• Fidelity — 25× in this paper · explained in 2 episodes
• Block Encoding — 14× in this paper · explained in 4 episodes
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Quantum Circuits — 3× in this paper · explained in 2 episodes
• Quantum Schur Transform — 2× in this paper
• Accuracy — 1× in this paper · explained in 1 episode
• Ancilla Qubits — 1× in this paper · explained in 1 episode
• Decode — 1× in this paper · explained in 2 episodes
• Linear Combination of Unitary — 1× in this paper
• Pairwise Comparisons — 1× in this paper · explained in 2 episodes
• Stabilizer States — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Surface codes: Towards practical large-scale quantum computation
• Quantum Low-Density Parity-Check Codes
• Quantum error correction below the surface code threshold
• Stabilisation of Quantum Computations by Symmetrisation
• Optimal purification of single qubits
• The Rate of Optimal Purification procedures
• Optimal probabilistic cloning and purification of quantum states
• No-Go Theorems for Quantum Resource Purification
• No Universal Purification in Quantum Mechanics
• No-Go Theorems for Universal Quantum State Purification via Classically Simulable Operations
• Streaming quantum state purification
• Protocols and Trade-Offs of Quantum State Purification
• Optimal Quantum Purity Amplification
• Power and limitations of distributed quantum state purification
• A Nonstabilizerness Resource Law for Universal Quantum State Purification
• Universal quantum state purification with energy-preserving operations
• Streaming quantum state purification for general mixed states
• Nonasymptotic bounds for quantum purity amplification
• Experimental Purification of Single Qubits
• Quantum fingerprinting

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• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
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• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity