Towards low overhead magic state distillation

Abstract

Magic state distillation is a resource intensive sub-routine for quantum computation. The ratio of noisy input states to output states with error rate at most $\epsilon$ scales as $O({\log }^{\gamma }(1/\epsilon ))$ (Bravyi and Haah, PRA 2012). In a breakthrough paper, Hastings and Haah (PRL 2018) showed that it is possible to construct distillation routines with sub-logarithmic overhead, achieving $\gamma \approx 0.6779$ and falsifying a conjecture that $\gamma$ is lower bounded by $1$. They then ask whether $\gamma$ can be made arbitrarily close to $0$. We answer this question in the affirmative for magic state distillation routines using qudits ($d$ dimensional quantum systems).

arXiv comment4 + 3 pages, comments welcome

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• Molecular Asymmetry and Optical Cycling: Laser Cooling Asymmetric Top Molecules
• Arithmetic Circuits for Multilevel Qudits Based on Quantum Fourier Transform
• Characterization of Control in a Superconducting Qutrit Using Randomized Benchmarking
• Pseudomagic Quantum States
• Lower bound for the T count via unitary stabilizer nullity
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• Morphing quantum codes
• Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications
• Constraints on magic state protocols from the statistical mechanics of Wigner negativity
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• Spectral Properties Versus Magic Generation in $T$-doped Random Clifford Circuits
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• Designing the Quantum Channels Induced by Diagonal Gates
• Mitigating Coherent Noise by Balancing Weight-2 $Z$-Stabilizers
• Certifying dimension of quantum systems by sequential projective measurements
• Climbing the Diagonal Clifford Hierarchy
• The qudit Pauli group: non-commuting pairs, non-commuting sets, and structure theorems
• Magic state distillation with punctured polar codes
• Counting stabiliser codes for arbitrary dimension
• Scaling W state circuits in the qudit Clifford hierarchy
• Rescaling decoder for 2D topological quantum color codes on 4.8.8 lattices
• Rigorous noise reduction with quantum autoencoders
• From Magic State Distillation to Dynamical Systems
• Low Overhead Qutrit Magic State Distillation
• Characterization of multi-level dynamics and decoherence in a high-anharmonicity capacitively shunted flux circuit
• Composability of global phase invariant distance and its application to approximation error management
• Experimental Approach to Demonstrating Contextuality for Qudits
• Measurement-free code-switching for low overhead quantum computation using permutation invariant codes
• Magic tricycles: Efficient magic state generation with finite block-length quantum LDPC codes
• Scalable platform for qudit-based quantum computing using polar molecules
• Adaptively secure unitary designs with constant non-Clifford cost