Low Overhead Qutrit Magic State Distillation

Abstract

We show that using qutrits rather than qubits leads to a substantial reduction in the overhead cost associated with an approach to fault-tolerant quantum computing known as magic state distillation. We construct a family of $[[9m-k,k,2]{]}_3$ triorthogonal qutrit error-correcting codes for any positive integers $m$ and $k$ with $k\le 3m-2$ that are suitable for magic state distillation. In magic state distillation, the number of ancillae required to produce a magic state with target error rate $\epsilon$ is $O({\log }^{\gamma }{\epsilon }^{-1})$, where the yield parameter $\gamma$ characterizes the overhead cost. For $k=3m-2$, our codes have $\gamma ={\log }_2(2+\frac{6}{3m-2})$, which tends to $1$ as $m\to \infty$. Moreover, the $[[20,7,2]{]}_3$ qutrit code that arises from our construction when $m=3$ already has a yield parameter of $1.51$ which outperforms all known qubit triorthogonal codes of size less than a few hundred qubits.

17 pages, 4 figures; v3: accepted in the journal Quantum

References in corpus (23)

• Application of a resource theory for magic states to fault-tolerant quantum computing
• A universal qudit quantum processor with trapped ions
• Magic state distillation with low overhead
• Demonstration of fault-tolerant universal quantum gate operations
• Control and Tomography of a Three Level Superconducting Artificial Atom
• Magic state distillation in all prime dimensions using quantum Reed-Muller codes
• High-Fidelity Qutrit Entangling Gates for Superconducting Circuits
• Multilevel distillation of magic states for quantum computing
• Encoding a magic state with beyond break-even fidelity
• Qudit versions of the qubit "pi-over-eight" gate
• Fault-Tolerant Postselected Quantum Computation: Schemes
• Diagonal gates in the Clifford hierarchy
• Noise Thresholds for Higher Dimensional Systems using the Discrete Wigner Function
• Complete unitary qutrit control in ultracold atoms
• Constraints on magic state protocols from the statistical mechanics of Wigner negativity
• Fault-tolerant Post-Selection for Low Overhead Magic State Preparation
• Classification of Small Triorthogonal Codes
• Asymptotically Good Quantum Codes with Transversal Non-Clifford Gates
• Constant-Overhead Magic State Distillation
• Good binary quantum codes with transversal CCZ gate
• Extending the Computational Reach of a Superconducting Qutrit Processor
• Coherent dynamics in a five-level atomic system
• Magic-state distillation with the four-qubit code

Cited by in corpus (1)

• Synthesis and Arithmetic of Single Qutrit Circuits