Asymptotically Optimal Topological Quantum Compiling

Abstract

In a topological quantum computer, universality is achieved by braiding and quantum information is natively protected from small local errors. We address the problem of compiling single-qubit quantum operations into braid representations for non-abelian quasiparticles described by the Fibonacci anyon model. We develop a probabilistically polynomial algorithm that outputs a braid pattern to approximate a given single-qubit unitary to a desired precision. We also classify the single-qubit unitaries that can be implemented exactly by a Fibonacci anyon braid pattern and present an efficient algorithm to produce their braid patterns. Our techniques produce braid patterns that meet the uniform asymptotic lower bound on the compiled circuit depth and thus are depth-optimal asymptotically. Our compiled circuits are significantly shorter than those output by prior state-of-the-art methods, resulting in improvements in depth by factors ranging from 20 to 1000 for precisions ranging between $10^{-10}$ and $10^{-30}$.

24 pages

References in corpus (3)

• Non-Abelian Anyons and Topological Quantum Computation
• A short introduction to Fibonacci anyon models
• Topological Quantum Compiling

Cited by in corpus (33)

• Circuit-centric quantum classifiers
• Quantum-assisted quantum compiling
• Introduction to topological quantum computation with non-Abelian anyons
• Topological Quantum Compiling with Reinforcement Learning
• LEAP: Scaling Numerical Optimization Based Synthesis Using an Incremental Approach
• Exact synthesis of single-qubit unitaries over Clifford-cyclotomic gate sets
• Normal form for single-qutrit Clifford+T operators and synthesis of single-qutrit gates
• T-count and T-depth of any multi-qubit unitary
• Fibonacci anyons versus Majorana fermions
• A practical phase gate for producing Bell violations in Majorana wires
• Exact gate decompositions for photonic quantum computing
• Canonical forms for single-qutrit Clifford+T operators
• Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits
• Exact and approximate continuous-variable gate decompositions
• Remarks on Matsumoto and Amano's normal form for single-qubit Clifford+T operators
• Heuristics for Quantum Compiling with a Continuous Gate Set
• Optimal Ancilla-free Pauli+V Circuits for Axial Rotations
• Systematically generated two-qubit anyon braids
• A framework for exact synthesis
• Topological Quantum Gates in Homotopy Type Theory
• Quantum teleportation using Ising anyons
• Measuring Topological Order
• Robust and Resource-Efficient Quantum Circuit Approximation
• Thermodynamic Analysis of Classical and Quantum Search Algorithms
• Local unitary representations of the braid group and their applications to quantum computing
• Topological quantum compilation of two-qubit gates
• Optimized Topological Quantum Compilation of Three-Qubit Controlled Gates in the Fibonacci Anyon Model: A Controlled-Injection Approach
• Weighted Quantum Channel Compiling through Proximal Policy Optimization
• The Quantum Monadology
• Genetic algorithm enhanced Solovay-Kitaev algorithm for quantum compiling of Fibonacci anyons
• Composability of global phase invariant distance and its application to approximation error management
• Density and unitarity of the Burau representation from a non-semisimple TQFT
• The construction of a universal quantum gate set for the SU(2)k (k=5,6,7) anyon models via genetic optimized algorithm