Practical approximation of single-qubit unitaries by single-qubit quantum Clifford and T circuits

Abstract

We present an algorithm, along with its implementation that finds T-optimal approximations of single-qubit Z-rotations using quantum circuits consisting of Clifford and T gates. Our algorithm is capable of handling errors in approximation down to size $10^{-15}$, resulting in optimal single-qubit circuit designs required for implementation of scalable quantum algorithms. Our implementation along with the experimental results are available in the public domain.

11 pages, 9 figures

References in corpus (6)

• Simulating chemistry using quantum computers
• Simulating chemistry efficiently on fault-tolerant quantum computers
• Asymptotically optimal approximation of single qubit unitaries by Clifford and T circuits using a constant number of ancillary qubits
• Efficient Decomposition of Single-Qubit Gates into $V$ Basis Circuits
• A State Distillation Protocol to Implement Arbitrary Single-qubit Rotations
• Floating Point Representations in Quantum Circuit Synthesis

Cited by in corpus (33)

• Q#: Enabling scalable quantum computing and development with a high-level domain-specific language
• Efficient synthesis of probabilistic quantum circuits with fallback
• Shorter gate sequences for quantum computing by mixing unitaries
• Arithmetic Circuits for Multilevel Qudits Based on Quantum Fourier Transform
• LEAP: Scaling Numerical Optimization Based Synthesis Using an Incremental Approach
• Multi-Neutrino Entanglement and Correlations in Dense Neutrino Systems
• Compressed quantum computation using the IBM Quantum Experience
• Normal form for single-qutrit Clifford+T operators and synthesis of single-qutrit gates
• Partially Fault-tolerant Quantum Computing Architecture with Error-corrected Clifford Gates and Space-time Efficient Analog Rotations
• T-count and T-depth of any multi-qubit unitary
• Fibonacci anyons versus Majorana fermions
• Projection algorithm for state preparation on quantum computers
• Criteria for universality of quantum gates
• Parallelizing quantum circuit synthesis
• Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits
• Repeat-Until-Success circuits with fixed-point oblivious amplitude amplification
• How to check universality of quantum gates?
• Deterministic Algorithms for Compiling Quantum Circuits with Recurrent Patterns
• Quantum Fully Homomorphic Encryption by Integrating Pauli One-time Pad with Quaternions
• Everything You Always Wanted to Know About Quantum Circuits
• Calculable lower bounds on the efficiency of universal sets of quantum gates
• Cost-optimal single-qubit gate synthesis in the Clifford hierarchy
• Quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian
• Generators and Relations for the Group On(Z[1/2])
• Probabilistic unitary synthesis with optimal accuracy
• Single-qubit rotation algorithm with logarithmic Toffoli count and gate depth
• Quantum Simulation of QED in Coulomb Gauge
• From Magic State Distillation to Dynamical Systems
• Quantum advantage in temporally flat measurement-based quantum computation
• Error Crafting in Mixed Quantum Gate Synthesis
• Composability of global phase invariant distance and its application to approximation error management
• A Novel Single-Layer Quantum Neural Network for Approximate SRBB-Based Unitary Synthesis
• Transversal architecture for megaquop-scale quantum simulation with neutral atoms