Simulating the dynamics of braiding of Majorana zero modes using an IBM quantum computer

Abstract

We simulate the dynamics of braiding Majorana zero modes on an IBM Quantum computer. We find the native quantum gates introduce too much noise to observe braiding. Instead, we use Qiskit Pulse to develop scaled two-qubit quantum gates that better match the unitary time evolution operator and enable us to observe braiding. This work demonstrates that quantum computers can be used for simulation, and highlights the use of pulse-level control for programming quantum computers and constitutes the first experimental evidence of braiding via dynamical Hamiltonian evolution.

References in corpus (45)

• Quantum Computing in the NISQ era and beyond
• Non-Abelian Anyons and Topological Quantum Computation
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Helical liquids and Majorana bound states in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• Search for Majorana fermions in superconductors
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Characterizing Quantum Supremacy in Near-Term Devices
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Training Schrödinger's cat: quantum optimal control
• Efficient Z-Gates for Quantum Computing
• Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems
• Procedure for systematically tuning up crosstalk in the cross resonance gate
• A simple all-microwave entangling gate for fixed-frequency superconducting qubits
• Fractional statistics in anyon collisions
• Mitigating measurement errors in multi-qubit experiments
• Flux-controlled quantum computation with Majorana fermions
• Coulomb-assisted braiding of Majorana fermions in a Josephson junction array
• Experimental Phase Diagram of a One-Dimensional Topological Superconductor
• Effective Hamiltonian models of the cross-resonance gate
• Adiabatic manipulations of Majorana fermions in a three-dimensional network of quantum wires
• Qiskit Pulse: Programming Quantum Computers Through the Cloud with Pulses
• Top-transmon: hybrid superconducting qubit for parity-protected quantum computation
• The Role of Interactions in an Electronic Fabry-Perot Interferometer Operating in the Quantum Hall Effect Regime
• Quantum advantage with noisy shallow circuits in 3D
• Reducing unitary and spectator errors in cross resonance with optimized rotary echoes
• Experimental and materials considerations for the topological superconducting state in electron and hole doped semiconductors: searching for non-Abelian Majorana modes in 1D nanowires and 2D heterostructures
• Speedup for quantum optimal control from automatic differentiation based on graphics processing units
• Magnetic field-tuned Aharonov-Bohm oscillations and evidence for non-Abelian anyons at v=5/2
• Aharonov-Bohm interference of fractional quantum Hall edge modes
• Primary-Filling e/3 Quasiparticle Interferometer
• Qiskit Backend Specifications for OpenQASM and OpenPulse Experiments
• Fabry-Perot Interferometry with Fractional Charges
• Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body Systems
• Detecting Majoranas in 1D wires by charge sensing
• Measurement Error Mitigation for Variational Quantum Algorithms
• Demonstrating non-Abelian braiding of surface code defects in a five qubit experiment
• Braidonium: a braiding quantum circuit based on the $4\pi$ Josephson effect
• Experimental implementation of non-Clifford interleaved randomized benchmarking with a controlled-S gate
• Vortex Majorana braiding in a finite time
• Interference measurements of non-Abelian e/4 & Abelian e/2 quasiparticle braiding
• Emulating Majorana fermions and their braiding by Ising spin chains

Cited by in corpus (42)

• Scalable error mitigation for noisy quantum circuits produces competitive expectation values
• Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware
• Pulse-efficient circuit transpilation for quantum applications on cross-resonance-based hardware
• Hamiltonian Simulation Algorithms for Near-Term Quantum Hardware
• Quantum Algorithms for Mixed Binary Optimization applied to Transaction Settlement
• Quantum simulation of dissipative collective effects on noisy quantum computers
• Effects of Dynamical Decoupling and Pulse-level Optimizations on IBM Quantum Computers
• Error-Mitigated Simulation of Quantum Many-Body Scars on Quantum Computers with Pulse-Level Control
• Large-scale quantum approximate optimization on non-planar graphs with machine learning noise mitigation
• A Comprehensive Review of Quantum Circuit Optimization: Current Trends and Future Directions
• Well-conditioned multi-product formulas for hardware-friendly Hamiltonian simulation
• Braiding-based quantum control of a Majorana qubit built from quantum dots
• Overcoming the Coherence Time Barrier in Quantum Machine Learning on Temporal Data
• Evaluation of Parameterized Quantum Circuits with Cross-Resonance Pulse-Driven Entanglers
• Pulse-efficient quantum machine learning
• Pulse-engineered Controlled-V gate and its applications on superconducting quantum device
• Filling up complex spectral regions through non-Hermitian disordered chains
• Symmetry breaking in geometric quantum machine learning in the presence of noise
• Suppressing Correlated Noise in Quantum Computers via Context-Aware Compiling
• SimuQ: A Framework for Programming Quantum Hamiltonian Simulation with Analog Compilation
• Exactly solving the Kitaev chain and generating Majorana-zero-modes out of noisy qubits
• Error suppression by a virtual two-qubit gate
• Optimal realization of Yang-Baxter gate on quantum computers
• Softening of Majorana edge states by long-range couplings
• Simulating spectroscopy experiments with a superconducting quantum computer
• Simulating long-range hopping with periodically-driven superconducting qubits
• Ising Meson Spectroscopy on a Noisy Digital Quantum Simulator
• Particle and thermal transport through one dimensional topological systems via Lindblad formalism
• Problem-tailored Simulation of Energy Transport on Noisy Quantum Computers
• Unveiling the non-Abelian statistics of $D(S_3)$ anyons via photonic simulation
• Isolated zero mode in a quantum computer from a duality twist
• Braiding fractional quantum Hall quasiholes on a superconducting quantum processor
• Variational Quantum Gate Optimization at the Pulse Level
• Expanding variational quantum eigensolvers to larger systems by dividing the calculations between classical and quantum hardware
• Theory of quantum error mitigation for non-Clifford gates
• Non-Abelian anyon statistics through AC conductance of a Majorana interferometer
• Characteristics, Implementation and Applications of Special Perfect Entangler Circuits
• Implementing a Ternary Decomposition of the Toffoli Gate on Fixed-FrequencyTransmon Qutrits
• Structure and scaling of Kitaev chain across a quantum critical point in real space
• Universal quantum operation of spin-3/2 Blume-Capel chains
• Superconducting magnetoelectric effects in mesoscopic hybrid structures
• Vertex Lattice Models Simulated with Quantum Circuits