Protocol Discovery for the Quantum Control of Majoranas by Differentiable Programming and Natural Evolution Strategies

Abstract

Quantum control, which refers to the active manipulation of physical systems described by the laws of quantum mechanics, constitutes an essential ingredient for the development of quantum technology. Here we apply Differentiable Programming (DP) and Natural Evolution Strategies (NES) to the optimal transport of Majorana zero modes in superconducting nanowires, a key element to the success of Majorana-based topological quantum computation. We formulate the motion control of Majorana zero modes as an optimization problem for which we propose a new categorization of four different regimes with respect to the critical velocity of the system and the total transport time. In addition to correctly recovering the anticipated smooth protocols in the adiabatic regime, our algorithms uncover efficient but strikingly counter-intuitive motion strategies in the non-adiabatic regime. The emergent picture reveals a simple but high fidelity strategy that makes use of pulse-like jumps at the beginning and the end of the protocol with a period of constant velocity in between the jumps, which we dub the jump-move-jump protocol. We provide a transparent semi-analytical picture, which uses the sudden approximation and a reformulation of the Majorana motion in a moving frame, to illuminate the key characteristics of the jump-move-jump control strategy. We verify that the jump-move-jump protocol remains robust against the presence of interactions or disorder, and corroborate its high efficacy on a realistic proximity coupled nanowire model. Our results demonstrate that machine learning for quantum control can be applied efficiently to quantum many-body dynamical systems with performance levels that make it relevant to the realization of large-scale quantum technology.

arXiv commentRevised manuscript: Addition of results on proximity coupled semiconducting nanowire, disorder and interactions. Extra discussions and new conclusion. 18 pages, 8 figures + appendix (12 pages, 8 figures)

References in corpus (117)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• 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
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Helical liquids and Majorana bound states in quantum wires
• Machine learning and the physical sciences
• Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning
• The Physical Implementation of Quantum Computation
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Machine learning phases of matter
• Real time evolution using the density matrix renormalization group
• Trapped-Ion Quantum Computing: Progress and Challenges
• Recent Trends in Deep Learning Based Natural Language Processing
• Majorana Zero Modes and Topological Quantum Computation
• Shortcuts to adiabaticity: concepts, methods, and applications
• Evolution Strategies as a Scalable Alternative to Reinforcement Learning
• Realizing Majorana zero modes in superconductor-semiconductor heterostructures
• Time-dependent variational principle for quantum lattices
• Introduction to topological superconductivity and Majorana fermions
• Many-body quantum state tomography with neural networks
• Majorana fermions in chains of magnetic atoms on a superconductor
• Time-evolution methods for matrix-product states
• Finding Density Functionals with Machine Learning
• Shortcuts to adiabaticity
• Probing condensed matter physics with magnetometry based on nitrogen-vacancy centres in diamond
• Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
• Building logical qubits in a superconducting quantum computing system
• Quantum spin dynamics and entanglement generation with hundreds of trapped ions
• Quantized Majorana conductance
• Milestones toward Majorana-based quantum computing
• Majorana Fermions in Semiconductor Nanowires: Fundamentals, Modeling, and Experiment
• Efficient Representation of Quantum Many-body States with Deep Neural Networks
• Coulomb-assisted braiding of Majorana fermions in a Josephson junction array
• Reconstructing quantum states with generative models
• Measurement-Only Topological Quantum Computation
• Reinforcement Learning in Different Phases of Quantum Control
• Active learning machine learns to create new quantum experiments
• Majorana qubit decoherence by quasiparticle poisoning
• Interaction Effects in Topological Superconducting Wires Supporting Majorana Fermions
• Majorana box qubits
• Soundness and completeness of quantum root-mean-square errors
• Speeding up adiabatic quantum state transfer by using dressed states
• Recurrent Neural Network Wave Functions
• Accelerated quantum control using superadiabatic dynamics in a solid-state lambda system
• Deep autoregressive models for the efficient variational simulation of many-body quantum systems
• Self-Learning Monte Carlo Method
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Differentiable Programming Tensor Networks
• Reinforcement Learning with Neural Networks for Quantum Feedback
• Controlling non-Abelian statistics of Majorana fermions on Majorana dimer lattices
• Majorana Fermions in superconducting 1D systems having periodic, quasiperiodic, and disordered potentials
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Majorana fermions in superconducting nanowires without spin-orbit coupling
• Geometric phases and quantum entanglement as building blocks for nonabelian quasiparticle statistics
• Probability distribution of Majorana end-state energies in disordered wires
• Topological superconducting phases in disordered quantum wires with strong spin-orbit coupling
• Adiabatic manipulations of Majorana fermions in a three-dimensional network of quantum wires
• Backflow Transformations via Neural Networks for Quantum Many-Body Wave-Functions
• Artificial Neural Network Methods in Quantum Mechanics
• Braiding without Braiding: Teleportation-Based Quantum Information Processing with Majorana Zero Modes
• Quantum Control Landscapes
• Optimizing Variational Quantum Algorithms using Pontryagin's Minimum Principle
• Majorana Fermions in Strongly Interacting Helical Liquids
• Introduction to quantum Fisher information
• Latent Space Purification via Neural Density Operators
• Failure of protection of Majorana based qubits against decoherence
• Fusion rules and vortices in $p_x+i{p}_y$ superconductors
• Topological superconductivity and Majorana fermions in half-metal / superconductor heterostructure
• Effects of gate-induced electric fields on semiconductor Majorana nanowires
• Speedup for quantum optimal control from automatic differentiation based on graphics processing units
• Optimal Protocols in Quantum Annealing and QAOA Problems
• Quantum brachistochrone curves as geodesics: obtaining accurate control protocols for time-optimal quantum gates
• Algorithmic differentiation and the calculation of forces by quantum Monte Carlo
• Effective theory approach to the Schrodinger-Poisson problem in semiconductor Majorana devices
• Interacting topological phases in multiband nanowires
• Gradient-based optimal control of open quantum systems using quantum trajectories and automatic differentiation
• Topological order in the Kitaev/Majorana chain in the presence of disorder and interactions
• Non-adiabatic processes in Majorana qubit systems
• Dephasing of Majorana-based qubits
• How quickly can anyons be braided? Or: How I learned to stop worrying about diabatic errors and love the anyon
• Majorana braiding with thermal noise
• Shortcuts to nonabelian braiding
• Glassy Phase of Optimal Quantum Control
• Boosting Majorana zero modes
• Efficient Representation of Topologically Ordered States with Restricted Boltzmann Machines
• Measurement-Only Topological Quantum Computation via Tunable Interactions
• Optimal Control of Majorana Zero Modes
• Emulating quantum teleportation of a Majorana zero mode qubit
• Dynamics of Majorana-based qubits operated with an array of tunable gates
• A differentiable programming method for quantum control
• Controlling quantum critical dynamics of isolated systems
• Majoranas in Noisy Kitaev Wires
• Automatic differentiation of dominant eigensolver and its applications in quantum physics
• Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines
• Variational optimization in the AI era: Computational Graph States and Supervised Wave-function Optimization
• Endstates in multichannel spinless p-wave superconducting wires
• Localization-enhanced and degraded topological-order in interacting p-wave wires
• Nonperturbative phase diagram of interacting disordered Majorana nanowires
• Error generation and propagation in Majorana-based topological qubits
• Braiding of non-Abelian anyons using pairwise interactions
• Kitaev spin models from topological nanowire networks
• Automatic Differentiable Monte Carlo: Theory and Application
• Number conserving analysis of measurement-based braiding with Majorana zero modes
• Effects of non-equilibrium noise on a quantum memory encoded in Majorana zero modes
• Stability of Gapped Ground State Phases of Spins and Fermions in One Dimension
• Feasibility of measurement-based braiding in the quasi-Majorana regime of semiconductor-superconductor heterostructures
• A Comparison of Automatic Differentiation and Continuous Sensitivity Analysis for Derivatives of Differential Equation Solutions
• Control of Stochastic Quantum Dynamics by Differentiable Programming
• Dissipative Majorana quantum wires
• Dynamical Phase Error in Interacting Topological Quantum Memories

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• Natural Evolutionary Strategies for Variational Quantum Computation
• Gradient Ascent Pulse Engineering with Feedback
• Optimal control of families of quantum gates
• Mitigating the fermion sign problem by automatic differentiation
• Optimizing the transport of Majorana zero modes in one-dimensional topological superconductors
• Optimal quantum control via genetic algorithms for quantum state engineering in driven-resonator mediated networks
• Automatic Differentiable Numerical Renormalization Group
• Out of Equilibrium Majoranas in Interacting Kitaev Chains
• Optimal Control in Disordered Quantum Systems
• Neural networks in quantum many-body physics: a hands-on tutorial
• Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
• Differentiable master equation solver for quantum device characterisation
• Dynamical Phase Error in Interacting Topological Quantum Memories
• Transport of Majorana Bound State in the presence of telegraph noise
• Shuttling Majorana zero modes in disordered and noisy topological superconductors
• Compatibility of Braiding and Fusion on Wire Networks
• Unsupervised Learning of Effective Quantum Impurity Models