Holonomic Surface Codes for Fault-Tolerant Quantum Computation

Abstract

Surface codes can protect quantum information stored in qubits from local errors as long as the per-operation error rate is below a certain threshold. Here we propose holonomic surface codes by harnessing the quantum holonomy of the system. In our scheme, the holonomic gates are built via auxiliary qubits rather than the auxiliary levels in multilevel systems used in conventional holonomic quantum computation. The key advantage of our approach is that the auxiliary qubits are in their ground state before and after each gate operation, so they are not involved in the operation cycles of surface codes. This provides an advantageous way to implement surface codes for fault-tolerant quantum computation.

14 pages, 6 figures

References in corpus (11)

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Cited by in corpus (29)

• Nonadiabatic geometric quantum computation with cat qubits via invariant-based reverse engineering
• Heralded atomic nonadiabatic holonomic quantum computation with Rydberg blockade
• Fast binomial-code holonomic quantum computation with ultrastrong light-matter coupling
• Path-shortening realizations of nonadiabatic holonomic gates
• Fault-tolerant multiqubit geometric entangling gates using photonic cat-state qubits
• Nonadiabatic holonomic multiqubit controlled gates
• Restoring Adiabatic State Transfer in Time-Modulated Non-Hermitian Systems
• Dynamically Corrected Nonadiabatic Holonomic Quantum Gates
• Demonstration of a non-Abelian geometric controlled-Not gate in a superconducting circuit
• Super-robust nonadiabatic geometric quantum control
• Nonadiabatic holonomic quantum computation on coupled transmons with ancillaries
• Multi-mode architectures for noise-resilient superconducting qubits
• Nonadiabatic geometric quantum gates that are insensitive to qubit-frequency drifts
• Nonadiabatic Holonomic Quantum Computation and Its Optimal Control
• Scalable nonadiabatic holonomic quantum computation on a superconducting qubit lattice
• Nonadiabatic holonomic quantum computation based on commutation relation
• Nonadiabatic Holonomic Quantum Computation via Path Optimization
• Noncyclic nonadiabatic holonomic quantum gates via shortcuts to adiabaticity
• Dark path holonomic qudit computation
• Holonomic implementation of CNOT gate on topological Majorana qubits
• Preparation of high fidelity entangled cat states with composite pulses
• Non-adiabatic holonomic quantum operations in continuous variable systems
• Holonomic swap and controlled-swap gates of neutral atoms via selective Rydberg pumping
• Quantum error pre-compensation for quantum noisy channels
• Topological state permutations in time-modulated non-Hermitian multiqubit systems with suppressed non-adiabatic transitions
• Robust Nonadiabatic Holonomic Quantum Gates on Decoherence-Protected Qubits
• Speeding up adiabatic holonomic quantum gates via $\pi$-pulse modulation
• Universal quantum gates by nonadiabatic holonomic evolution for the surface electron
• Geometric and holonomic quantum computation