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Non-Adiabatic Holonomic Quantum Computation in Decoherence-Free Subspaces
G. F. Xu, J. Zhang, D. M. Tong, Erik Sjoqvist, L. C. Kwek
TL;DR
The paper addresses the open problem of non-adiabatic holonomic quantum computation in decoherence-free subspaces. It constructs holonomic single- and two-qubit gates using three neighboring physical qubits under collective dephasing, realizing a universal gate set.
Problem
Non-adiabatic holonomic quantum computation in decoherence-free subspaces remained an open problem despite the practical importance of combining decoherence protection with geometric control.
Method
The scheme encodes one logical qubit in three neighboring physical qubits undergoing collective dephasing and uses holonomic gates within the resulting decoherence-free subspace.
Results
The construction realizes two noncommuting single-qubit holonomic gates and a holonomic CNOT, forming a universal set in decoherence-free subspaces.
Takeaways & Limitations
The scheme removes the long run-time requirement of adiabatic evolution while combining decoherence-free-subspace stabilization with geometric holonomic control.
Takeaways & Limitations
Two physical qubits are insufficient because their decoherence-free subspace admits no nontrivial Hamiltonian satisfying the non-adiabatic holonomic conditions.
Abstract
from arXiv · showhide
Quantum computation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantum computation in decoherence-free subspaces have been proposed in the past few years. However, non-adiabatic holonomic quantum computation in decoherence-free subspaces, which avoids long run-time requirement but with all the robust advantages, remains an open problem. Here, we demonstrate how to realize non-adiabatic holonomic quantum computation in decoherence-free subspaces. By using only three neighboring physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of quantum gates.