Nonadiabatic Holonomic Quantum Computation in Decoherence-Free Subspaces

Nonadiabatic geometric quantum computation in decoherence-free subspaces based on unconventional geometric phases

“…Specifically, we use three physical qubits undergoing collective dephasing to encode one logical qubit, and further realize a universal set of geometric gates in DFSs nonadiabatically and unconventionally. Similarly to the schemes of nonadiabatic holonomic quantum computation in DFSs or noiseless subsystems [13,[21][22][23][24]29], our scheme uses Hamiltonians with three-level structures. However, the dynamical phases of our scheme are proportional to the total phases, while the dynamical phases of the schemes of nonadiabatic holonomic quantum computation in DFSs or noiseless subsystems are equal to 0.…”

“…Despite this, impressive progress has been made in this direction [13,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] and many works have been done to realize GQC in decoherence-free subspaces (DFSs) [13,[15][16][17][18][19][20][21][22][23][24]. Among these works, most of them realized conventional GQC in DFSs [13,15,16,[20][21][22][23][24]. Since unconventional GQC in DFSs shares all the robustness of conventional GQC in DFSs while avoiding the additional operations required to cancel the dynamical phases, realizing unconventional GQC in DFSs is of more practical importance.…”

“…Although adiabatic GQC has geometric robustness, the evolution time associated with adiabatic requirement is usually longer than the coherence time and thus the practical computation is seriously collapsed. To overcome this problem, nonadiabatic GQC based on nonadiabatic and Abelian geometric phases [8] was proposed [9,10], and more interestingly nonadiabatic holonomic quantum computation, which is based on nonadiabatic and non-Abelian geometric phase [11], was recently found [12,13]. In realizing both adiabatic and nonadiabatic geometric gates, dynamical phases are usually removed and this kind of schemes is known as conventional GQC.…”

Non-Adiabatic Universal Holonomic Quantum Gates Based on Abelian Holonomies

“…Non-adiabatic implementations based on non-abelian holonomies have recently been reported in [11][12][13][14][15]. A non-adiabatic geometric quantum computation (GQC) scheme based on abelian holonomies was proposed by Zhu and Wang [16][17][18] for NMR and Josephson charge qubits.…”

Composite nonadiabatic holonomic quantum computation

“…Nonadiabatic holonomic quantum computation is a promising method to suppress control errors [3,4]. Nonadiabatic holonomic gates depend only on evolution paths of a quantum system but not on evolution details, and thus they are robust against certain control errors.…”