Geometric quantum gates with superconducting qubits

Abstract

We suggest a scheme to implement a universal set of non-Abelian geometric transformations for a single logical qubit composed of three superconducting transmon qubits coupled to a single cavity. The scheme utilizes an adiabatic evolution in a rotating frame induced by the effective tripod Hamiltonian which is achieved by longitudinal driving of the transmons. The proposal is experimentally feasible with the current state of the art and could serve as a first proof of principle for geometric quantum computing.Comment: 7 pages, 5 figure

Measurement scheme for the Lamb shift in a superconducting circuit with broadband environment

“…An alternative approach is to drive the system continuously, in the case where there are no issues with timing the pulses and the measurement can be carried out slower. Floquet theory can be a good starting point to study this option in more detail [18].…”

“…By adiabatically tuning the control fields of the sluice (left and right effective Josephson couplings and gate voltage of the island) along a closed path in the parameter space, the accumulated Berry phase [13] has been studied experimentally by observing the transferred Cooper pair current as a function of the total phase across the sluice [14]. Furthermore, the impact of the environmental degrees of freedom have been investigated in a setup where an additional resistor is coupled capacitively to the sluice island [15][16][17][18]. The peculiarity of this architecture is that the temperature of the system is determined by that of the resistor.…”

Quantum effect of inductance on geometric Cooper-pair transport

“…26 Furthermore, the development of the sluice has given rise to proposals to implement geometric quantum computing featuring similar architectures. 27,28 The sluice itself has been proposed to be used as a Landau-Zener-Stückelberg interferometer. 29 During the past few years, theoretical effort has been put into modeling the sluice coupled to a dissipative environment.…”

Universal holonomic quantum gates in decoherence-free subspace on superconducting circuits

“…Therefore, even with newly demonstrated good coherent times of multilevels in the transmon qubit [32], the implementation of a nontrivial two-qubit holonomic gate, which needs much more complicated cavity-induced interaction between two three-level systems [26], is still very challenging. Alternatively, there are schemes using circuits more complicated than transmons to mimic a multilevel system [7,16,20]. However, this will inevitably introduce additional noises from the environment because more circuits and control elements are needed.…”

“…As geometric phases are determined by the global property of the evolution path, the geometric method of quantum computation has been shown to possess some built-in noiseresilience features [3][4][5][6][7][8][9][10]. In general, the holonomies do not commute with each other, and thus can be used to construct a universal set of quantum gates [11][12][13][14][15][16][17][18][19][20][21][22][23], i.e., the holonomic quantum computation (HQC).…”