Abstract
Stark shift on a superconducting qubit in circuit quantum electrodynamics (QED) has been used to construct universal quantum entangling gates on superconducting resonators in previous works. It is a second-order coupling effect between the resonator and the qubit in the dispersive regime, which leads to a slow state-selective rotation on the qubit. Here, we present two proposals to construct the fast universal quantum gates on superconducting resonators in a microwave-photon quantum processor composed of multiple superconducting resonators coupled to a superconducting transmon qutrit, that is, the controlled-phase (c-phase) gate on two microwave-photon resonators and the controlled-controlled phase (cc-phase) gates on three resonators, resorting to quantum resonance operations, without any drive field. Compared with previous works, our universal quantum gates have the higher fidelities and shorter operation times in theory. The numerical simulation shows that the fidelity of our c-phase gate is 99.57% within about 38.1 ns and that of our cc-phase gate is 99.25% within about 73.3 ns.
Highlights
Stark shift on a superconducting qubit in circuit quantum electrodynamics (QED) has been used to construct universal quantum entangling gates on superconducting resonators in previous works
Universal quantum gates are the key elements in a universal quantum computer, especially the controlled-phase (c-phase) gate or its equivalent gate – the controlled-not (CNOT) gate
There are some interesting physical systems used for the construction of universal quantum gates, such as photons[3,4,5,6,7,8,9], nuclear magnetic resonance[10,11,12,13,14], quantum dots[15,16,17,18,19,20,21,22], diamond nitrogen-vacancy center[23,24,25], and cavity quantum electrodynamics (QED)[26,27]
Summary
Step i), by tuning off the interaction between the transmon qutrit and rb, and resonating ra and the two lowest energy levels jgæq and jeæq of the qutrit (va vg,e) with the operation time of t~. Step iii), by turning off the interaction between the qutrit and rb, and resonating ra and the energy p levels jgæq and jeæq of operation yf. If the operation time in step i) is taken to t~ 2gag,e , one can get the final state of the system as This is just the result of another c-phase gate operation on the resonators ra and rb, which indicates that the p phase shift happens only if there is one microwave photon in ra and no microwave photon in rb.
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