Higher Energy Levels in Qubit Networks

Alexander Simm, Shai Machnes, Frank K. Wilhelm

We show that it is theoretically possible to use higher energy levels for storing and controlling two qubits within a superconducting transmon. This is done by identifying energy levels as product states between multiple effecitve qubits. As a proof of concept we realise a complete set of gates necessary for universal computing by numerically optimising control pulses for single qubit gates on each of the qubits, entangling gates between the two qubits in one transmon, and an entangling gate between two qubits from two coupled transmons. The optimisation considers parameters which could make it possible to validate this experimentally. With these control pulses it is in principle possible to double the number of available qubits without any overhead in hardware. The additional qubits could be used in algorithms which need many short-living qubits such as syndrom qubits in error correction or by embedding effecitve higher connectivity in qubit networks.

David S. Simon

Денис Дмитриевич Сукачев

Michael Peterer, Samuel James Bader, Xiaoyue Jin +7 more

We present measurements of coherence and successive decay dynamics of higher energy levels of a superconducting transmon qubit. By applying consecutive π pulses for each sequential transition frequency, we excite the qubit from the ground state up to its fourth excited level and characterize the decay and coherence of each state. We find the decay to proceed mainly sequentially, with relaxation times in excess of 20 μs for all transitions. We also provide a direct measurement of the charge dispersion of these levels by analyzing beating patterns in Ramsey fringes. The results demonstrate the feasibility of using higher levels in transmon qubits for encoding quantum information.

Dibyendu Chatterjee, Arijit Roy

A four-level qubit system is applied to realize quantum half-adder operation.The half-adder circuit is obtained in terms of a quantum CPHASE gate realized by the qubits comprised of four energy levels [C.P. Yang, Prog.Theor.Phys.128, 587 (2012)], and such a CPHASE gate is demonstrated using the transmon.Commonly, higher energy levels are very sensitive and are easily perturbed by the noise sources.Compared to other qubit systems, the higher energy levels of the transmon are less prone to noise such as charge noise, flux noise and other noises.Further, the order of the dephasing time of the higher energy levels (third and fourth energy levels) is nearly the same as that of the lower energy levels of the transmon when the ratio between the Josephson energy and the charging energy 1.A system of three transmons coupled to a single high quality-factor superconducting coplanar resonator is demonstrated to obtain two-and three-qubit CPHASE gates which are in turn used to obtain the quantum half-adder operation.The main advantage of this quantum half-adder scheme is the reduction in the number of required elementary gates, leading to a significant increase in operational speed and robustness compared to the other existing half-adder schemes.The operational time of a complete half-adder operation is ∼37 ns.The methods presented in this article can also be implemented for more complicated quantum circuits.. . . . .

Mrinmoy Samanta, Debkanta Ghosh, Rivu Gupta +1 more

We examine the cooling of networks of oscillators through repeated unitary evolution followed by conditional measurement on a finite-dimensional auxiliary system, coupled via Jaynes-Cummings type interaction. We prove that near-perfect cooling of the oscillator to vacuum is fundamentally impossible when the auxiliary system is a qubit, establishing a no-cooling theorem for a two-level regulator. Moving beyond this limitation, we reveal a twofold dimensional advantage of higher-dimensional auxiliaries - reducing the number of required cycles, and enabling the efficient cooling of oscillators with higher initial energies. We further show that, while extending the network leads to a saturation of this dimensional advantage at moderate auxiliary dimensions, near-perfect cooling remains achievable for linear network configurations but fails for star networks. Moreover, we highlight the adaptability of the proposed protocol by demonstrating efficient cooling of hybrid continuous- and discrete-variable systems that naturally support the generation of non-Gaussian and entangled quantum resources.