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arXiv:0801.4417 · Physical Review Letters

Controllable Coherent Population Transfers in Superconducting Qubits for Quantum Computing

L. F. Wei, J. R. Johansson, Li-Xiang Cen, Sahel Ashhab, Franco Nori

Published Mar 18, 2008• 129 citations
arXivHTMLPDF

Abstract

We propose an approach to coherently transfer populations between selected quantum states in one- and two-qubit systems by using controllable Stark-chirped rapid adiabatic passages. These evolution-time insensitive transfers, assisted by easily implementable single-qubit phase-shift operations, could serve as elementary logic gates for quantum computing. Specifically, this proposal could be conveniently demonstrated with existing Josephson phase qubits. Our proposal can find an immediate application in the readout of these qubits. Indeed, the broken parity symmetries of the bound states in these artificial atoms provide an efficient approach to design the required adiabatic pulses.

DOI
10.1103/physrevlett.100.113601

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We propose an approach to coherently transfer populations between selected quantum states in one- and two-qubit systems by using controllable Stark-chirped rapid adiabatic passages. These evolution-time insensitive transfers, assisted by easily implementable single-qubit phase-shift operations, could serve as elementary logic gates for quantum computing. Specifically, this proposal could be conveniently demonstrated with existing Josephson phase qubits. Our proposal can find an immediate application in the readout of these qubits. Indeed, the broken parity symmetries of the bound states in these artificial atoms provide an efficient approach to design the required adiabatic pulses.
In this article, the scheme of quantum computing based on the Stark-chirped rapid adiabatic passage (SCRAP) technique [L. F. Wei, J. R. Johansson, L. X. Cen, S. Ashhab, and F. Nori, Phys. Rev. Lett. 100, 113601 (2008)] is extensively applied to implement quantum state manipulations in flux-biased Josephson phase qubits. The broken-parity symmetries of bound states in flux-biased Josephson junctions are utilized to conveniently generate the desirable Stark shifts. Then, assisted by various transition pulses, universal quantum logic gates as well as arbitrary quantum state preparations can be implemented. Compared with the usual $\ensuremath{\pi}$-pulse operations widely used in experiments, the adiabatic population passages proposed here are insensitive to the details of the applied pulses and thus the desirable population transfers can be satisfyingly implemented. The experimental feasibility of the proposal is also discussed.
This thesis is based upon the work published in the following two articles entitled: Robust Operation of a Universal Set of Logic Gates for Quantum Computation using Adiabatic Population Transfer between Molecular Levels [37], and Piecewise Adiabatic Passage with a Series of Femtosecond Pulses [54]. Both papers involve using the concept of a quantum control phenomenon, known as adiabatic passage in different manners, in order to achieve particular goals. In the first paper we present a robust construction of a set of logic gates operating on a system of qubits encoded in the ro-vibrational eigenstates of an Na₂ molecule using the optical Adiabatic Population Transfer (APT) method. We demonstrate the operation of a complete universal gate-set for quantum computation on a two-qubit system with gate fidelities approaching 99.99%. Like other APT-based processes, the method is robust against substantial fluctuations in the intensity of the laser pulse. Our construction is easily scalable to dealing with a larger number of qubits. The second line of research developed from the desire to merge the robustness of an adiabatic process, as presented in the previous paper, with the speed and additional level of control available by using pulse shaping techniques of broadband pulses. Therein we develop a method of executing complete population transfers between quantum states in a piecewise manner using a series of femtosecond laser pulses. The method can be applied to a large class of problems as it benefits from the high peak powers and large spectral bandwidths afforded by femtosecond pulses. The degree of population transfer is found to be robust to a wide variation in the absolute and relative intensities, durations, and time ordering of the pulses. The method is studied in detail for atomic sodium where piecewise adiabatic population transfer, as well as the induction of Ramsey-type interferences, is demonstrated.
We propose a scheme for coherent control of population transfer and arbitrary superpositions of quantum states by a single-chirped laser pulse in a Λ-type excited-doublet four-level system. It is shown that selective, efficient, and robust population transfer from the initial state to the target states (excited or ground) can be achieved via chirped adiabatic passage when the pulse bandwidth is smaller than about 1/10 of the energy separations between the excited-doublet levels and between the ground states. Moreover, arbitrary coherent superpositions between the excited-doublet states, or between the higher ground state and either of the excited-doublet states, can be created by appropriately tuning the chirp rate and detuning the laser field. The proposed flexible method of coherent control of population transfer and arbitrary superpositions between the initially unpopulated states requires only a single pulse, and is robust against variations in the laser parameters, which has potential applications in quantum information processing.
We propose and experimentally demonstrate the method of population transfer by piecewise adiabatic passage between two quantum states. Coherent excitation of a two-level system with a train of ultrashort laser pulses is shown to reproduce the effect of an adiabatic passage, conventionally achieved with a single frequency-chirped pulse. By properly adjusting the amplitudes and phases of the pulses in the excitation pulse train, we achieve complete and robust population transfer to the target state. The piecewise nature of the process suggests a possibility for the selective population transfer in complex quantum systems.
Realization of the highly efficient hybrid atom-photon gates is vital to the quantum interface that integrates atoms and superconducting resonators. Here we propose a scheme to realize the hybrid state transfer and controlled-PHASE gate based on Raman chirped shortcut to adiabatic passage. The scheme is fast to protect the quantum state from the decoherence effects in the hybrid interface, as well as is robust due to the geometric phase. We show that this two-qubit gate is more resilient than the Raman pulse and Raman chirped adiabatic passage against the variations in the vacuum coupling strength and two-photon detuning. Its fast and robust features make it especially suitable for long-term storage and optical readout of superconducting qubits, and moreover, entanglement swapping between two disparate components.
We propose a control approach to transfer the population between selected quantum states in the non-Markovian open quantum system. This transfers, assisted by single qubit phase shift operations can generate universal logic gates for quantum computing. We find that the occupation probability behaves differently for different environmental conditions, such as the temperature and the ratio between the frequency of the quantum system of interest, and the cut-off frequency of Ohmic reservoir. We provide an active control over non-Markovian open quantum system for the quantum state engineering.