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Journal of Modern Optics

Creation of quantum Householder reflection using shortcut to adiabatic passage

Mahdi Ebrahimpour, M. Saadati-Niari, N. Shirkhanghah

Published Sep 30, 2025• 1 citation
Publisher

Abstract

In this work, we propose the implementation of a quantum Householder reflection (QHR) by employing the shortcut to adiabatic passage (STA) method within the framework of the stimulated Raman adiabatic passage (STIRAP) technique. We consider a (d+2)-level quantum system consisting of d + 1 ground states and a single excited state. Among the ground states, d states span the QHR subspace, while the remaining ground state serves as an ancillary state. The d ground states are coupled to the excited state via pump pulses, whereas the ancillary state is coupled to the excited state through a Stokes pulse. In addition, each of the d ground states is coupled to the ancillary state by means of a corresponding shortcut pulse. We demonstrate that, by employing a two-step STA-STIRAP sequence and appropriately adjusting the relative phases of the Stokes and shortcut pulses, a QHR operator can be realized. As a case study to verify the proposed approach, we implement the quantum Fourier transform (QFT) and Grover's search algorithm using two specific QHRs.

DOI
10.1080/09500340.2025.2564916

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In this work, we propose the implementation of a quantum Householder reflection (QHR) by employing the shortcut to adiabatic passage (STA) method within the framework of the stimulated Raman adiabatic passage (STIRAP) technique. We consider a (d+2)-level quantum system consisting of d + 1 ground states and a single excited state. Among the ground states, d states span the QHR subspace, while the remaining ground state serves as an ancillary state. The d ground states are coupled to the excited state via pump pulses, whereas the ancillary state is coupled to the excited state through a Stokes pulse. In addition, each of the d ground states is coupled to the ancillary state by means of a corresponding shortcut pulse. We demonstrate that, by employing a two-step STA-STIRAP sequence and appropriately adjusting the relative phases of the Stokes and shortcut pulses, a QHR operator can be realized. As a case study to verify the proposed approach, we implement the quantum Fourier transform (QFT) and Grover's search algorithm using two specific QHRs.
We derive an adiabatic technique that implements the most general SU(ddd) transformation in a quantum system of ddd degenerate states, featuring a qudit. This technique is based on the factorization of the SU(ddd) transformation into ddd generalized quantum Householder reflections, each of which is implemented by a two-shot stimulated Raman adiabatic passage with appropriate static phases. The energy of the lasers needed to synthesize a single Householder reflection is shown to be remarkably constant as a function of ddd. This technique is directly applicable to a linear trapped ion system with d+1d+1d+1 ions. We implement the quantum Fourier transform numerically in a qudit with d=4d=4d=4 (defined as a quartit) as an example.
Multistate stimulated Raman adiabatic passage (STIRAP) is a process which allows for adiabatic population transfer between the two ends of a chainwise-connected quantum system. The process requires large temporal areas of the driving pulsed fields (pump and Stokes) in order to suppress the nonadiabatic couplings and thereby to make adiabatic evolution possible. To this end, in the present paper a variation of multistate STIRAP, which accelerates and improves the population transfer, is presented. In addition to the usual pump and Stokes fields it uses shortcut fields applied between the states, which form the dark state of the system. The shortcuts cancel the couplings between the dark state and the other adiabatic states thereby resulting (in the ideal case) in a unit transition probability between the two end states of the chain. Specific examples of five-state systems formed of the magnetic sublevels of the transitions between two degenerate levels with angular momenta Jg=2{J}_{g}=2Jg​=2 (of ground or lower level) and Je=1{J}_{e}=1Je​=1 or Je=2{J}_{e}=2Je​=2 (of excited or upper level) are considered in detail, for which the shortcut fields are derived analytically. The proposed method is simpler than the usual ``shortcuts to adiabaticity'' recipe, which prescribes shortcut fields between all states of the system, while the present proposal uses shortcut fields between the sublevels forming the dark state only. The results are of potential interest in applications where high-fidelity quantum control is essential, e.g., quantum information, atom optics, formation of ultracold molecules, cavity QED, etc.
Abstract Robust quantum control is essential for the development of quantum computers, which rely on precise manipulation of qubits. One form of quantum control is stimulated Raman adiabatic passage (STIRAP), which ordinarily is a state transfer protocol but was extended by Kis and Renzoni (2002 Phys. Rev. A 65 032318) to perform qubit rotations. Shortcut methods to adiabaticity for STIRAP have been shown to speed up adiabatic processes, beyond the adiabatic criterion, with high fidelity. Here, we apply shortcut to adiabaticity methods to the STIRAP qubit rotation scheme to improve the performance of quantum logic gates. The scheme can be implemented via direct connections between ground states in a 4-level Λ system or effective connections in a 5-level Λ system with modified pulses that implement transitionless quantum driving via the addition of a counterdiabatic driving term. We show that the extended shortcut to adiabaticity method serves to improve the fidelity of qubit rotations in the diabatic regime.
The technique of stimulated Raman shortcut to adiabatic passage (STIRSAP) is implemented to chainwise and N-pod systems. In chainwise systems, for large detuning conditions, the population of the middle states can be suppressed during the time evolution of the system and therefore, the Hamiltonian of an N-state system is reduced to an effective two-level system, using adiabatic elimination technique. Applying the STIRSAP method in two-level systems, the modified Rabi frequencies for fast population transfer are achieved. For N + 1-pod systems, assuming that N Stokes pulses have the same time dependence, we reduce the Hamiltonian of the original system to a three-state system. For both resonance and detuning conditions, we can reduce the three-state Hamiltonian to an effective two-state one. Using the STIRSAP technique, robust population transfer can be achieved from an initial ground state to an arbitrary coherent superposition of all ground states.
In this paper, we carry out the non-Hermitian stimulated Raman shortcut-to-adiabatic passage (NH-STIRSAP) to create ultracold deeply-bound molecules. The open three-level molecular system is supposed to have irreversible decays out of all levels. Under the assumption of large single-photon detuning and/or strong loss rate of the excited level, the NH three-level system can be theoretically reduced to an effective two-level system. By continuously using the counter-diabatic driving of the shortcut-to-adiabaticity, an auxiliary field is produced to couple the Feshbach level with the ground level. In the numerical calculations, we firstly consider the case of decaying only from the excited level, which is the main loss of the system. Under the NH-STIRSAP, the calculations reveal that complete population transfer from the Feshbach to the ground level can occur even if the adiabatic condition is not fulfilled. Therefore, the creation efficiency of ultracold deeply-bound molecules is greatly improved. The results hold equally for counter-intuitive and intuitive time sequence of the Stokes and pump pulse. If the decays from the Feshbach and ground level are also included, the NH-STIRSAP can still restore most of that efficiency, which performs much better than typical stimulated Raman adiabatic passage. Finally, we point out that the robustness and fast transfer speed of the NH-STIRSAP facilitate the creation and detection of ultracold deeply-bound molecules.
Abstract Stimulated Raman adiabatic passage (STIRAP) is a widely used protocol to realize high-fidelity and robust quantum control in various quantum systems. However, further application of this protocol in superconducting qubits is limited by population leakage caused by the only weak anharmonicity. Here, we introduce an optimally controlled shortcut-to-adiabatic (STA) technique to speed-up the STIRAP protocol in a superconducting qudit. By modifying the shapes of the STIRAP pulses, we experimentally realize a fast (32 ns) and high-fidelity (0.996 ± 0.005) quantum state transfer. In addition, we demonstrate that our protocol is robust against control parameter perturbations. Our stimulated Raman shortcut-to-adiabatic passage transition provides an efficient and practical approach for quantum information processing.