Abstract
High-fidelity qubit initialization is of significance for efficient error correction in fault tolerant quantum algorithms. Combining two best worlds, speed and robustness, to achieve high-fidelity state preparation and manipulation is challenging in quantum systems, where qubits are closely spaced in frequency. Motivated by the concept of shortcut to adiabaticity, we theoretically propose the shortcut pulses via inverse engineering and further optimize the pulses with respect to systematic errors in frequency detuning and Rabi frequency. Such protocol, relevant to frequency selectivity, is applied to rare-earth ions qubit system, where the excitation of frequency-neighboring qubits should be prevented as well. Furthermore, comparison with adiabatic complex hyperbolic secant pulses shows that these dedicated initialization pulses can reduce the time that ions spend in the excited state by a factor of 6, which is important in coherence time limited systems to approach an error rate manageable by quantum error correction. The approach may also be applicable to superconducting qubits, and any other systems where qubits are addressed in frequency.
Highlights
Fast and high-fidelity manipulation of qubit states is one of the primary requirements for fault tolerant quantum information processing and quantum computing
We theorectically propose a protocol for designing pulses that can manipulate qubits closely spaced in frequency in a three-level system between two arbitrary states with a high fidelity
Bearing these boundary values in Eq (9) in mind, and considering the requirements on both the robustness and off-resonant excitations as described in the Introduction, we make an ansatz on γ(t), which fulfills Eq (9) and reads π nπ γ(t) an n=1 sin t, tf where an is the coefficient of each sinusoidal component, which will be discussed shortly
Summary
In a laser adapted interaction picture and within the rotating wave approximation, we write the Hamiltonian of a three-level system, as shown in Fig. 1, in stimulated Raman adiabatic passage for a “one-photon resonance” case in bases of |1 , |e , and |0 as [18, 38]. In the following we employ the LR invariants theory to find the solution of the Schrodinger equation [39]. Γ and β are time-dependent variables to be designed, and relate to the Rabi frequencies as: Ωp(t) = 2[βcot γ(t) sin β(t) + γcos β(t)],. Ωs(t) = 2[βcot γ(t) cos β(t) − γsin β(t)]. In these equations βand γdenote the time derivative of β and γ, respectively. We focus on the case where H(t) in Eq (1) drives the 3-level system from an initial state, for example |1 , to an arbitrary superposition target state |ψtg = cos θa |1 + sin θaeiφa |0 (θa and φa are arbitrary angles) or vice versa, along the invariant eigenstate |φ0(t)
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