Abstract
We present a general systematic approach to design robust and high-fidelity quantum logic gates with Raman qubits using the technique of composite pulses. We use two mathematical tools -- the Morris-Shore and Majorana decompositions -- to reduce the three-state Raman system to an equivalent two-state system. They allow us to exploit the numerous composite pulses designed for two-state systems by extending them to Raman qubits. We construct the NOT, Hadamard, and rotation gates by means of the Morris-Shore transformation with the same uniform approach: sequences of pulses with the same phases for each gate but different ratios of Raman couplings. The phase gate is constructed by using the Majorana decomposition. All composite Raman gates feature very high fidelity, beyond the quantum computation benchmark values, and significant robustness to experimental errors. All composite phases and pulse areas are given by analytical formulas, which makes the method scalable to any desired accuracy and robustness to errors.
Highlights
Composite pulses (CPs)—sequences of pulses with welldefined relative phases—have enjoyed tremendous success as a basic control tool of simple quantum systems over the past 40 years
Many new types of CPs have been developed in order to boost the fidelity of some well-known quantum control techniques, e.g., rapid adiabatic passage [13,31], stimulated Raman adiabatic passage [15,32], Ramsey interferometry [9,17], and dynamical decoupling [14]
Composite pulse sequences feature a unique combination of ultrahigh fidelity similar to resonant excitation and robustness to experimental errors similar to adiabatic techniques
Summary
Composite pulses (CPs)—sequences of pulses with welldefined relative phases—have enjoyed tremendous success as a basic control tool of simple quantum systems over the past 40 years. Our method uses two powerful mathematical techniques: the Morris-Shore transformation [47] and the Majorana decomposition [48], which map the threestate Raman system onto equivalent two-state systems. We briefly introduce these two techniques and design composite implementations of the single-qubit gates used in quantum computing. We assume that the Raman qubit consists of two ground states, |0 and |1 , coupled to an excited state |2 , as illustrated. Both the Morris-Shore (MS) transformation [47] and the Majorana decomposition [48] allow one to reduce the three-state Raman system to a two-state problem, Fig. 1 (right). To apply the MS transformation, a two-photon resonance is assumed, as shown schematically in Fig. 1 (top left). If we apply a sequence of such pairs of pulses, each with some relative phase φk, we can use the phases as free parameters to construct composite Raman gates
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