Abstract
An array of ultracold neutral atoms held in optical micro-traps is a promising platform for quantum computation. One of the major bottlenecks of this platform is the weak coupling strength between adjacent atoms, which limits the speed of two-qubit gates. Here, we present a method to perform a fast universal square-root-SWAP gate with fermionic atoms. The basic idea of the gate is to release the atoms into a harmonic potential positioned in between the two atoms. By properly tailoring the interaction parameter, the collision process between the atoms generates entanglement and yields the desired gate. We prove analytically that in the limit of broad atomic wave-packets, the fidelity of the gate approaches unity. We demonstrate numerically that with typical experimental parameters, our gate can operate on a microsecond timescale and achieves a fidelity higher than 0.998. Moreover, the gate duration is independent of the initial distance between the atoms. A gate with such features is an important milestone towards all-to-all connectivity and fault tolerance in quantum computation with neutral atoms.
Highlights
Quantum mechanics poses a computational challenge: The dimension of the Hilbert space grows exponentially with the system size
Many physical systems have been suggested as carriers of quantum information, including superconducting circuits [6,7,8,9,10], trapped ions [11,12,13,14,15,16,17,18], ultracold atoms [19,20,21,22,23], photons [24,25,26,27], defects in solids [28,29,30], and quantum dots [31,32,33,34]
The prevalent paradigm for quantum computation starts with initialization of the quantum bits (“qubits”), application of a series of oneand two-qubit gates from a small set of universal gates, and a measurement of the qubits’ final state [35]
Summary
Quantum mechanics poses a computational challenge: The dimension of the Hilbert space grows exponentially with the system size. A universal two-qubit SWAP gate can be implemented by allowing the atoms to tunnel between the two traps and exploiting the short-range interaction [69,70]. We solve analytically the two-particle dynamics and prove that the fidelity of the gate approaches unity as the squeezing parameter of the atomic wave packets in the central harmonic trap increases. Since the squeezing parameter is set by the ratio of the initial width of the Gaussian wave packet to the oscillator length [see Eq (9)], increasing the trapping frequency of the harmonic potential both shortens the gate duration and increases its fidelity. Since the value of γ (t ) is most important during this interval, we find numerically that the gate fidelities achieved with a constant interaction parameter are only slightly smaller than those obtained with a time-dependent one
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