Abstract
Quantum computing and quantum simulation can be implemented by concatenation of one- and two-qubit gates and interactions. For most physical implementations, however, it may be advantageous to explore state components and interactions that depart from this universal paradigm and offer faster or more robust access to more advanced operations on the system. In this article, we show that adiabatic passage along the dark eigenstate of excitation exchange interactions can be used to implement fast multi-qubit Toffoli (C$_k$-NOT) and fan-out (C-NOT$^k$) gates. This mechanism can be realized by simultaneous excitation of atoms to Rydberg levels, featuring resonant exchange interaction. Our theoretical estimates and numerical simulations show that these multi-qubit Rydberg gates are possible with errors below 1% for up to 20 qubits. The excitation exchange mechanism is ubiquitous across experimental platforms and we show that similar multi-qubit gates can be implemented in superconducting circuits.
Highlights
In the circuit model paradigm of quantum computing, a quantum algorithm is implemented as a sequence of oneand two-qubit gates chosen from a suitable universal gate set [1]
The excitation exchange mechanism is ubiquitous across experimental platforms, and we show that similar multiqubit gates can be implemented in superconducting circuits
In Appendix F, we briefly present how the qubit interaction parameters are obtained from the circuit capacitances and Josephson energies, and we discuss the multiqubit gate fidelities achievable with realistic physical parameters
Summary
In the circuit model paradigm of quantum computing, a quantum algorithm is implemented as a sequence of oneand two-qubit gates chosen from a suitable universal gate set [1]. Rydberg excited atoms.—Another prominent scheme for quantum computing and simulation with neutral atoms employs lasers to excite atoms to high lying and strongly interacting Rydberg states This scheme gives rise to the excitation blockade mechanism [33], which works on ensemble qubits [34]. Rather than the blockade mechanism, our gate makes use of the strong dipolar exchange interactions between Rydberg excited atoms, and it employs adiabatic following of a multiply Rydberg excited dark eigenstate under variation of laser excitation amplitudes This method leads to robust implementation of the fan-out and Toffoli gates with infidelities at the 1% level for up to k 1⁄4 20 control and target qubits. In the Appendixes, we supplement our error estimates with more detailed models, and we present numerical simulations in support of the error scalings identified in the main text
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