Arbitrary controlled-phase gate on fluxonium qubits using differential ac-Stark shifts

Abstract

Large scale quantum computing motivates the invention of two-qubit gate schemes that not only maximize the gate fidelity but also draw minimal resources. In the case of superconducting qubits, the weak anharmonicity of transmons imposes profound constraints on the gate design, leading to increased complexity of devices and control protocols. Here we demonstrate a resource-efficient control over the interaction of strongly-anharmonic fluxonium qubits. Namely, applying an offresonant drive to non-computational transitions in a pair of capacitively-coupled fluxoniums induces a ZZ-interaction due to unequal ac-Stark shifts of the computational levels. With a continuous choice of frequency and amplitude, the drive can either cancel the static ZZ-term or increase it by an order of magnitude to enable a controlled-phase (CP) gate with an arbitrary programmed phase shift. The cross-entropy benchmarking of these non-Clifford operations yields a sub 1% error, limited solely by incoherent processes. Our result demonstrates the advantages of strongly-anharmonic circuits over transmons in designing the next generation of quantum processors.

Optimizing frequency allocation for fixed-frequency superconducting quantum processors

“…We have also shown that using the differential AC-Stark shift to realize a CZ entanglement gate gives an extra degree of freedom on the entanglement drive fre-quency and improves the yield of this architecture, thus improving the scaling possibility of this architecture. Fixed-frequency quantum processor with transmon is currently one of the most developed architectures for multi-qubit systems, however, other qubit designs like fluxonium [23] can also realize quantum processors and will have different frequency constraints that can potentially give an advantage over transmon in terms of yield.…”

“…Differential AC-Stark shift or SiZZle -A control-Z gate with simultaneous AC-Stark shift entangling gate has recently been proposed and demonstrated for both fluxonium [23] and transmon architectures [19,24] as an alternative to the CR gate. The constraints for this gate are similar to those for the CR case with the modification that the drive frequency can now vary between the frequency of the control and the target transmon.…”

Non-perturbative analytical diagonalization of Hamiltonians with application to coupling suppression and enhancement in cQED

“…The Hamiltonian interaction term is written as ζσ z1 σ z2 , acting on the two qubits. Typically, in superconducting systems, it arises from the interaction of the |11 state with the non-computational state in the physical qubits, and can both be used as a resource for entangling gates [21][22][23][24] or viewed as cross-talk noise that needs to be suppressed [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”

“…One implementation is using a transmon and a capacitively shunt flux qubit (CSFQ) [25,26]. Other methods include using additional off-resonant drive [39][40][41] and different types of qubits have also been proposed [38].…”

“…In the first regime, where the leakagelevel-mediated ZZ interaction can be used to generate CZ gates [21][22][23][24], we consider the two-excitation manifold and compute accurate approximations of the ZZ interaction strength applicable to the full parameter regime for gate implementation. In the second scenario, we study the suppression of ZZ interactions [10,[25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] in the traditional setup of resonator mediated coupling without direct qubit-qubit interaction. We compute the perturbative expansion of the ZZ interaction up to the 8th order perturbation as parametric expressions.…”