Robust quantum gates for qubit clusters with fixed coupling

F. Setiawan, Hoi-Yin Hui, J. P. Kestner +1 more

David W. Kanaar, J. P. Kestner

A major current challenge in solid-state quantum computing is to scale qubit arrays to a larger number of qubits. This is hampered by the complexity of the control wiring for the large number of independently tunable interqubit couplings within these arrays. One approach to simplifying the problem is to use a qubit array with fixed Ising (ZZ) interactions. When simultaneously driving a specific subset of qubits in such a system, the dynamics are confined to a set of commuting $\text{su}(2)$ subalgebras. Within these $\text{su}(2)\mathrm{s}$ we describe how to perform X-gates and $\frac{\ensuremath{\pi}}{2}\phantom{\rule{4pt}{0ex}}\text{ZZ}$ rotations robustly against either leakage, which is the main source of error in transmon qubits, or coupling fluctuations, which is the main source of infidelity in flux or semiconductor spin qubits. These gates together with virtual-$z$ gates form a universal set of gates for quantum computing. We construct this set of robust gates for two-edge, three-edge, and four-edge vertices, which compose all existing superconducting qubit and semiconductor spin qubit arrays.

Fach Physik

Nguyen H. Le, Max Cykiert, Eran Ginossar

Abstract We propose a scheme for scalable and robust quantum computing on two-dimensional arrays of qubits with fixed longitudinal coupling. This opens the possibility for bypassing the device complexity associated with tunable couplers required in conventional quantum computing hardware. Our approach is based on driving a subarray of qubits such that the total multi-qubit Hamiltonian can be decomposed into a sum of commuting few-qubit blocks, and efficient optimisation of the unitary evolution within each block. The driving pulses are optimised to implement a target gate on the driven qubits, and at the same time identity gates on the neighbouring undriven qubits, cancelling any unwanted evolution due to the constant qubit-qubit interaction. We show that it is possible to realise a universal set of quantum gates with high fidelity on the basis blocks, and by shifting the driving pattern one can realise an arbitrary quantum circuit on the array. Allowing for imperfect Hamiltonian characterisation, we use robust optimal control to obtain fidelities around 99.99% despite 1% uncertainty in the qubit-qubit and drive-qubit couplings, and a detuning uncertainty at 0.1% of the qubit-qubit coupling strength. This robust feature is crucial for scaling up as parameter uncertainty is significant in large devices.

Nguyen H. Le, Max Cykiert, Eran Ginossar

We show how robust and scalable quantum computing can be realized on an arbitrarily large two dimensional arrays of qubits with fixed longitudinal couplings despite significant uncertainty in all the qubit-qubit and drive-qubit coupling strengths. This opens the possibility for bypassing the fabrication complexity associated with tunable couplers required in conventional quantum computing hardware. Our approach is based on driving a chosen subarray of qubits such that the total multi-qubit Hamiltonian can be decomposed into a sum of commuting few-qubit blocks and on efficient optimization of the unitary evolution within each block. Robust optimal control is then employed to implement a universal set of quantum gates with fidelities around 99.99% despite 1% uncertainty in the Hamiltonian's parameters. This robust feature is crucial for scaling up as uncertainty in the properties of qubits is substantial in large devices.

Svetoslav S. Ivanov, Nikolay V. Vitanov