The research aims to create high-fidelity entangling operations crucial for universal quantum computing. Achieving fault-tolerant quantum computation requires gate fidelities above 0.99. While single-qubit gate fidelities routinely surpass this threshold, high-fidelity two-qubit gates remain challenging. Various qubit architectures, including ion traps and silicon-based quantum dots, have demonstrated high-fidelity two-qubit gates. Superconducting qubits, particularly transmons, have also shown promise with gates like CZ and CR exceeding 0.99 fidelity. This paper proposes a novel four-qubit quantum gate, termed the 'diamond gate,' leveraging quantum interference to achieve controlled two-qubit operations. The diamond gate natively implements multiple unitaries, making it valuable for quantum simulation and compilation. The authors propose a superconducting transmon implementation with capacitive coupling in a diamond geometry, building upon previous research on 2D transmon arrays but with different coupling and objectives.

The introduction thoroughly reviews existing high-fidelity two-qubit gate implementations across various qubit architectures. High-fidelity results (above 0.99) are reported for ion traps using Mølmer-Sørensen gates and for silicon-based quantum dots using controlled-rotation gates. Superconducting transmon qubits have demonstrated high fidelity with gates such as CZ, CR, iSWAP, νISWAP, bSWAP, RIP, and parametric CZ gates, typically achieved through direct qubit coupling or via intermediary coupling elements like resonators. This review sets the stage for the proposed diamond gate, highlighting the ongoing challenges and the potential advantages of the new approach.

The paper analyzes a four-qubit system with two target and two control qubits, modeled by a Hamiltonian incorporating non-interacting and interaction terms. The interaction Hamiltonian includes capacitive couplings (J and Jc) between control and target qubits. The analysis employs the rotating wave approximation (|Ω| ≫ |J, Jc|) and assumes the target qubits are on resonance. A Magnus expansion within Floquet theory (|Δ| ≫ |J, Jc|) is used to approximate the time evolution. This approximation is exact when Jc = 0, but a non-zero Jc is needed to initialize entangled Bell states for control. The diamond gate is defined as a four-way controlled two-qubit gate, where the control qubit state determines the operation on the target qubits (four possibilities). Numerical simulations using the Lindblad master equation in QuTip incorporate decoherence (relaxation and dephasing) to assess gate fidelity. Average fidelity, defined as an integral over input states, is used as a performance metric. The effects of various infidelities (crosstalk, noise, control state infidelity, and qubit decoherence) are investigated through simulations. Finally, a more detailed model incorporating the second excited state of transmons (qutrits) is explored, analyzing leakage effects and proposing crosstalk engineering to mitigate these issues.

The analytical and numerical findings demonstrate the functionality and high fidelity of the diamond gate. The theoretical analysis, using Floquet theory and the Magnus expansion, shows that the Hamiltonian generates the desired four-way controlled two-qubit gate. Numerical simulations using realistic superconducting qubit parameters and decoherence models show that the gate achieves average fidelities around 0.99 within a gate time of approximately 60 ns (parameter set 1). The simulations also show a trade-off between gate speed and fidelity. The impact of various infidelities, such as crosstalk, noise, control state infidelity, and decoherence, is analyzed. The results reveal that the gate is relatively robust against noise and control state infidelity. Crucially, the inclusion of higher energy levels in the transmon spectrum reveals potential leakage issues. The authors propose a novel technique of engineering crosstalk to mitigate leakage by tuning the crosstalk strength to a specific value where destructive interference cancels unwanted leakage processes. This crosstalk engineering leads to preserving gate functionality, albeit potentially increasing gate time.

The diamond gate successfully addresses the need for high-fidelity entangling operations in quantum computing. Its ability to implement multiple controlled two-qubit gates in a single device is a significant advance. The high fidelities achieved in simulations, coupled with the proposed mitigation strategy for leakage, demonstrate the practicality of this design. The proposed architectural scheme for extending the diamond gate to larger-scale quantum computers is a promising approach for constructing highly connected quantum systems. This work significantly contributes to the development of scalable and fault-tolerant quantum computers. The crosstalk engineering technique is especially noteworthy, providing a passive method to address a common issue in superconducting qubit systems. Future work could explore different qubit platforms or more sophisticated control schemes to further improve gate performance.

This paper presents a novel four-qubit quantum gate, the diamond gate, achieving high fidelity in simulations. The ability to perform multiple controlled two-qubit operations and the proposed mitigation strategy for leakage through crosstalk engineering are key contributions. The design is scalable and paves the way for constructing highly connected quantum computers. Future research could investigate optimized control strategies and explore applications of the diamond gate in specific quantum algorithms.

The study is primarily based on numerical simulations. Experimental verification is needed to confirm the predicted fidelities and gate performance. The analysis focuses on a specific type of superconducting transmon qubit. The performance might vary for different qubit types or implementations. The crosstalk engineering technique involves a trade-off, potentially increasing gate time for certain operations.