Quantum computing hinges on the ability to perform high-fidelity quantum gates. Two-qubit gates are crucial for creating entangled states, enabling computations beyond classical capabilities. While spin qubits in quantum dots offer advantages like semiconductor compatibility and long coherence times, integrating universal gate sets – combining single-qubit rotations with entangling two-qubit gates – has proved difficult. Previous work demonstrated SWAP oscillations, but a universal set remained elusive. This research addresses this gap by demonstrating a complete set of high-fidelity single and two-qubit gates on a silicon double quantum dot device. The success of this endeavor is critical due to the inherent limitations in existing approaches: in quantum dot systems, exchange interaction between spins facilitates two-qubit gate implementation. However, the exchange interaction's interplay with the Zeeman energy difference between qubits significantly impacts the feasibility of implementing SWAP and CPHASE gates. Previous experiments predominantly focused on CPHASE gates due to the relative ease of implementation compared to SWAP gates in the presence of a Zeeman energy difference. This work aims to create a more versatile and efficient approach by performing all three gates, minimizing gate operation times and maximizing fidelity.

Prior research extensively explored the potential of spin qubits in quantum dots for quantum computing. Loss and DiVincenzo proposed the use of quantum dots for quantum computation using the exchange interaction between neighboring spins. Subsequent experiments demonstrated coherent manipulation of coupled electron spins, including SWAP oscillations. However, challenges in realizing high-fidelity universal gate sets above 1 Kelvin persisted. Previous demonstrations of two-qubit logic gates primarily relied on CPHASE, avoiding the challenges associated with SWAP gate implementation when facing a significant Zeeman energy difference. Some studies utilized driven rotations to implement controlled-rotation (CROT) operations, contributing to the development of universal quantum logic. Existing approaches often necessitate a significant Zeeman energy difference between qubits, requiring specialized techniques such as the integration of nanomagnets to achieve sufficient distinguishability between qubits. This paper builds upon these foundational studies, tackling the long-standing challenge of integrating high-fidelity SWAP and CPHASE gates with single-qubit rotations in a single silicon-based device while operating above 1 Kelvin. The integration of these components into a universal quantum logic gate set is a significant step towards the practical implementation of scalable quantum computers.

The experimental setup utilizes electron spin states confined in a silicon double quantum dot fabricated using an overlapping gate architecture on an isotopically enriched ²⁸Si epilayer. Two plunger gates (P₁ and P₂) and a barrier gate (B) control the detuning energy (ε) and tunnel coupling (*t*) between the quantum dots. Spin manipulation is achieved via electron spin resonance (ESR) using an on-chip microwave line. Spin readout is performed at the (1,5)-(2,4) charge anticrossing, exploiting Pauli spin blockade. The researchers use adiabatic and diabatic pulse sequences for coherent control. The adiabatic sequence ramps the detuning energy slowly to minimize unintended SWAP rotations when implementing CPHASE gates. The diabatic sequence abruptly changes the detuning, optimizing SWAP oscillations for the SWAP gate implementation. A composite pulse sequence is used for implementing a high-fidelity SWAP gate by combining alternating diabatic and adiabatic exchange pulses, correcting for the effects of the finite Zeeman energy difference. CROT operations are implemented via driven rotations, utilizing the exchange interaction's influence on the resonance frequencies of the qubits. The system is characterized by measuring the exchange interaction (*J*) via detuning, extracting the Zeeman energy difference (Δ*E*_z), and performing Ramsey and Carr-Purcell-Meiboom-Gill experiments to assess coherence times. Time-dependent simulations of the Heisenberg Hamiltonian are used to model the experimental results and estimate fidelities, considering experimental noise sources, such as charge noise characterized by a 1/*f* noise spectrum. All experiments are performed at a temperature of approximately 1.05 K and an external magnetic field of 250 mT.

The study successfully demonstrates the implementation of single-qubit rotations alongside CROT, CPHASE, and SWAP two-qubit gates on the same silicon double quantum dot device, operating above 1 Kelvin. The researchers achieved short gate times: CROT (660 ns), adiabatic CPHASE (152 ns), diabatic CPHASE (67 ns), and composite SWAP (88 ns). Theoretical analysis, considering experimental noise sources, predicts gate fidelities exceeding 99% for the diabatic CPHASE and composite SWAP gates. The CROT gate showed a lower predicted fidelity (89%) primarily due to its longer gate time and susceptibility to noise. The experimental data shows good agreement with the theoretical models of the noise. The use of adiabatic and diabatic pulse sequences proved crucial in overcoming limitations imposed by the finite Zeeman energy difference between qubits. The high-fidelity implementation of the SWAP gate, using composite pulses, is a notable achievement, surpassing alternatives using CPHASE and CROT operations. The experiments achieved maximum coherence times exceeding 63 µs and 44 µs using the Carr-Purcell-Meiboom-Gill pulse sequence for the different qubit states, significantly advancing the performance of silicon-based qubits at elevated temperatures.

The results demonstrate the feasibility of creating high-fidelity universal gate sets in silicon quantum dots at temperatures exceeding 1 Kelvin, eliminating the need for cryogenic cooling requirements of prior research. This is a substantial step towards creating scalable and practical quantum computers. The ability to perform a multitude of two-qubit gates, instead of relying on sequences of simpler gates, directly reduces operational overhead and potential error accumulation. The short gate times and high predicted fidelities showcase the potential for improved quantum algorithms. The relatively small magnetic field used is also beneficial for the scalability of quantum dot arrays, enabling efficient shuttling and long-distance connectivity between qubits. The research significantly advances the field by demonstrating the possibility of integrating quantum circuits that seamlessly combine qubits and classical control electronics at elevated temperatures.

This research successfully demonstrated the implementation of a universal set of high-fidelity single-qubit and two-qubit gates in silicon double quantum dots operating above 1 Kelvin. The use of adiabatic and diabatic pulse sequences was key to overcoming challenges posed by the finite Zeeman energy difference, enabling fast and high-fidelity CPHASE and SWAP gate implementations. This work significantly advances the field of silicon-based quantum computing by paving the way for scalable quantum integrated circuits operating at higher temperatures. Future research could focus on further optimizing gate fidelities, investigating alternative control schemes to reduce noise sensitivity, and exploring the implementation of these gate sets in larger-scale quantum dot arrays.

The current study primarily focuses on a two-qubit system. Scaling up to larger quantum processors will require addressing challenges related to crosstalk and the complexity of control electronics. The fidelity of the CROT gate is slightly lower than the other two-qubit gates, which warrants further investigation. While the predicted fidelities for the diabatic CPHASE and composite SWAP are high, experimental verification on these specific gates is necessary. The model of the noise used in the simulations might not capture all sources of decoherence, potentially affecting the accuracy of the predicted fidelities.