Efficient Z-Gates for Quantum Computing (1612.00858v2)

Abstract: For superconducting qubits, microwave pulses drive rotations around the Bloch sphere. The phase of these drives can be used to generate zero-duration arbitrary "virtual" Z-gates which, combined with two $X_{\pi/2}$ gates, can generate any SU(2) gate. Here we show how to best utilize these virtual Z-gates to both improve algorithms and correct pulse errors. We perform randomized benchmarking using a Clifford set of Hadamard and Z-gates and show that the error per Clifford is reduced versus a set consisting of standard finite-duration X and Y gates. Z-gates can correct unitary rotation errors for weakly anharmonic qubits as an alternative to pulse shaping techniques such as DRAG. We investigate leakage and show that a combination of DRAG pulse shaping to minimize leakage and Z-gates to correct rotation errors (DRAGZ) realizes a 13.3~ns $X_{\pi/2}$ gate characterized by low error ($1.95[3]\times 10^{-4}$) and low leakage ($3.1[6]\times 10^{-6}$). Ultimately leakage is limited by the finite temperature of the qubit, but this limit is two orders-of-magnitude smaller than pulse errors due to decoherence.

• The paper demonstrates that virtual Z-gates improve quantum gate fidelity by reducing error per Clifford gate through strategic phase adjustments.
• It shows that these gates effectively correct unitary rotation errors in superconducting qubits, offering a practical alternative to complex DRAG techniques.
• Combined pulse shaping with VZ-gates (DRAGZ) significantly suppresses leakage errors, enabling simpler calibration and more robust quantum circuits.

Efficient Z-Gates for Quantum Computing

The paper "Efficient Z-Gates for Quantum Computing" addresses the implementation and utility of virtual Z-gates (VZ-gates) in the context of superconducting qubits. This paper provides a comprehensive analysis of how these gates, which can be generated through phase adjustments of microwave pulses, contribute to improved fidelity and error correction in quantum computing.

Overview of Virtual Z-Gates

For superconducting qubits, rotations on the Bloch sphere—which represent quantum state transformations—are typically executed using X and Y gates with finite durations. These gates are driven by microwave pulses tuned to the qubit's resonance frequency. In contrast, rotations about the Z axis, or Z-gates, alter the phase between the qubit states $|0\rangle$ and $|1\rangle$. This paper demonstrates the theoretical basis and practical implementation of using phase adjustments in the microwave control hardware to create virtual Z-gates that do not require additional pulse time, distinguishing them from traditional gates.

Key Findings and Results

1. Fidelity Improvement: The authors employ randomized benchmarking to show that sequences composed of virtual Z-gates interposed with traditional X and Y gates lead to improved Clifford gate fidelity. The error per Clifford gate using this approach is significantly reduced compared to sequences employing only finite-duration gates.
2. Efficiency in Error Correction: VZ-gates are shown to effectively correct unitary rotation errors common in superconducting qubits, particularly those driven by weakly anharmonic transmon qubits. This presents an alternative to the Derivative Removal by Adiabatic Gate (DRAG) technique that typically addresses such errors but is often complex to implement.
3. Leakage Suppression: The paper explores how employing pulse shaping techniques like DRAG, combined with VZ-gates (termed DRAGZ in the paper), effectively suppresses leakage errors. This combined approach achieves a balance between fidelity optimization and leakage reduction. The reported leakage rate after implementing DRAGZ is two orders of magnitude smaller than other sources of pulse error such as decoherence.
4. Theoretical Application and Gate Construction: The ability of VZ-gates to be seamlessly incorporated into quantum circuits is further leveraged by illustrating their capacity to simplify the execution of arbitrary single-qubit gates. It can be synthesized by combining VZ-gates with a minimal number of fixed finite-duration gates ($X_{\pi/2}$), thus simplifying calibration complexity.

Implications for Quantum Systems

The implications of this work are substantial for scaling quantum systems. As quantum processors aim for increased qubit numbers and system scales, the ability to reduce gate errors and enhance operational fidelity is crucial. The negligible duration and high accuracy of VZ-gates propose significant advantages in implementing quantum algorithms efficiently and reliably. Additionally, the strategies discussed for mitigating leakage and rotation errors without resorting exclusively to complex pulse-shaping methods could simplify control mechanisms in quantum processors.

Speculation on Future Developments

Future work may further explore the integration of VZ-gates in entangling operations and the broader multi-qubit context. With qubit cross-talk and phase decoherence being persistent challenges in the development of quantum computers, research might focus on the extension of these VZ-gate principles to multi-qubit operations and error correction codes. There is also a potential area of exploration in optimizing the digital phase control methods for VZ-gates in various quantum computing architectures.

In conclusion, the paper presents integral findings on improving gate fidelity and error correction mechanisms in quantum computing through the use of VZ-gates. The insights set a promising pathway for developing more robust quantum operations in superconducting platforms and potentially beyond, supporting the progression towards practical and scalable quantum computing solutions.