Abstract Variational algorithms such as the quantum approximate optimization algorithm have attracted attention due to their potential for solving problems using near-term quantum computers. The ZZ interaction typically generates the primitive two-qubit gate in such algorithms applied for a time, typically a variational parameter, γ. Different compilation techniques exist with respect to the implementation of two-qubit gates. Due to the importance of the ZZ-gate, we present an error analysis comparing the continuous-angle controlled phase gate (CP) against the fixed angle controlled Z-gate (CZ). We analyze both techniques under the influence of coherent over-rotation and depolarizing noise. We show that CP and CZ compilation techniques achieve comparable ZZ-gate fidelities if the incoherent error is below 0.03% and the coherent error is below 0.8%. Thus, we argue that for small coherent and incoherent error a non-parameterized two-qubit gate such as CZ in combination with virtual Z decomposition for single-qubit gates could lead to a significant reduction in the calibration required and, therefore, a less error-prone quantum device. We show that above a coherent error of 0.04π (2%), the CZ gate fidelity depends significantly on γ.
Variational algorithms such as the Quantum Approximate Optimization Algorithm have attracted attention due to their potential for solving problems using near-term quantum computers. The
ZZ interaction typically generates the primitive two-qubit gate in such algorithms applied for a time, typically a variational parameter,
γ. Different compilation techniques exist with respect to the implementation of two-qubit gates. Due to the importance of the
ZZ-gate, we present an error analysis comparing the continuous-angle controlled phase gate (CP) against the fixed angle controlled
Z-gate (CZ). We analyze both techniques under the influence of coherent over-rotation and depolarizing noise. We show that CP and CZ compilation techniques achieve comparable
ZZ-gate fidelities if the incoherent error is below
0.03% and the coherent error is below
0.8%. Thus, we argue that for small coherent and incoherent error a non-parameterized two-qubit gate such as CZ in combination with virtual
Z decomposition for single-qubit gates could lead to a significant reduction in the calibration required and, therefore, a less error-prone quantum device. We show that above a coherent error of
0.04π (
2%), the CZ gate fidelity depends significantly on
γ.
Abstract Two-qubit gates are important components of quantum computing. However, unwanted interactions between qubits (so-called parasitic gates) can be particularly problematic and degrade the performance of quantum applications. In this work, we present two software methods to mitigate parasitic two-qubit gate errors. The first approach is built upon the Cartan’s KAK decomposition and keeps the original unitary decomposition for the error-free native two-qubit gate. It counteracts a parasitic two-qubit gate by only applying single-qubit rotations and therefore has no two-qubit gate overhead. We show the optimal choice of single-qubit mitigation gates. The second approach applies a numerical optimisation algorithm to re-compile a target unitary into the error-parasitic two-qubit gate plus single-qubit gates. We demonstrate these approaches on the CPhase-parasitic iSWAP-like gates. The KAK-based approach helps decrease unitary infidelity by a factor of 3 compared to the noisy implementation without error mitigation. When arbitrary single-qubit rotations are allowed, recompilation could completely mitigate the effect of parasitic errors but may require more native gates than the KAK-based approach. We also compare their average gate fidelity under realistic noise models, including relaxation and depolarising errors. Numerical results suggest that different approaches are advantageous in different error regimes, providing error mitigation guidance for near-term quantum computers.
Abstract Limited by the decoherence of qubits as well as the errors of quantum gates, near-term superconducting quantum computers can only run low-depth quantum circuits to achieve acceptable fidelity. One possible way to overcome these limitations is to construct quantum circuits with additional high-fidelity expressive multi-qubit gates. Recently, a new three-qubit gate, denoted as Controlled-CPHASE-SWAP (CCZS), has been implemented through simultaneous Controlled-Z (CZ) gates. The CCZS gate takes less time than a single CZ gate and can be implemented at the coherence limit. However, how to use the CCZS gate in quantum circuit synthesis remains unexplored. In this paper, we construct the quantum fan-out/parity gates, the controlled-phase gate and the locally fully connected CZ gates with the CCZS gate, respectively. Furthermore, applications of the CCZS gate in quantum error correction, quantum Fourier transform and quantum approximate optimization algorithm are also proposed. We evaluate the performance of the CCZS gate in quantum circuit synthesis through simulation and explore its potential advantages over CZ gates.
The possibility to utilize different types of two-qubit gates on a single quantum computing platform adds flexibility in the decomposition of quantum algorithms.A larger hardware-native gate set may decrease the number of required gates, provided that all gates are realized with high fidelity.Here, we benchmark both controlled-Z (CZ) and exchange-type (iSWAP) gates using a parametrically driven tunable coupler that mediates the interaction between two superconducting qubits.Using randomized benchmarking protocols we estimate an error per gate of 0.9 ± 0.03 and 1.3 ± 0.4% for the CZ and the iSWAP gate, respectively.We argue that spurious ZZ-type couplings are the dominant error source for the iSWAP gate, and that phase stability of all microwave drives is of utmost importance.Such differences in the achievable fidelities for different two-qubit gates have to be taken into account when mapping quantum algorithms to real hardware.
Continuous gate sets are a key ingredient for near-term quantum algorithms. Here, we demonstrate a hardware-efficient, continuous set of controlled arbitrary-phase ( CZ θ ) gates acting on flux-tunable transmon qubits. This implementation is robust to control pulse distortions on time scales longer than the duration of the gate, making it suitable for deep quantum circuits. Our calibration procedure makes it possible to parameterize the continuous gate set with a single control parameter, the idle time between the two rectangular halves of the net-zero control pulse. For calibration and characterization, we develop a leakage measurement based on coherent amplification, and a new cycle design for cross-entropy benchmarking. We demonstrate gate errors of 0.7 % and leakage of 4 × 10 − 4 across the entire gate set. This native gate set has the potential to reduce the depth and improve the performance of near-term quantum algorithms compared to decompositions into CZ π gates and single-qubit gates. Moreover, we expect the calibration and benchmarking methods to find further possible applications.
We propose and validate on real quantum computing hardware a new method for extended two-qubit gate set design, replacing iterative, fine calibration with fast characterization of a small number of gate parameters which are then tracked and corrected in circuit compilation. Coherent contributions to the pulse unitary that would traditionally be considered sources of error are treated as part of the gate definition, and compensated in software via single-qubit rotations. This approach enables rapid device-wide generation of high-fidelity two-qubit entangling gates, which are combined with standard calibrated gates to produce an expanded gate set. We show how these gates are directly usable as part of a quantum compiler, synthesizing generic two-qubit circuit blocks into minimal-duration sequences of the characterized gates interleaved with compensating single-qubit rotations. Benchmarking against circuits compiled using the default
CX gate alone on 127-qubit IBM hardware shows up to 7X improvement in success probability for Quantum Fourier Transform circuits up to 26 qubits, and up to 9X lower mean-square error in Trotter simulations of the one-dimensional transverse-field Ising model. Our hardware-agnostic characterization and compilation methodology makes it practical to scale up expressive gate sets on quantum computing architectures while minimizing the need for onerous fine-tuning of low-level control waveforms.