This review aims to provide researchers, experimentalists, and quantum engineers with an updated and technically grounded perspective on the implementation of quantum gates in superconducting NISQ devices. The goal is to establish a comprehensive bridge between theoretical quantum circuit synthesis and its practical, experimental implementation, focusing on superconducting quantum technologies. We systematically examine the diverse landscape of superconducting qubits and processor architectures, ranging from conventional transmons to alternative and unconventional designs, evaluating their unique design trade-offs, connectivity constraints, device physics, and materials impact. Moving from theory to actual implementation, we detail how single- and two-qubit operations are synthesized via microwave-driven and flux-activated pulses. We here present our pulse engineering, wave shaping, calibration workflows, demonstrating how to bridge the gap between abstract gate models and real-world hardware limitations in the direction of a hardware-software co-design framework. To validate these operations, we choose benchmarking methodologies with the purpose to get the more efficient metric for the specific evaluation aspect, including truth tables and quantum process tomography. Therefore, we both discuss the theoretical concepts behind the gate synthesis and show experimental implementation of most fundamental gates by proposing a practical workflow.
Summary form only given. Entangled states are increasingly important for a number of emergent quantum technologies, including cryptography, teleportation, and computation. In order to fully exploit the potential of these technologies, the ability to create, manipulate and characterize arbitrary quantum states is vital. Here we present theoretical and experimental investigations on the production of general quantum states (e.g., partially mixed and partially entangled) of two qubits, represented by the polarization degrees of freedom of photons.
We propose two Clifford+
T synthesis algorithms that are optimal with respect to
T-count. The first algorithm, called deterministic synthesis, approximates any single-qubit unitary by a single-qubit Clifford+
T circuit with the minimum
T-count. The second algorithm, called probabilistic synthesis, approximates any single-qubit unitary by a probabilistic mixture of single-qubit Clifford+
T circuits with the minimum
T-count. For most of single-qubit unitaries, the runtimes of deterministic synthesis and probabilistic synthesis are
ε−1/2−o(1) and
ε−1/4−o(1), respectively, for an approximation error
ε. Although this complexity is exponential in the input size, we demonstrate that our algorithms run in practical time at
ε≈10−15 and
ε≈10−22, respectively. Furthermore, we show that, for most single-qubit unitaries, the deterministic synthesis algorithm requires at most
3log2(1/ε)+o(log2(1/ε)) T-gates, and the probabilistic synthesis algorithm requires at most
1.5log2(1/ε)+o(log2(1/ε)) T-gates. Remarkably, complexity analyses in this work do not rely on any numerical or number-theoretic conjectures.