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arXiv:2503.24274 · Journal of Superconductivity and Novel Magnetism

Implementation and Readout of Maximally Entangled Two-Qubit Gates Quantum Circuits in a Superconducting Quantum Processor

Viviana Stasino, P. Mastrovito, Carlo Cosenza, Anna Levochkina, Martina Esposito, Domenico Montemurro, Giovanni Piero Pepe, Alessandro Bruno, Francesco Tafuri, D. Massarotti, Halima Giovanna Ahmad

Published Apr 1, 2025• 3 citations
arXivHTMLPDF

Abstract

Abstract Besides noticeable challenges in implementing low-error single- and two-qubit quantum gates in superconducting quantum processors, the readout technique and analysis are a key factor in determining the efficiency and performance of quantum processors. Being able to efficiently implement quantum algorithms involving entangling gates and asses their output is mandatory for quantum utility. In a transmon-based 5-qubit superconducting quantum processor, we compared the performance of quantum circuits involving an increasing level of complexity, from single-qubit circuits to maximally entangled Bell circuits. This comparison highlighted the importance of the readout analysis and helped us optimize the protocol for more advanced quantum algorithms. Here, we report the results obtained from the analysis of the outputs of quantum circuits using two readout paradigms, referred to as “multiplied readout probabilities” and “conditional readout probabilities.” The first method is suitable for single-qubit circuits, while the second is essential for accurately interpreting the outputs of circuits involving two-qubit gates.

DOI
10.1007/s10948-025-06968-x

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Abstract Besides noticeable challenges in implementing low-error single- and two-qubit quantum gates in superconducting quantum processors, the readout technique and analysis are a key factor in determining the efficiency and performance of quantum processors. Being able to efficiently implement quantum algorithms involving entangling gates and asses their output is mandatory for quantum utility. In a transmon-based 5-qubit superconducting quantum processor, we compared the performance of quantum circuits involving an increasing level of complexity, from single-qubit circuits to maximally entangled Bell circuits. This comparison highlighted the importance of the readout analysis and helped us optimize the protocol for more advanced quantum algorithms. Here, we report the results obtained from the analysis of the outputs of quantum circuits using two readout paradigms, referred to as “multiplied readout probabilities” and “conditional readout probabilities.” The first method is suitable for single-qubit circuits, while the second is essential for accurately interpreting the outputs of circuits involving two-qubit gates.
Higher-dimensional gates involving more than two qubits could play a major role in boosting the performance of quantum processors. While native two-qubit gates are ubiquitous on the superconducting-qubit platform, realizing high-fidelity three-qubit gates is challenging and typically requires multiple two-qubit gates, which leads to error accumulation. The authors utilize a multimodal ``trimon'' circuit to realize $n\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}v\phantom{\rule{0}{0ex}}e$ three-qubit gates that enable efficient implementation of important quantum algorithms, such as Grover's search. These results point to improved processor performance when the trimon is used as a building block for larger systems.
Achieving high-fidelity single-qubit gates, two-qubit gates, and qubit readout is critical for building scalable, error-corrected quantum computers. However, device parameters that enhance one operation often degrade the others, making simultaneous optimization challenging. Here, we demonstrate that careful tuning of qubit-coupler coupling strengths in a superconducting circuit with two transmon qubits coupled via a tunable coupler enables high-fidelity single- and two-qubit gates, without compromising readout performance. Furthermore, we introduce a new calibration protocol for diabatic controlled- Z gates, phased-averaged leakage error amplification (PALEA), which enables efficient suppression of coherent gate errors and leakage to noncomputational states. Using PALEA in combination with careful tuning of qubit-coupler coupling strengths, we achieve a 40 h-averaged CZ gate fidelity of 99.93 %, simultaneous single-qubit gate fidelities of 99.98 %, and readout fidelities over 99.94 % in a single device. Our results demonstrate a viable path toward scaling up superconducting quantum processors while maintaining consistently high gate and readout fidelities.
Quantum algorithms on near-term quantum processors are typically executed using shallow quantum circuits composed of one- and two-qubit gates. However, as circuit depth and gate number increase, gate imperfections and qubit decoherence begin to dominate, limiting algorithmic complexity. An alternative approach is to explore gates involving more than two qubits. In previous work (X. Wu et al., Physical Review X 14, 041030 (2024)), we demonstrated a new superconducting qubit architecture with user-selectable two-qubit interactions via a reconfigurable router, used to connect pairs of qubits. Here, we leverage this novel architecture to realize programmable and efficient multi-qubit operations involving more than two qubits, resulting in faster preparation of multi-qubit entangled states with good fidelities. We also successfully apply model-free reinforcement learning to perform multi-qubit gates, including training a two-qubit controlled-Z gate as well as three-qubit controlled-SWAP and controlled-controlled-phase (Fredkin and Toffoli) gates. Higher nnnth-order gates may also be feasible, using our high-connectivity router design. This could provide a more efficient and higher-fidelity implementation of complex quantum algorithms and a more practical approach to quantum computation.
Quantum computing utilizes quantum mechanics to perform computations with superconducting qubits being the more mature technology as of writing in realizing a quantum computer. In this thesis, we describe an implementation of a Quantum Processor Unit (QPU), which is used to execute instructions in the form of microwave pulses on a superconducting qubit device through the use of signal generators and to perform qubit readout. We further extend the QPU as a platform to perform qubit characterization tasks such as spectroscopy and decoherence measurements in order to determine and optimize the working parameters to perform quantum gate operations. We also demonstrate the use of the QPU in performing qubit experiments such as Gauss Sum Factorization in determining the factors of an integer and the Bell Inequality test in examining the entanglement strength between a pair of qubits. We bridge the divide of quantum computation and qubit hardware in the compilation of quantum circuits into microwave pulse sequences for the QPU to execute. The process of compilation, as well as hardware limitations and pre-compilation optimization procedures are discussed. Finally, we show an example of executing a variational quantum algorithm and break down this example in all layers from the quantum circuit provided by the user to the pulse sequence that will be executed on the QPU.
Quantum computing is a novel paradigm for information processing that promises computational speedup for certain computational tasks while not being driven by Moore's law. Superconducting circuits based on Josephson junctions are one of the leading approaches for implementing the quantum bits, or qubits, in a quantum processor. Most superconducting qubit architectures involve circuit quantum electrodynamics, where the qubits are analogous to artificial atoms that are coupled to superconducting linear resonant cavities. This scheme allows for the readout of individual qubits, the manipulation of single-qubit states, and the generation of entanglement between qubits. The performance of current state-of-the-art systems is limited by decoherence of the qubits and associated gate errors. Nonetheless, experiments have been performed that already demonstrate a significant computational speedup compared to classical processing. Future implementations of fault-tolerant quantum computers will require the development of quantum error correction. Initial tests of elements of error correction in superconducting qubit arrays are underway.
We present the experimental implementation of two-qubit quantum algorithms in a superconducting circuit. Our processor incorporates local and fast flux biasing of two transmon qubits within a circuit QED architecture. An off-resonant cavity bus shields the qubits from the external environment and couples them to each other via virtual photon exchange. Meanwhile, integrated short-circuited coplanar waveguides proximal to each qubit allow nanosecond control of their frequencies. We demonstrate flux-controlled single-qubit z rotations and a qubit-qubit conditional phase (c-phase) interaction with a coupling strength tunable by two orders of magnitude. These operations are combined with frequency-multiplexed x and y rotations to form a set of gates universal for quantum computation. Dispersive frequency shifts of the cavity bus allow tomography of the two-qubit state, and accurate determination of state purity, fidelity and entanglement. The processor is first programmed to generate and detect entanglement on demand using sequences of five single-qubit operations and one c-phase. The four Bell states are generated with fidelities better than 90%, corresponding to a concurrence of 0.85 or an entanglement of formation of 0.8. Next, the Grover search algorithm is implemented by concatenating eight single-qubit and two c-phases operations. The fidelity of the algorithm output states to the theoretical ideal is ~ 80%, consistent with the observed T1 times ~ 1 us and the total duration ~ 130 ns of the algorithm sequence. We also program and execute the Deutsch-Jozsa algorithm, finding similar performance. Prospects for scaling the processor beyond two qubits will be discussed. Research supported by NSF, NSA and ARO.