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physica status solidi (b)

Simulation of Two‐Qubit Gates with a Superconducting Qudit

Yuqian Dong, Qiang Liu, Jianhua Wang, Qingshi Li, Xiaoyan Yu, Wen Zheng, Yong Li, Dong Lan, Xinsheng Tan, Yang Yu

Published Dec 14, 2021• 4 citations
Publisher

Abstract

Herein, a two‐qubit system is experimentally simulated through a four‐level superconducting circuit. By mapping the energy levels of the two‐qubit system to a noncomposite system, some two‐qubit gates with designed microwave pulses, such as Hadamard and CNOT gates, are implemented. Furthermore, the Shannon entropy of the simulated two‐qubit system is measured and the log 2 uncertainty relation is verified, which describes that the noncomposite single‐qudit system possesses hidden quantum correlations.

DOI
10.1002/pssb.202100500

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Herein, a two‐qubit system is experimentally simulated through a four‐level superconducting circuit. By mapping the energy levels of the two‐qubit system to a noncomposite system, some two‐qubit gates with designed microwave pulses, such as Hadamard and CNOT gates, are implemented. Furthermore, the Shannon entropy of the simulated two‐qubit system is measured and the log 2 uncertainty relation is verified, which describes that the noncomposite single‐qudit system possesses hidden quantum correlations.
In article number 2100500, Xinsheng Tan, Yang Yu, and co-workers use a four-level superconducting quantum loop to simulate a two-qubit quantum system. By mapping the energy levels of the two-qubit system to a non-composite system, simulations of several quantum gate operations, including the CNOT gate and the Hadamard gate, are completed in a convenient way. Furthermore, the authors generate entangled states to verify the log2 entropic inequality. The results indicate that the superconducting qudit is indeed a huge quantum platform for quantum information.
We theoretically study operations with a four-level superconducting circuit as a two-qubit system. Using a mapping on a two-qubit system, we show how to implement iswap gates and Hadamard gates through pulses on transitions between particular pairs of energy levels. Our approach allows one to prepare pure two-qubit entangled states with desired form of reduced density matrices of the same purity and, in particular, arbitrary identical reduced states of qubits. We propose using schemes for the Hadamard gate and two-qubit entangled states with identical reduced density matrices in order to verify logNlogNlogN inequalities for Shannon and R\'enyi entropies for the considered noncomposite quantum system.
We study a class of entropic inequalities obtained for noncomposite quantum system realized by a many-level superconducting circuit. By using a mapping on bipartite quantum states, we consider possible realization schemes of various quantum logic gates for noncomposite quantum systems. In this framework, we discuss logN entropic inequalities for Shannon and R eniy entropies based on the quantum Fourier transform. Implementation of the quantum Fourier transform on a quantum processor based on many-level superconducting circuits opens a way for experimental verication of logN entropic inequalities.
This tutorial aims at giving an introductory treatment of the circuit analysis of superconducting qubits, i.e., two-level systems in superconducting circuits.It also touches upon couplings between such qubits and how microwave driving and these couplings can be used for single-and two-qubit gates, as well as how to include noise when calculating the dynamics of the system.We also discuss higher-dimensional superconducting qudits.The tutorial is intended for new researchers with limited or no experience with the field but should be accessible to anyone with a bachelor's degree in physics.The tutorial introduces the basic methods used in quantum circuit analysis, starting from a circuit diagram and ending with a quantized Hamiltonian, that may be truncated to the lowest levels.We provide examples of all the basic techniques throughout the discussion, while in the last part of the tutorial we discuss several of the most commonly used circuits for quantum-information applications.This includes both worked examples of single qubits and examples of how to analyze the coupling methods that allow multiqubit operations.In several detailed appendices, we provide the interested reader with an introduction to more advanced techniques for handling larger circuit designs.
The quantum gate is the foundation of quantum computation and simulation in superconducting circuits. In recent years, quantum systems with three energy levels have attracted much attention. Therefore, it is essential to study the protocol of the quantum‐state transfer in qutrits. Herein, the all‐microwave schemes are studied to realize the state transfer and quantum gates. First, the ∣fg>–∣ge> transition is designed in a superconducting circuit with a relatively large coupling. We measured the Stark shift in cases where the experimental parameters did not satisfy the dispersive condition. Then, by carefully calibrating the pulse parameters, the regular Rabi oscillation and the state transfer are realized between the second excited state of two qubits via stimulated Raman adiabatic passage.
Compared with a qubit, a qudit (i.e., a ddd-level or ddd-state quantum system) provides a larger Hilbert space to store and process information. On the other hand, qudit-based hybrid quantum computing usually requires performing hybrid quantum gates with qudits that are different in their nature or in their encoding format. In this work, we consider the qutrit case, i.e., the case for a qudit with d=3d=3d=3. We propose a simple method to realize a hybrid quantum controlled-sum gate with one superconducting (SC) qutrit and a cat-state qutrit. This gate plus single-qutrit gates form a universal set of ternary logic gates for quantum computing with qutrits. Our proposal is based on circuit QED and operates essentially by employing a SC ququart (a four-level quantum system) dispersively coupled to a microwave cavity. The gate implementation is quite simple because it only requires a single basic operation. Neither classical pulse nor measurement is needed. The auxiliary higher energy level of the SC ququart is virtually excited during the gate operation, thus decoherence from this level is greatly suppressed. As an application of this gate, we discuss the generation of a hybrid maximally entangled state of one SC qutrit and one cat-state qutrit. We further analyze the experimental feasibility of creating such a hybrid entangled state in circuit QED. This proposal is quite general and can be extended to accomplish the same task in a wide range of physical system, such as a four-level natural or artificial atom coupled to an optical or microwave cavity.