Arbitrary logic state preparation protocol. Top panel: The surface code is divided into 5 regions, the central data qubit, regions I, II, III and IV. The logical operators Z ̂_L and X ̂_L intersect at the central data qubits. Lower panel: The protocol circuit. All qubits are reset to the ├├|0┤⟩ state at the start of the circuit. Then, the data qubits in regions I and III are prepared for ├ ├|+┤⟩ by the Hadamard gate, and the central data qubit is prepared for the target state ├ ├|ψ┤⟩ by rotation gates . A surface code cycle is then applied, projecting the state of the data qubits into logical state space. Credit: Yangsen Ye et al.
Quantum computers have the potential to outperform conventional computers in certain tasks, particularly for complex optimization problems. However, quantum computers are also vulnerable to noise, which can lead to calculation errors.
Engineers attempted to design fault-tolerant quantum computing approaches, which could be more resilient to noise and thus could be scaled up more robustly. A common approach to achieving fault tolerance is to prepare magic states, which introduce so-called non-Clifford gates.
Researchers from the University of Science and Technology of China, Henan Key Laboratory of Quantum Information and Cryptography, and Hefei National Laboratory recently demonstrated the preparation of a logical magic state with fidelity beyond the distillation threshold on a superconducting quantum processor. Their article, published in Physical Examination Lettersdescribes a viable and efficient strategy for generating high-fidelity logical magic states, an approach to achieve fault-tolerant quantum computing.
“We have a long-term plan in the field of quantum error correction,” Professor Xiao-Bo Zhu, co-author of the paper, told Phys.org. “After the completion of our previous work on a distance 3 surface code for repeated error correction, we consider our next goal to be the preparation of logical magic states.”
The ultimate goal of Professor Zhu and his colleagues’ recent research is to realize universal, robust, and fault-tolerant quantum computing. Preparing logical magic states is a key step to implementing non-Clifford logic gates, which in turn lead to the realization of fault-tolerant quantum computing.
“In simple terms, the basic idea of our protocol is to first inject the state to be prepared into one of the qubits in the surface code, and then “propagate” the state information to all of the surface code, thereby achieving logical state preparation.” Professor Zhu explained. “In this protocol, the choice of the injection position of the state to be prepared and the initialization states of the other qubits is important.”
Experimental results of the different logical states prepared. (a) Fidelity of the logical state with post-selection in the Bloch sphere. The fidelity of the preparation of the different logical states is represented by a circle divided into several annular sectors, each representing a point on the Bloch sphere, the radial direction representing the polar angle θ and the tangential direction representing the azimuthal angle φ. . The average logical fidelity obtained is 0.8983. (b) Logical measurement results of X ̂_L, Y ̂_L, Z ̂_L as a function of polar angle θ or azimuthal angle φ. The colored dotted curves are the result of an adjustment with the trigonometric function. (c) The logical density matrices of magical states. The real and imaginary parts are represented separately, and the transparent wireframes represent the difference from the ideal density matrix. Credit: Yangsen Ye et al.
The protocol proposed by this team of researchers describes a simple, experimentally viable and scalable strategy for preparing high-fidelity raw magic states in superconducting quantum processors. In their recent study, Professor Zhu and his colleagues applied this protocol on Zuchongzhi 2.1, a 66-qubit quantum professor with a tunable coupling design.
“The design of this processor allows us to manipulate the interaction between two adjacent qubits, ensuring that our quantum gates are sufficiently faithful despite a high degree of parallelism,” said Professor Zhu. “This design also allows scaling of qubits on a single processor.”
When the researchers implemented their protocol on the Zuchongzhi 2.1 processor, they obtained very promising results. Specifically, they non-destructively prepared three logical magic states with logical fidelities of 0.8771 ± 0.0009, 0.9090 ± 0.0009, and 0.8890 ± 0.0010, respectively, which are above the threshold from the state distillation protocol, 0.859 (for the H-type magic state) and 0.827 (for the T-type magic state).
“We have achieved a critical milestone in the development of fault-tolerant computation based on the surface code by successfully preparing a distance-three logical magic state with fidelity exceeding the distillation threshold,” said Professor Zhu. “This result implies that we can introduce low-fidelity magic states into the magic state distillation circuit, undergo multiple distillations to obtain sufficiently high-fidelity magic states, and then use them to construct fault-tolerant non-Clifford logic gates. “
In the future, the protocol developed by Professor Zhu and colleagues could be used by other research teams to realize high-fidelity raw logical magic states, using a wider range of superconducting quantum processors. Ultimately, this could contribute to the realization of robust fault-tolerant quantum computing, which could in turn enable the development of larger-scale quantum computers.
“In the field of quantum error correction, we plan to continue to explore two main research directions,” Professor Zhu added. “First, we aim to improve the performance of a logical qubit (or error-corrected quantum memory) by reducing the physical manipulation error rate and increasing the number of encoded qubits, thereby suppressing the error rate. logical error at practical levels. Second, we conduct experimental research on error-corrected logic operations, such as network surgery, for application in future fault-tolerant quantum computing.
More information:
Yangsen Ye et al, Preparing a logical magic state with fidelity beyond the distillation threshold on a superconducting quantum processor, Physical Examination Letters (2023). DOI: 10.1103/PhysRevLett.131.210603
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