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IEEE International Conference on Quantum Computing and Engineering (QCE)

Preparing High-Fidelity Magic States on IBM Quantum Processors

Younghun Kim, Martin E. Sevior, Muhammad Usman

Published Aug 30, 2025• 0 citations
Publisher

Abstract

The surface code family is a promising approach to implementing fault-tolerant quantum computations. Universal fault-tolerance quantum computing requires error-corrected nonClifford operations, in addition to Clifford gates, and for the former, it is important to experimentally demonstrate additional resources known as magic states. Another challenge is to efficiently embed surface codes into quantum hardware with connectivity constraints. This work simultaneously addresses both challenges by employing a qubit-efficient rotated heavyhexagonal surface code for IBM quantum processors (ibm_fez) and implementing the magic state injection protocol. Our work reports error thresholds for both logical bit- and phase-flip errors, of$\approx 0.37 \%$and$\approx 0.31 \%$, respectively, which are higher than the threshold values previously reported with traditional embedding. The post-selection-based preparation of logical magic states$\vert H_{L}\rangle$and$\vert T_{L}\rangle$achieves fidelities of$0.8806 \pm 0.0002$and$0.8665 \pm 0.0003$, respectively, which are both above the magic state distillation threshold. Our work demonstrates the potential for realising nonClifford logical gates by producing high-fidelity logical magic states on IBM quantum devices.

DOI
10.1109/qce65121.2025.10406

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The surface code family is a promising approach to implementing fault-tolerant quantum computations. Universal fault-tolerance quantum computing requires error-corrected nonClifford operations, in addition to Clifford gates, and for the former, it is important to experimentally demonstrate additional resources known as magic states. Another challenge is to efficiently embed surface codes into quantum hardware with connectivity constraints. This work simultaneously addresses both challenges by employing a qubit-efficient rotated heavyhexagonal surface code for IBM quantum processors (ibm_fez) and implementing the magic state injection protocol. Our work reports error thresholds for both logical bit- and phase-flip errors, of≈0.37%\approx 0.37 \%≈0.37%and≈0.31%\approx 0.31 \%≈0.31%, respectively, which are higher than the threshold values previously reported with traditional embedding. The post-selection-based preparation of logical magic states∣HL⟩\vert H_{L}\rangle∣HL​⟩and∣TL⟩\vert T_{L}\rangle∣TL​⟩achieves fidelities of0.8806±0.00020.8806 \pm 0.00020.8806±0.0002and0.8665±0.00030.8665 \pm 0.00030.8665±0.0003, respectively, which are both above the magic state distillation threshold. Our work demonstrates the potential for realising nonClifford logical gates by producing high-fidelity logical magic states on IBM quantum devices.
The surface code family is a promising approach to implementing fault-tolerant quantum computations. Universal fault-tolerance requires error-corrected non-Clifford operations, in addition to Clifford gates, and for the former, it is imperative to experimentally demonstrate additional resources known as magic states. Another challenge is to efficiently embed surface codes into quantum hardware with connectivity constraints. This work simultaneously addresses both challenges by employing a qubit-efficient rotated heavy-hexagonal surface code for IBM quantum processors (ibm_fez) and implementing the magic state injection protocol. Our work reports error thresholds for both logical bit- and phase-flip errors, of [Formula: see text] and [Formula: see text], respectively, which are higher than the threshold values previously reported with traditional embedding. The post-selection-based preparation of logical magic states [Formula: see text] and [Formula: see text] achieve fidelities of [Formula: see text] and [Formula: see text], respectively, which are both above the magic state distillation threshold. The post-selection process yields an average success rate of [Formula: see text]. Additionally, we report the minimum fidelity among injected arbitrary single logical qubit states as [Formula: see text]. Our work demonstrates the potential for realising non-Clifford logical gates by producing high-fidelity logical magic states on IBM quantum devices.
Fault-tolerant quantum computing based on surface code has emerged as an attractive candidate for practical large-scale quantum computers to achieve robust noise resistance. To achieve universality, magic states preparation is a commonly approach for introducing non-Clifford gates. Here, we present a hardware-efficient and scalable protocol for arbitrary logical state preparation for the rotated surface code, and further experimentally implement it on the Zuchongzhi 2.1 superconducting quantum processor. An average of 0.8983±0.0002 logical fidelity at different logical states with distance three is achieved, taking into account both state preparation and measurement errors. In particular, the logical magic states |A^{π/4}⟩_{L}, |H⟩_{L}, and |T⟩_{L} are prepared nondestructively with logical fidelities of 0.8771±0.0009, 0.9090±0.0009, and 0.8890±0.0010, respectively, which are higher than the state distillation protocol threshold, 0.859 (for H-type magic state) and 0.827 (for T-type magic state). Our work provides a viable and efficient avenue for generating high-fidelity raw logical magic states, which is essential for realizing non-Clifford logical gates in the surface code.
Implementing fault-tolerant quantum computing necessitates the realization of logical non-Clifford gates, which requires the preparation of specific quantum states known as magic states. However, IBM’s heavy-hexagon structure, which has limited qubit connectivity, presents challenges in adapting quantum error correction codes such as the surface code. Several methods have been proposed to address these challenges by adapting the surface code to the heavy-hexagon architecture. In this study, we implement the magic state injection process within two distinct implementations of surface codes (standard and rotated methods) suitable for the heavy-hexagon structure and compare their logical error rates. Furthermore, we propose initialization methods to enhance the performance of magic state injection in the heavy-hexagon structure, thereby efficiently achieving logical non-Clifford gates with reduced error rates.
Fault-tolerant quantum computing based on the surface code requires magic states to achieve universality. The initially prepared magic states have low fidelity and need to be purified by a costly procedure called magic state distillation. The high spatial-temporal cost for distillation can be reduced by improving the fidelity of initial magic states. Prior works have investigated state injection approaches on the regular surface code. In this work, we propose a magic state injection method for the rotated surface code that requires fewer physical qubits to encode one logical qubit. Analytical results show that our method could achieve lower logical error rates than the state-of-the-art approach for the regular surface code in [1]. When both the two-qubit gate and single-qubit operation error rates are p, the new method results in a logical error rate to 34p/15 compared to 46p/15 in [1]. This fidelity improvement and fewer qubit encoding requirement would help reduce the overhead of fault-tolerant quantum computation, which is crucial for practical implementation in the near term.
In fault-tolerant quantum computing with the surface code, non-Clifford gates are crucial for universal computation. However, implementing these gates is usually more challenging and resource-intensive than Clifford gates. Methods such as distilling a high-fidelity magic state from noisy copies or transforming to higher-dimensional codes require a significant qubit count overhead. In this work, we propose a new protocol that combines magic state preparation and code transformation to realize logical non-Clifford operations, which has the potential for reducing the qubit count overhead, provided an efficient decoding algorithm exists for the intermediate non-Abelian code involved. Our approach begins with a special logical state in the Z4{{\mathbb{Z}}}_{4}Z4​ surface code. By applying a sequence of transformations, the system goes through different topological codes, including the non-Abelian D 4 quantum double model. This process ultimately produces a magic state encoded in the Z2{{\mathbb{Z}}}_{2}Z2​ surface code. A logical T gate can be implemented in the standard Z2{{\mathbb{Z}}}_{2}Z2​ surface code by gate teleportation. In our analysis, we employ a framework where the topological codes are represented by their topological orders and all the transformations are considered as topological manipulations such as gauging symmetries and condensing anyons. This perspective is particularly useful for understanding transformations between topological codes.
Fault-tolerant logical operations are fundamental for scalable quantum computation. Here, we report the experimental realization of lattice-surgery operations between a pair of distance-three surface-code logical qubits on a planar superconducting processor. During repeated syndrome extraction cycles, the logical qubits exhibit per-cycle error rates of 0.0365(2)0.0365(2)0.0365(2) and 0.0282(1)0.0282(1)0.0282(1), respectively, after leakage events are rejected. By leveraging joint initialization and lattice splitting, we deterministically prepare a logical Bell state, confirming genuine bipartite entanglement via the error-corrected logical state fidelity. We further execute a two-qubit Deutsch-Jozsa algorithm at the logical level to demonstrate algorithmic utility in a fault-tolerant framework. Finally, to achieve universal control, we implement magic-state injection and gate teleportation to realize continuous non-Clifford rotations about the logical XXX axis. For the logical RX(π/4)R_{X}(π/4)RX​(π/4) gate, we achieve a logical gate fidelity of 0.943−9+100.943_{-9}^{+10}0.943−9+10​ conditioned on the absence of detected errors. These results establish lattice surgery as a practical and versatile paradigm for logical computation in near-term surface-code architectures, representing a critical milestone toward scalable fault-tolerant quantum advantage in superconducting circuits.