Hybrid early fault-tolerant quantum computing with bosonic ancillas
ORAL
Abstract
As a natural extension from noisy intermediate-scale quantum (NISQ) devices to fully fault-tolerant (FT) quantum computers, early FT designs of quantum algorithms and architectures are gaining increasing attention due to their potential to surpass classical simulators and become realizable and useful in the near future.
In many early fault-tolerant algorithms, arbitrary-angle rotation gates, such as $R_z(\theta)$, play a crucial role in encoding classical information into quantum circuits. However, the fully fault-tolerant implementation of these gates involves complex T-gate compilation and the costly procedures of magic state distillation and injection.
In this work, we propose a hybrid early FT architecture, where Clifford gates are performed fault-tolerantly on surface codes using standard discrete-level qubits, while arbitrary-angle rotation gates are initially performed on cat states encoded in bosonic cavities and then injected into surface codes.
By leveraging the error structure and Hamiltonian-control techniques, we ensure that bosonic operations, including arbitrary-angle rotations, can tolerate all first-order errors during their implementation, as is shown in our previous work [PRX 14, 031016 (2024)].
We design a fault-tolerant circuit to teleport the arbitrary-angle state encoded in the cat code to a surface code. Numerical results show that, with current hardware, we can prepare arbitrary-angle states on surface codes with an infidelity around 1e−4 using feasible bosonic and transmon hardware parameters (with p=1e−3), allowing the reliable execution of about 10,000 rotation gates on a quantum computer. Furthermore, when transmon gate noise is reduced to p=1e-4, the gate infidelity improves to approximately 1e-6, enabling the execution of up to a million rotation gates.
Finally, we discuss how our technique can be combined with recent small-angle state preparation schemes from [arXiv:2303.17380], highlighting its practical applications in digital quantum simulation.
In many early fault-tolerant algorithms, arbitrary-angle rotation gates, such as $R_z(\theta)$, play a crucial role in encoding classical information into quantum circuits. However, the fully fault-tolerant implementation of these gates involves complex T-gate compilation and the costly procedures of magic state distillation and injection.
In this work, we propose a hybrid early FT architecture, where Clifford gates are performed fault-tolerantly on surface codes using standard discrete-level qubits, while arbitrary-angle rotation gates are initially performed on cat states encoded in bosonic cavities and then injected into surface codes.
By leveraging the error structure and Hamiltonian-control techniques, we ensure that bosonic operations, including arbitrary-angle rotations, can tolerate all first-order errors during their implementation, as is shown in our previous work [PRX 14, 031016 (2024)].
We design a fault-tolerant circuit to teleport the arbitrary-angle state encoded in the cat code to a surface code. Numerical results show that, with current hardware, we can prepare arbitrary-angle states on surface codes with an infidelity around 1e−4 using feasible bosonic and transmon hardware parameters (with p=1e−3), allowing the reliable execution of about 10,000 rotation gates on a quantum computer. Furthermore, when transmon gate noise is reduced to p=1e-4, the gate infidelity improves to approximately 1e-6, enabling the execution of up to a million rotation gates.
Finally, we discuss how our technique can be combined with recent small-angle state preparation schemes from [arXiv:2303.17380], highlighting its practical applications in digital quantum simulation.
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Presenters
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Pei Zeng
University of Chicago
Authors
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Pei Zeng
University of Chicago
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Guo Zheng
University of Chicago
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Qian Xu
California Institute of Technology
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Liang Jiang
University of Chicago