Optimizing control for implementing error correction in superconducting quantum circuits

Liang Jiang

Hai Li Xu, Wanchun Li, Tao Chen +2 more

ABSTRACT Nonadiabatic holonomic quantum computation (NHQC) leverages non‐Abelian geometric phases within a nonadiabatic framework to achieve fast and robust quantum gate operations. However, the practical implementation of NHQC is challenged by the imperfect control inherent in experimental environments. Ensuring deep suppression of control error is critical. In this work, we propose a dynamically optimized NHQC scheme to construct universal super‐robust holonomic quantum gates. The proposed scheme is implemented by strategically designing a set of dynamically correcting pulses to achieve cyclic evolution, while ensuring that unwanted and disruptive dynamical phase elements, including previously neglected cross‐coupling terms, are not accumulated. This constructed super‐robust NHQC scheme efficiently safeguards the cyclic evolution process and makes the holonomic gate immune to control error by effectively correcting the error up to the fourth order. Furthermore, when integrated with decoherence‐free subspace (DFS) encoding in superconducting quantum circuits, our scheme can achieve high‐fidelity holonomic gates, and demonstrate robust resilience against both control errors and collective dephasing errors. Consequently, our work offers a promising pathway toward the realization of scalable and fault‐tolerant holonomic quantum computation.

Michel Devoret

Zi Wang, Guohua Gao, 武光明

Charles Yuan, Michael Carbin

Numerous quantum algorithms require the use of quantum error correction to overcome the intrinsic unreliability of physical qubits. However, quantum error correction imposes a unique performance bottleneck, known as T -complexity, that can make an implementation of an algorithm as a quantum program run more slowly than on idealized hardware. In this work, we identify that programming abstractions for control flow, such as the quantum if-statement, can introduce polynomial increases in the T -complexity of a program. If not mitigated, this slowdown can diminish the computational advantage of a quantum algorithm. To enable reasoning about the costs of control flow, we present a cost model that a developer can use to accurately analyze the T -complexity of a program under quantum error correction and pinpoint the sources of slowdown. To enable the mitigation of these costs, we present a set of program-level optimizations that a developer can use to rewrite a program to reduce its T -complexity, predict the T -complexity of the optimized program using the cost model, and then compile it to an efficient circuit via a straightforward strategy. We implement the program-level optimizations in Spire, an extension of the Tower quantum compiler. Using a set of 11 benchmark programs that use control flow, we empirically show that the cost model is accurate, and that Spire's optimizations recover programs that are asymptotically efficient, meaning their runtime T -complexity under error correction is equal to their time complexity on idealized hardware. Our results show that optimizing a program before it is compiled to a circuit can yield better results than compiling the program to an inefficient circuit and then invoking a quantum circuit optimizer found in prior work. For our benchmarks, only 2 of 8 tested quantum circuit optimizers recover circuits with asymptotically efficient T -complexity. Compared to these 2 optimizers, Spire uses 54 × − 2400 × less compile time.

Charles Yuan, Michael Carbin

Numerous quantum algorithms require the use of quantum error correction to overcome the intrinsic unreliability of physical qubits. However, error correction imposes a unique performance bottleneck, known as T-complexity, that can make an implementation of an algorithm as a quantum program run more slowly than on idealized hardware. In this work, we identify that programming abstractions for control flow, such as the quantum if-statement, can introduce polynomial increases in the T-complexity of a program. If not mitigated, this slowdown can diminish the computational advantage of a quantum algorithm. To enable reasoning about the costs of control flow, we present a cost model that a developer can use to accurately analyze the T-complexity of a program and pinpoint the sources of slowdown. We also present a set of program-level optimizations, that a developer can use to rewrite a program to reduce its T-complexity, predict the T-complexity of the optimized program using the cost model, and then compile it to an efficient circuit via a straightforward strategy. We implement the program-level optimizations in Spire, an extension of the Tower quantum compiler. Using a set of 11 benchmark programs that use control flow, we show that the cost model is accurate, and that Spire's optimizations recover programs that are asymptotically efficient, meaning their runtime T-complexity under error correction is equal to their time complexity on idealized hardware. Our results show that optimizing a program before it is compiled to a circuit can yield better results than compiling the program to an inefficient circuit and then invoking a quantum circuit optimizer found in prior work. For our benchmarks, only 2 of 8 tested circuit optimizers recover circuits with asymptotically efficient T-complexity. Compared to these 2 optimizers, Spire uses 54x to 2400x less compile time.