الملخص
Protecting quantum information from noise is essential for reliable quantum computation and quantum memories. Quantum state purification addresses this challenge by processing multiple noisy copies of an unknown quantum state to produce an output state of higher fidelity. Here we establish nearly tight upper and lower bounds on the non-Clifford resources required to implement the symmetric-projection purification protocol. For $n$ copies of a $d$-dimensional system, we construct a Clifford+T circuit that block-encodes the symmetric projector with operator-norm error at most $ε$ using $\widetilde{O}(n)$ T gates, where the tilde-$O$ notation suppresses polylogarithmic factors in $n$, $d$, and $1/ε$. Conversely, using stabilizer nullity, we prove that any Clifford+T implementation of such a block encoding with error $ε<\frac{1}{2}\sqrt{1-1/n}$ requires at least $2n-2$ T gates, even allowing arbitrary positive normalization and clean stabilizer ancillas. Taken together, these results establish the nearly optimal scaling of non-Clifford cost with the number of copies and uncover the fundamental resource requirements for coherent symmetry projection in quantum state purification.
الكلمات المفتاحية
الموضوع
بيانات النشر
- المجلة
- غير متاح
- وصول مفتوح
- وصول مفتوح أخضر
اقتبس هذه المقالة
APA 7
Tang, J., Nie, J., He, K., Wang, X., & Sun, X. (2026). Nearly Optimal T-Count for Symmetry-Based Quantum State Purification. https://omanscience.com/ar/articles/nearly-optimal-t-count-for-symmetry-based-quantum-state-purification
MLA 9
Tang, Jialiang, et al. "Nearly Optimal T-Count for Symmetry-Based Quantum State Purification." https://omanscience.com/ar/articles/nearly-optimal-t-count-for-symmetry-based-quantum-state-purification.
شيكاغو (المؤلف–التاريخ)
Tang, Jialiang, Junhong Nie, Keming He, Xin Wang, and Xiaoming Sun. 2026. "Nearly Optimal T-Count for Symmetry-Based Quantum State Purification." https://omanscience.com/ar/articles/nearly-optimal-t-count-for-symmetry-based-quantum-state-purification.
هارفارد
Tang, J., Nie, J., He, K., Wang, X. and Sun, X. (2026) 'Nearly Optimal T-Count for Symmetry-Based Quantum State Purification', Available at: https://omanscience.com/ar/articles/nearly-optimal-t-count-for-symmetry-based-quantum-state-purification.
فانكوفر
Tang J, Nie J, He K, Wang X, Sun X. Nearly Optimal T-Count for Symmetry-Based Quantum State Purification. https://omanscience.com/ar/articles/nearly-optimal-t-count-for-symmetry-based-quantum-state-purification
IEEE
J. Tang, J. Nie, K. He, X. Wang, and X. Sun, "Nearly Optimal T-Count for Symmetry-Based Quantum State Purification," https://omanscience.com/ar/articles/nearly-optimal-t-count-for-symmetry-based-quantum-state-purification.