Proves efficient simulators emulate random unitary completions of isometries with error scaling exponentially in completion dimension. Shows exponential query separation between isometry dilation access and channel queries, improving quantum switch lower bounds.
Random Purifications of Isometries and Channels
iq.fp2.dev
November 4, 2026 at 4:59 AM
Proves efficient simulators emulate random unitary completions of isometries with error scaling exponentially in completion dimension. Shows exponential query separation between isometry dilation access and channel queries, improving quantum switch lower bounds.
Every isometry of the plane is the composition of at most three reflections on lines. As a corollary you get a classification of said isometries.
My favourite at 15.
My favourite at 15.
October 30, 2026 at 5:32 PM
Every isometry of the plane is the composition of at most three reflections on lines. As a corollary you get a classification of said isometries.
My favourite at 15.
My favourite at 15.
Will man Denken wissenschaftlich und substratunabhängig formulieren, braucht man das Vokabular und die bewiesenen Lemmas der hochdimensionalen Mathematik, Packungsdichte, Quasi-Orthogonalität, Sparsity, Restricted Isometry. 11/14
October 30, 2026 at 5:31 PM
Will man Denken wissenschaftlich und substratunabhängig formulieren, braucht man das Vokabular und die bewiesenen Lemmas der hochdimensionalen Mathematik, Packungsdichte, Quasi-Orthogonalität, Sparsity, Restricted Isometry. 11/14
Will man Denken wissenschaftlich und substratunabhängig formulieren, braucht man das Vokabular und die bewiesenen Lemmas der hochdimensionalen Mathematik, Packungsdichte, Quasi-Orthogonalität, Sparsity, Restricted Isometry. 11/14
October 30, 2026 at 5:31 PM
Will man Denken wissenschaftlich und substratunabhängig formulieren, braucht man das Vokabular und die bewiesenen Lemmas der hochdimensionalen Mathematik, Packungsdichte, Quasi-Orthogonalität, Sparsity, Restricted Isometry. 11/14
Weiter zur Sparsity der Aktivierungen und dem Restricted Isometry Property Theorem von Candès und Tao, die zusammen garantieren, dass sich eine überschaubare Anzahl konkreter Konzepte aus der riesigen Menge aller sprachlich formulierbaren Gedankenkonzepte überhaupt ... 6/14
October 30, 2026 at 5:31 PM
Weiter zur Sparsity der Aktivierungen und dem Restricted Isometry Property Theorem von Candès und Tao, die zusammen garantieren, dass sich eine überschaubare Anzahl konkreter Konzepte aus der riesigen Menge aller sprachlich formulierbaren Gedankenkonzepte überhaupt ... 6/14
Weiter zur Sparsity der Aktivierungen und dem Restricted Isometry Property Theorem von Candès und Tao, die zusammen garantieren, dass sich eine überschaubare Anzahl konkreter Konzepte aus der riesigen Menge aller sprachlich formulierbaren Gedankenkonzepte überhaupt ... 6/14
October 30, 2026 at 5:31 PM
Weiter zur Sparsity der Aktivierungen und dem Restricted Isometry Property Theorem von Candès und Tao, die zusammen garantieren, dass sich eine überschaubare Anzahl konkreter Konzepte aus der riesigen Menge aller sprachlich formulierbaren Gedankenkonzepte überhaupt ... 6/14
Takahiro Kajisa: Rank-one Factored Gradient Descent without Restricted Isometry: Application to Quantum Pure State Tomography on Multi-Qubits https://arxiv.org/abs/2610.34696 https://arxiv.org/pdf/2610.34696 https://arxiv.org/html/2610.34696
October 28, 2026 at 7:00 AM
Takahiro Kajisa: Rank-one Factored Gradient Descent without Restricted Isometry: Application to Quantum Pure State Tomography on Multi-Qubits https://arxiv.org/abs/2610.34696 https://arxiv.org/pdf/2610.34696 https://arxiv.org/html/2610.34696
Novel max-sliced gradient descent approach for quantum state tomography eliminates restricted isometry requirement, achieving 100% recovery success on 4-qubit systems using practical partial-weight Pauli measurements accessible in real experiments.
#QuantumTomography #QuantumAlgorithms #Research
#QuantumTomography #QuantumAlgorithms #Research
Factored Gradient Descent for Quantum State Tomography Without Restricted Isometry
arxiv.org
October 27, 2026 at 8:39 AM
Novel max-sliced gradient descent approach for quantum state tomography eliminates restricted isometry requirement, achieving 100% recovery success on 4-qubit systems using practical partial-weight Pauli measurements accessible in real experiments.
#QuantumTomography #QuantumAlgorithms #Research
#QuantumTomography #QuantumAlgorithms #Research
Phương pháp hạ dốc gradient max-sliced mới cho tomography trạng thái lượng tử loại bỏ yêu cầu isometry hạn chế, đạt 100% thành công phục hồi trên hệ thống 4-qubit bằng cách sử dụng các phép đo Pauli trọng số một phần có thể tiếp cận trong các thí nghiệm thực.
Hạ Dốc Gradient Phân Tích cho Tomography Trạng Thái Lượng Tử Không Cần Isometry Hạn Chế
arxiv.org
October 27, 2026 at 8:42 AM
Phương pháp hạ dốc gradient max-sliced mới cho tomography trạng thái lượng tử loại bỏ yêu cầu isometry hạn chế, đạt 100% thành công phục hồi trên hệ thống 4-qubit bằng cách sử dụng các phép đo Pauli trọng số một phần có thể tiếp cận trong các thí nghiệm thực.
Rank-one Factored Gradient Descent without Restricted Isometry: Application to Quantum Pure State Tomography on Multi-Qubits
https://arxiv.org/pdf/2610.34696
Takahiro Kajisa.
https://arxiv.org/pdf/2610.34696
Takahiro Kajisa.
https://arxiv.org/abs/2610.34696
arXiv abstract link
arxiv.org
October 27, 2026 at 9:33 AM
Rank-one Factored Gradient Descent without Restricted Isometry: Application to Quantum Pure State Tomography on Multi-Qubits
https://arxiv.org/pdf/2610.34696
Takahiro Kajisa.
https://arxiv.org/pdf/2610.34696
Takahiro Kajisa.
🔄 Updated Arxiv Paper
Title: Rank-one Factored Gradient Descent without Restricted Isometry: Application to Quantum Pure State Tomography on Multi-Qubits
Authors: Takahiro Kajisa
Read more: https://arxiv.org/abs/2610.34696
Title: Rank-one Factored Gradient Descent without Restricted Isometry: Application to Quantum Pure State Tomography on Multi-Qubits
Authors: Takahiro Kajisa
Read more: https://arxiv.org/abs/2610.34696
October 27, 2026 at 8:02 AM
🔄 Updated Arxiv Paper
Title: Rank-one Factored Gradient Descent without Restricted Isometry: Application to Quantum Pure State Tomography on Multi-Qubits
Authors: Takahiro Kajisa
Read more: https://arxiv.org/abs/2610.34696
Title: Rank-one Factored Gradient Descent without Restricted Isometry: Application to Quantum Pure State Tomography on Multi-Qubits
Authors: Takahiro Kajisa
Read more: https://arxiv.org/abs/2610.34696
Takahiro Kajisa: Rank-one Factored Gradient Descent without Restricted Isometry: Application to Quantum Pure State Tomography on Multi-Qubits https://arxiv.org/abs/2610.34696 https://arxiv.org/pdf/2610.34696 https://arxiv.org/html/2610.34696
October 27, 2026 at 7:00 AM
Takahiro Kajisa: Rank-one Factored Gradient Descent without Restricted Isometry: Application to Quantum Pure State Tomography on Multi-Qubits https://arxiv.org/abs/2610.34696 https://arxiv.org/pdf/2610.34696 https://arxiv.org/html/2610.34696
วิธี max-sliced gradient descent ที่เป็นนวัตกรรมสำหรับ quantum state tomography ขจัดข้อกำหนด restricted isometry และบรรลุความสำเร็จการกู้คืน 100% บนระบบ 4-qubit โดยใช้การวัด Pauli ที่มีน้ำหนักบางส่วน ซึ่งสามารถนำไปใช้ได้ในการทดลองจริง
#ทรมาณควอนตัม #อัลกอริทึมควอนตัม #วิจัย
#ทรมาณควอนตัม #อัลกอริทึมควอนตัม #วิจัย
Factored Gradient Descent สำหรับ Quantum State Tomography โดยไม่มี Restricted Isometry
iq.fp2.dev
October 27, 2026 at 8:41 AM
วิธี max-sliced gradient descent ที่เป็นนวัตกรรมสำหรับ quantum state tomography ขจัดข้อกำหนด restricted isometry และบรรลุความสำเร็จการกู้คืน 100% บนระบบ 4-qubit โดยใช้การวัด Pauli ที่มีน้ำหนักบางส่วน ซึ่งสามารถนำไปใช้ได้ในการทดลองจริง
#ทรมาณควอนตัม #อัลกอริทึมควอนตัม #วิจัย
#ทรมาณควอนตัม #อัลกอริทึมควอนตัม #วิจัย
Violate the isometry
October 20, 2026 at 9:00 PM
Violate the isometry
uneven dream (2015)
isometry world
isometry world
October 15, 2026 at 12:55 AM
uneven dream (2015)
isometry world
isometry world
Honor thy reason as a hidden isometry
October 15, 2026 at 11:00 AM
Honor thy reason as a hidden isometry
isometry 😌
Btw really like that last one
Btw really like that last one
October 13, 2026 at 6:32 AM
isometry 😌
Btw really like that last one
Btw really like that last one
Xunmeng Wu, Jian-Feng Cai, Zongben Xu, Zai Yang: Lifted Restricted Isometry Property and Fast Algorithm for Spectral Compressed Sensing With Near-Optimal Sample Complexity https://arxiv.org/abs/2610.18032 https://arxiv.org/pdf/2610.18032 https://arxiv.org/html/2610.18032
October 14, 2026 at 6:51 AM
Xunmeng Wu, Jian-Feng Cai, Zongben Xu, Zai Yang: Lifted Restricted Isometry Property and Fast Algorithm for Spectral Compressed Sensing With Near-Optimal Sample Complexity https://arxiv.org/abs/2610.18032 https://arxiv.org/pdf/2610.18032 https://arxiv.org/html/2610.18032
What is the isometry of the subcomplexe?
October 8, 2026 at 12:00 PM
What is the isometry of the subcomplexe?
Is there isometry?
October 4, 2026 at 7:00 AM
Is there isometry?
Dibyayan Chakraborty, Yann Vax\`{e}s: Additive Quasi-isometry via rooted graph partitions and layering partition https://arxiv.org/abs/2609.36186 https://arxiv.org/pdf/2609.36186 https://arxiv.org/html/2609.36186
September 30, 2026 at 6:47 AM
Dibyayan Chakraborty, Yann Vax\`{e}s: Additive Quasi-isometry via rooted graph partitions and layering partition https://arxiv.org/abs/2609.36186 https://arxiv.org/pdf/2609.36186 https://arxiv.org/html/2609.36186
No, the other “Lie”. though my father did publish articles on Lie Groups! www.researchgate.net/scientific-c...
L.N. Mann's research works | University of Massachusetts Amherst, Amherst Center (UMass Amherst) and other places
L.N. Mann's 5 research items with 3 citations and 247 reads, including: Perturbations of invariant metrics and associated isometry groups
www.researchgate.net
September 28, 2026 at 11:59 AM
No, the other “Lie”. though my father did publish articles on Lie Groups! www.researchgate.net/scientific-c...
Jayadev S. Athreya, Sascha Troscheit: The quasi-isometry classes of Galton--Watson trees https://arxiv.org/abs/2609.23882 https://arxiv.org/pdf/2609.23882 https://arxiv.org/html/2609.23882
September 22, 2026 at 6:50 AM
Jayadev S. Athreya, Sascha Troscheit: The quasi-isometry classes of Galton--Watson trees https://arxiv.org/abs/2609.23882 https://arxiv.org/pdf/2609.23882 https://arxiv.org/html/2609.23882
W. Burstein, A. Iosevich, B. Krause: Restricted isometry of sampled Fourier and Hadamard matrices via entropic descent https://arxiv.org/abs/2609.22568 https://arxiv.org/pdf/2609.22568 https://arxiv.org/html/2609.22568
September 22, 2026 at 6:42 AM
W. Burstein, A. Iosevich, B. Krause: Restricted isometry of sampled Fourier and Hadamard matrices via entropic descent https://arxiv.org/abs/2609.22568 https://arxiv.org/pdf/2609.22568 https://arxiv.org/html/2609.22568
Pietro Fr\'e, Mario Trigiante, Antoine Van Proeyen: Homogeneous Non Symmetric Special K\"ahler Geometries as Broken Isometry Metrics on Symmetric CV {K}\"ahler Manifolds:a new tool for $r=2$ ... https://arxiv.org/abs/2609.23395 https://arxiv.org/pdf/2609.23395 https://arxiv.org/html/2609.23395
September 22, 2026 at 6:54 AM
Pietro Fr\'e, Mario Trigiante, Antoine Van Proeyen: Homogeneous Non Symmetric Special K\"ahler Geometries as Broken Isometry Metrics on Symmetric CV {K}\"ahler Manifolds:a new tool for $r=2$ ... https://arxiv.org/abs/2609.23395 https://arxiv.org/pdf/2609.23395 https://arxiv.org/html/2609.23395