Seminars

日時：4月17日（水） 14:30-16:00

場所：理化学研究所 和光キャンパス 研究本館 4階 445-447

Title: Operator Growth in Open Quantum Systems : Perspectives from Lindbladian SYK via Krylov Complexity

Abstract:
In this talk, I will discuss some general features of operator growth in open quantum systems governed by Lindbladian evolution. I will introduce two orthonormalization techniques, namely Arnoldi and BiLanczos algorithms, using which I will capture the evolution of the operator in an appropriate basis. In these bases, many features of the evolution of operators (including relevant time scales) will emerge naturally. I will motivate these bases choices from results in closed quantum systems. I will utilize the paradigmatic setup of the Sachdev-Ye-Kitaev model to describe the system and environment, and closely related system-environment interaction. I will present numerical results in this setup and derive some analytical results. I will also discuss the nature of correlation function and spectral function in such open quantum systems. Then I will discuss features of a large class of probes (that do not rely on the same choice of basis) in such systems. I will end by mentioning implications of these results in other areas of research, and some open questions/future directions.

[1] Operator dynamics in Lindbladian SYK: a Krylov complexity perspective, JHEP 01 (2024) 094   
[2] Operator growth in open quantum systems: lessons from the dissipative SYK, JHEP 03 (2023) 054

日時：9月8日（木） 14:00-16:00

場所：オンライン（Zoom） 

Title: Transport coefficients of Lieb-Liniger model and related models

Abstract:
Lieb-Liniger model is a one-dimensional Bose gas with a two-body contact interaction. This model is known to be integrable and has divergent transport coefficients. Additionally, when we experimentally realize a one-dimensional Bose gas by confining a three-dimensional Bose gas, a three-body interaction appears to break the integrability. These facts motivate us to study transport coefficients of the one-dimensional Bose gas with two-body and three-body interactions theoretically. Furthermore, the Lieb-Liniger model is known to be the dual of the Cheon-Shigehara model, where the thermodynamic properties of one of the models at weak coupling coincide with that of the other at strong coupling. It is not well studied whether the duality extends beyond the thermodynamics to the correlation functions, so finding a transport coefficient that satisfies the duality is significant.

    In this seminar, we discuss two topics related to the above. First, we calculate the thermal conductivity of the one-dimensional Bose gas with two-body and three-body interactions perturbatively. Since there are a series of diagrams that are naively higher order in the perturbation but become the lowest order due to the pinch singularities, we have to sum up all contributions from such diagrams even though we evaluate the Kubo formula in the lowest order. Second, we apply Girardeau’s Bose-Fermi mapping to the Kubo formula for the bulk viscosity, showing that the bulk viscosities of the two models are identical at the same scattering length. We also compute their bulk viscosities perturbatively in the weak-coupling limit, which via the duality serve as those of the two models in the strong-coupling limit.

[1] T.Tanaka and Y.Nishida, Thermal conductivity of a weakly interacting Bose gas by quasi-one dimensionality, arXiv preprint arXiv:2203.04936 (2022).

[2] T.Tanaka and Y.Nishida, Bulk viscosity of dual Bose and Fermi gases in one dimension, arXiv preprint arXiv:2206.07848 (2022).

日時：5月26日（水） 16:00-17:00

場所：オンライン（Zoom） 参加登録は前日までに、右よりお願いします forms.gle/Z9igaNko3nstaDes5 

タイトル：1次元及び2次元デュアルユニタリ量子回路の計算能力 

アブストラクト：

　量子コンピュータは古典コンピュータを凌駕する計算能力を持つと信じられている。そのため量子コンピュータを古典コンピュータで効率よくシミュレートすることが、一般には不可能だと考えられている。ところが、いくつかの量子回路は量子特有の相関を生み出すにもかかわらず、古典コンピュータで効率よくシミュレート出来る[1,2]。古典シミュレート可能な量子回路を新たに構築することは、どの様な制限の下で量子特有の計算能力を失うか、またどの様な要素が量子加速に必要かを調べる上で重要である。一方で最近、デュアルユニタリ量子回路と呼ばれる量子回路が非平衡多体系の可解模型として注目を集めており、熱力学極限における局所物理量の期待値や相関関数が厳密に求められている[3]。

　本セミナーでは、1次元及び2次元デュアルユニタリ量子回路を量子計算モデルと見なし、その計算能力について調べた研究結果を発表する[4]。具体的には、我々はデュアルユニタリ量子回路の局所物理量の期待値を計算出力とするモデルについて考えた。その結果、回路深さが浅い時（量子ビット数程度まで）は、局所物理量の期待値が古典シミュレート可能になる一方で、回路深さが十分深い時はこの量子回路が万能量子計算可能になる事が分かった。それに加えて、デュアルユニタリ量子回路全体の出力を古典コンピュータによりサンプルすることは、計算量的仮定の下で困難である事がわかった。

　本発表では、量子計算や量子回路モデルの基礎知識から話す予定である。

[1] D. Gottesman, Stabilizer codes and quantum error correction, PhD thesis, California Institute of Technology (1997).

[2] L. G. Valiant, Quantum circuits that can be simulated classically in polynomial time, SIAM Journal on Computing 31, 1229 (2002).

[3] L. Piroli, B. Bertini, J. I. Cirac, and T. Prosen, Exact dynamics in dual-unitary quantum circuits, Physical Review B 101, 094304 (2020).

[4] R. Suzuki , K. Mitarai, and K. Fujii, Computational power of one-and two-dimensional dual-unitary quantum circuits, arXiv preprint arXiv:2103.09211 (2021). 

FY2024

*

FY2022

*H-Y. Huang et al., "Predicting many properties of a quantum system from very few measurements," Nature Physics volume 16, pages 1050–1057 (2020).

*S. Aaronson and A. Arkhipov, "The computational complexity of linear optics," STOC '11: Proceedings of the forty-third annual ACM symposium on Theory of computing (2011).

*D. E. Parker et al., "A Universal Operator Growth Hypothesis," Phys. Rev. X 9, 041017 (2019).