東京大学生産技術研究所の李と申します。
羽田野研究室では、下記の通りセミナーを開催致します。
皆様の奮ってのご参加をお待ちしております。
なお、当研究室におけるセミナー情報は、次のリンクよりご覧頂けます。
hatano-lab.iis.u-tokyo.ac.jp/seminar-j.html
当セミナーは原則として現地会場での開催となりますが、オンライン参加をご希望の方はご連絡下さい。
＊本案内は複数のメーリングリストにお送りしております。重複して受け取られました方は何卒ご容赦下さい。
Dear All,
This is Jaeha Lee from the Institute of Industrial Science, the University of Tokyo.
We are pleased to announce an upcoming seminar as follows.
Information regarding our seminar series is available on our web site.
hatano-lab.iis.u-tokyo.ac.jp/seminar-e.html
Those who are interested are welcome to join us on-site. For those who wish to join us online, please feel free to contact us.
* Apologies if you have received multiple copies of this announcement.
記
日時：２０２５年１０月１０日（金）１３時３０分〜 / Friday, 10th October 2025, 13:30 JST –
場所：東京大学生産技術研究所 研究実験棟Ｉ大会議室 / The large conference room, Research and Testing Complex I, IIS, the University of Tokyo
来場：http://hatano-lab.iis.u-tokyo.ac.jp/access-j.html / hatano-lab.iis.u-tokyo.ac.jp/access-e.html
講師：三橋洋亮（Mitsuhashi Yosuke）さん（理研 / RIKEN）
演題：Unitary Designs in Symmetric Quantum Random Circuits
要旨：
What emerges from the interplay of two fundamental notions in physics, symmetry and randomness? Symmetry is central to understanding phases of matter and useful for designing efficient algorithms. Randomness, on the other hand, appears in many topics such as quantum information processing, quantum chaos, and thermalization. However, generating truly random unitaries, i.e., sampling from the uniform distribution over the unitary group, is prohibitively hard. To address this, unitary t-designs are employed, which are distributions that reproduce the uniform distribution up to the t-th moment. For example, the Clifford group forms a unitary 3-design [1], and local random circuits asymptotically form unitary t-designs for all t [2].
This naturally leads to the following question: Do symmetry-constrained versions of these distributions form unitary designs over the symmetric unitary subgroup up to the same order? We address this question in the following two cases.
First, we consider subgroups of the Clifford group that respect a given symmetry. In Ref. [3], we prove that such symmetric Clifford groups form unitary 3-designs if and only if the symmetry constraint can be expressed as commutation with some Pauli subgroup. Moreover, we present an explicit procedure for uniformly sampling symmetric Clifford gates using only 2-qubit gates, making the scheme implementable in realistic setups.
Next, we study symmetric local random circuits on qudit systems, which are composed of random unitaries acting on randomly selected k qudits for some given k. In Ref. [4], we show that symmetry induces a fundamental upper bound on the achievable design order, and the tight upper bound is formulated as a simple integer optimization problem. By solving the optimization problem, we explicitly obtain the tight upper bound for three physically relevant symmetry groups, Z_2, U(1), and SU(2).
[1] H. Zhu, Multiqubit Clifford groups are unitary 3-designs, Phys. Rev. A 96, 062336 (2017).
[2] F. G. L. S. Brandao, A. W. Harrow, and M. Horodecki, Local random quantum circuits are approximate polynomial-designs, Commun. Math. Phys. 346, 397 (2016).
[3] Y. Mitsuhashi and N. Yoshioka, Clifford Group and Unitary Designs under Symmetry, PRX Quantum 4, 040331 (2023).
[4] Y. Mitsuhashi, R. Suzuki, T. Soejima, and N. Yoshioka, Unitary Designs of Symmetric Local Random Circuits, Phys. Rev. Lett. 134, 180404 (2025).
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李 宰河
〒277-8574 千葉県柏市柏の葉５－１－５
東京大学生産技術研究所
電 話：04-7136-6962
メール：lee@iis.u-tokyo.ac.jp
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