Jun 21, 2024
- Speaker:
- Yi Liu (刘熠), BIMSA
- Title:
- 高性能计算与地学模型
- Time:
- 16:00 ~ 17:00 (Beijing Time)
- Venue:
- Shuangqing Building A626 (双清办公楼A座626)
- Abstract:
- 介绍高性能计算在地球系统模式与地理计算中的应用。
May 29, 2024
- Speaker:
- Ce Shen (沈策), BIMSA
- Title:
- Fusion Rules of Edge Excitations in Topological Order
- Time:
- 10:33 ~ 12:00 (Beijing Time)
- Venue:
- A3-3-301
- Online:
- Zoom: 242 742 6089
- Abstract:
- We re-examine the issue of boundary excitations at topological boundaries or junction defects between different topological boundaries in nonchiral bosonic topological orders in 2+1 dimensions. Through physical reasoning, we derive a formula that connects the fusion rules of boundary excitations with the “half-linking” number between condensed anyons and confined boundary excitations. This formula serves as a direct analogue to the Verlinde formula. Additionally, we illustrate how these half-linking numbers can be calculated in specific Abelian and non-Abelian scenarios.
May 10, 2024
- Speaker:
- Xingyu Ren (任兴宇), The Chinese University of Hong Kong
- Title:
- Towards a Complete Classification of Interacting Fermionic Symmetry-Protected Topological Phases
- Time:
- 16:00 ~ 17:00 (Beijing Time)
- Venue:
- Shuangqing Building B626 (双清办公楼B626)
- Online:
- Tencent Meeting 953 7541 0477 (PASSWORD 2024)
- Abstract:
- The topological quantum matters are classified by the interplay between symmetries and entanglement patterns. One of the three main categories of topological quantum matters is called symmetry-protected topological (SPT) phases, which are short-range entangled but protected by symmetries. SPT phases have seen a complete classification for bosonic systems a decade ago, whereas their fermionic counterpart (FSPT) remains an open challenge. Given a symmetry group, the classification result of SPT phases is a (stacking) group: every group element in this group is a distinct SPT phase, and the group multiplication corresponds to stacking two SPT phases to obtain a new SPT phase. In this talk, we will introduce a fruitful systematic construction of interacting FSPT called fluctuating domain wall decorations and show how to reach the complete classification of FSPT up to 4+1 dimensions based on this construction.
Apr 26, 2024
- Speaker:
- Zijian Wang, Tsinghua University
- Title:
- Intrinsic mixed-state topological order
- Time:
- 14:00 ~ 15:00 (Beijing Time)
- Venue:
- Shuangqing Building B626 (双清办公楼B626)
- Online:
- Tencent Meeting 953 7541 0477 (PASSWORD 2024)
- Abstract:
- In the common point of view, decoherence is a major obstacle to the preparation of topological order in noisy intermediate-scale quantum devices. Today, I will discuss an intriguing scenario where decoherence can also give rise to new types of topological order. Specifically, we construct concrete examples by proliferating fermionic anyons in the toric code via local quantum channels. The resulting mixed states retain long-range entanglement, which manifests in the nonzero topological entanglement negativity, though the topological quantum memory is destroyed by decoherence. Therefore, the identified states represent a novel intrinsic mixed-state quantum topological order, which has no counterpart in pure states. Through the lens of quantum anomalies of 1-form symmetries, we then provide general constructions of intrinsic mixed-state topological order, and reveal the existence of non-bosonic deconfined anyons as another key feature of these novel phases. Moreover, when these deconfined anyons have nontrivial braiding statistics, we prove that the mixed states must be bipartite long-range entangled for any bipartition.
Apr 19, 2024
- Speaker:
- Shuo Liu (刘铄), Tsinghua University
- Title:
- Symmetry restoration and quantum Mpemba effect in symmetric random circuits
- Time:
- 16:00 ~ 17:00 (Beijing Time)
- Venue:
- Shuangqing Building B626 (双清办公楼B626)
- Online:
- Tencent Meeting: 953 7541 0477 (PASSWORD: 2024)
- Abstract:
- An intriguing quantum Mpemba effect (QME) occurs in the non-equilibrium dynamics of subsystem symmetry restoration, implying that symmetry is restored faster for more asymmetric initial states. However, previous works have primarily focused on U(1) symmetry restoration in integrable systems. In this talk, we will discuss symmetry restoration and QME in symmetric random quantum circuits. With the lens of quantum thermalization, we provide an understanding of the presence and absence of QME with different symmetries and different sets of initial states.
Apr 12, 2024
- Speaker:
- Yijia Xu (许逸佳), University of Maryland, QuICS
- Title:
- Clifford operations and homological codes for rotors and oscillators
- Time:
- 16:00 ~ 17:00 (Beijing Time)
- Venue:
- Shuangqing Building B626 (双清办公楼B626)
- Online:
- Tencent Meeting: 953 7541 0477 (PASSWORD: 2024)
- Abstract:
- We develop quantum information processing primitives for the planar rotor, the state space of a particle on a circle. By interpreting rotor wavefunctions as periodically identified wavefunctions of a harmonic oscillator, we determine the group of bosonic Gaussian operations inherited by the rotor. This n-rotor Clifford group, U(1)n(n+1)/2⋊GLn(Z), is represented by continuous U(1) gates generated by polynomials quadratic in angular momenta, as well as discrete GLn(Z) momentum sign-flip and sum gates. We classify homological rotor error-correcting codes [arXiv:2303.13723] and various rotor states based on equivalence under Clifford operations. Reversing direction, we map homological rotor codes and rotor Clifford operations back into oscillators by interpreting occupation-number states as rotor states of non-negative angular momentum. This yields new multimode homological bosonic codes protecting against dephasing and changes in occupation number, along with their corresponding encoding and decoding circuits. In particular, we show how to non-destructively measure the oscillator phase using conditional occupation-number addition and post selection. We also outline several rotor and oscillator varieties of the GKP-stabilizer codes [arXiv:1903.12615].
Mar 22, 2024
- Speaker:
- Yishuai Niu (牛一帅), BIMSA
- Title:
- Difference-of-Sums-of-Squares and Difference-of-Convex-Sums-of-Squares Decompositions for Polynomials
- Time:
- 16:00 ~ 17:00 (Beijing Time)
- Venue:
- Shuangqing Building A626
- Online:
- Tencent Meeting: 953 7541 0477 (PASSWORD: 2024)
- Abstract:
- In our recent paper, we have developped polynomial decomposition techniques based on sums-of-squares (SOS), namely the difference-of-sums-of-squares (D-SOS) and the difference-of-convex-sums-of-squares (DC-SOS). Particularly noteworthy is the utility of the DC-SOS decomposition in formulating polynomial optimization problems within the realm of difference-of-convex (DC) programming. This talk will focus on two aspects: (1) The decomposability of any polynomial in terms of D-SOS and DC-SOS. We first introduce the cone of convex-sums-of-squares (CSOS) polynomials and discuss its interconnections with sums-of-squares (SOS) polynomials, non-negative polynomials, and SOS-convex polynomials. Subsequently, we introduce the sets of D-SOS and DC-SOS polynomials, demonstrating that any polynomial can be expressed in terms of D-SOS and DC-SOS formulations. The task of determining D-SOS and DC-SOS decompositions can be cast as a semi-definite program, solvable with any desired precision in polynomial time using interior point methods. (2) How to efficiently construct D-SOS and DC-SOS decompositions. We will present several practical algorithms for exact D-SOS and DC-SOS polynomial decompositions without solving any SDP. Numerical results of D-SOS and DC-SOS decompositions and their parallel versions will be reported.
Mar 15, 2024
- Speaker:
- Li Gao (高力), Wuhan University
- Title:
- Relative entropy decay of quantum Markov semigroups
- Time:
- 16:00 ~ 17:00 (Beijing Time)
- Venue:
- Shuangqing Building A626 (双清办公楼A626)
- Online:
- Tencent Meeting: 953 7541 0477 (PASSWORD: 2024)
- Abstract:
- Functional inequalities are potent tools in analyzing the convergence time of Markov processes. Specifically, the modified log-Sobolev inequality (in short, MLSI) concerns the convergence of the time evolution in terms of relative entropy. In this talk, I will present a simple, information-theoretic approach to modified logarithmic Sobolev inequalities for quantum Markov semigroup. Our result gives an asymptotic tight estimate for the MLSI constant, which improves the previous known bound by replacing the dimension constant by its logarithm. This talk is based on a joint work with Marius Junge, Nicholas, LaRacunte, and Haojian Li.
Mar 08, 2024
- Speaker:
- Ce Shen (沈策), Baidu (百度)
- Title:
- 量子计算在金融衍生品定价中的应用
- Time:
- 16:00 ~ 17:00 (Beijing Time)
- Venue:
- Shuangqing Building A626 (双清办公楼A626)
- Online:
- Zoom Meeting: 559 700 6085 (PASSWORD: BIMSA)
- Abstract:
- This talk focuses on recent applications of quantum computing in option pricing. We start by introducing the background of financial options and the problem of option pricing. The problem of option pricing is reduced to a problem of calculating expectations over a probability distribution, which can be solved by Monte Carlo simulation. We then discuss in detail the Quantum Monte Carlo algorithm and explain how it achieves acceleration over the classical monte carlo method.
Mar 01, 2024
- Speaker:
- Yu-An Chen (陈昱安), Peking University
- Title:
- Error-correcting Codes for Quantum Simulation of Fermions
- Time:
- 16:00 ~ 17:00 (Beijing Time)
- Venue:
- Shuangqing Building A626 (双清办公楼A626)
- Online:
- Tencent Meeting 712 608 88756
- Abstract:
- This talk focuses on the simulation of fermionic systems on arbitrary graphs, including two-dimensional lattices. We start by examining the one-dimensional Jordan-Wigner transformation and its expansion to two-dimensional exact bosonization. This method is crucial for simulating fermions using emergent fermions in the ℤ2 toric code. We then discuss how fermionic observables and Pauli matrices can be interconnected through locality-preserving mappings. We show that all fermion-to-qubit mappings are achievable from the two-dimensional exact bosonization by applying Clifford circuits. Furthermore, our exploration includes ℤ2 lattice gauge theories and Pauli stabilizer codes, where we propose new methods to improve the code distances of stabilizer codes in fermion simulations on a two-dimensional lattice without decreasing the fermionic code rate. We modify the Bravyi-Kitaev Superfast simulation (BKSF) and demonstrate its error-correcting properties on various two-dimensional lattices. This talk provides a detailed and accessible overview of the current state of fermion simulation, bosonization techniques, and quantum error correction, demonstrating their importance in quantum computing.