Plethysm is in #BQP https://arxiv.org/abs/2602.08441v1

Authors: Matthias Christandl, Aram W. Harrow, Greta Panova, Pietro M. Posta, Michael WalterSome representation-theoretic multiplicities, such as the Kostka and the Littlewood-Richardson coefficients, admit a combinatorial interpretation that places their computation in the complexity class #P. Whether this holds more generally is considered an important open problem in mathematics and computer sci

Chủ tịch nước Lương Cường quyết định thăng 2 Thứ trưởng BQP Nguyễn Văn Gấu, Lê Đức Thái từ Trung tướng lên Thượng tướng. #Vietnam #Quốc_phòng #Thượng_tướng #BQP #Defense

https://vtcnews.vn/hai-thu-truong-bo-quoc-phong-duoc-thang-quan-ham-thuong-tuong-ar985061.html

On additive error approximations to #BQP

Mason L. Rhodes, Sam Slezak, Anirban Chowdhury, Yi\u{g}it Suba\c{s}{\i}
https://arxiv.org/abs/2411.02602 https://arxiv.org/pdf/2411.02602 https://arxiv.org/html/2411.02602

arXiv:2411.02602v1 Announce Type: new
Abstract: Counting complexity characterizes the difficulty of computing functions related to the number of valid certificates to efficiently verifiable decision problems. Here we study additive approximations to a quantum generalization of counting classes known as #BQP. First, we show that there exist efficient quantum algorithms that achieve additive approximations to #BQP problems to an error exponential in the number of witness qubits in the corresponding verifier circuit, and demonstrate that the level of approximation attained is, in a sense, optimal. We next give evidence that such approximations can not be efficiently achieved classically by showing that the ability to return such approximations is BQP-hard. We next look at the relationship between such additive approximations to #BQP and the complexity class DQC$_1$, showing that a restricted class of #BQP problems are DQC$_1$-complete.

Solving Sharp Bounded-error Quantum Polynomial Time Problem by Evolution methods

Zhen Guo, Li You
https://arxiv.org/abs/2406.03222 https://arxiv.org/pdf/2406.03222

arXiv:2406.03222v1 Announce Type: new
Abstract: Counting ground state degeneracy of a $k$-local Hamiltonian is important in many fields of physics. Its complexity belongs to the problem of sharp bounded-error quantum polynomial time (#BQP) class and few methods are known for its solution. Finding ground states of a $k$-local Hamiltonian, on the other hand, is an easier problem of Quantum Merlin Arthur (QMA) class, for which many efficient methods exist. In this work, we propose an algorithm of mapping a #BQP problem into one of finding a special ground state of a $k$-local Hamiltonian. We prove that all traditional methods, which solve the QMA problem by evolution under a function of a Hamiltonian, can be used to find the special ground state from a well-designed initial state, thus can solve the #BQP problem. We combine our algorithm with power method, Lanczos method, and quantum imaginary time evolution method for different systems to illustrate the detection of phase boundaries, competition between frustration and quantum fluctuation, and potential implementations with quantum circuits.