Related papers: The abelian state hidden subgroup problem: Learnin…
The impossibility of simultaneously cloning non-orthogonal states lies at the foundations of quantum theory. Even when allowing for approximation errors, cloning an arbitrary unknown pure state requires as many initial copies as needed to…
The hidden subgroup problem~(HSP) is one of the most important problems in quantum computation. Many problems for which quantum algorithm achieves exponential speedup over its classical counterparts can be reduced to the Abelian HSP.…
Hamiltonian Learning is a process of recovering system Hamiltonian from measurements, which is a fundamental problem in quantum information processing. In this study, we investigate the problem of learning the symmetric Hamiltonian from its…
The exploration of neural network quantum states has become widespread in the studies of complicated quantum many-body systems. However, achieving high precision remains challenging due to the exponential growth of Hilbert space size and…
Many quantum algorithms, including Shor's celebrated factoring and discrete log algorithms, proceed by reduction to a hidden subgroup problem, in which a subgroup H of a group G must be determined from a quantum state y uniformly supported…
Drawing the quantum phase diagram of a many-body system in the parameter space of its Hamiltonian can be seen as a learning problem, which implies labelling the corresponding ground states according to some classification criterium that…
The Hidden Subgroup Problem is used in many quantum algorithms such as Simon's algorithm and Shor's factoring and discrete log algorithms. A polynomial time solution is known in case of abelian groups, and normal subgroups of arbitrary…
This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…
We study single-copy stabilizer learning, the problem of identifying a stabilizer group of dimension $n-t$ from an $n$-qubit quantum state $\rho$. We obtain two complementary results. First, in the average case, logarithmic-depth local…
Hidden Subgroup Problem(HSP) seeks to identify an unknown subgroup H of a group G for a given injective function f defined on cosets of H. Here we present an initialization-free quantum algorithm for solving HSP in the case where G is a…
Many exponential speedups that have been achieved in quantum computing are obtained via hidden subgroup problems (HSPs). We show that the HSP over Weyl-Heisenberg groups can be solved efficiently on a quantum computer. These groups are…
The Hidden Subgroup Problem (HSP) is a computational problem which includes as special cases integer factorization, the discrete logarithm problem, graph isomorphism, and the shortest vector problem. The celebrated polynomial-time quantum…
Bell sampling is a simple yet powerful tool based on measuring two copies of a quantum state in the Bell basis, and has found applications in a plethora of problems related to stabiliser states and measures of magic. However, it was not…
Only a few states in high-dimensional systems can be identified as (un)steerable using existing theoretical or experimental methods. We utilize semidefinite programming (SDP) to construct a dataset for steerability detection in…
Quantum machine learning has received significant attention in recent years, and promising progress has been made in the development of quantum algorithms to speed up traditional machine learning tasks. In this work, however, we focus on…
Almost all of the most successful quantum algorithms discovered to date exploit the ability of the Fourier transform to recover subgroup structure of functions, especially periodicity. The fact that Fourier transforms can also be used to…
Not all entangled states can exhibit quantum steering, and determining whether a given entangled state is steerable is a crucial problem in quantum information theory. The main challenge lies in verifying the existence of a local…
In this paper we show that certain special cases of the hidden subgroup problem can be solved in polynomial time by a quantum algorithm. These special cases involve finding hidden normal subgroups of solvable groups and permutation groups,…
The analysis of symmetry in quantum systems is of utmost theoretical importance, useful in a variety of applications and experimental settings, and is difficult to accomplish in general. Symmetries imply conservation laws, which partition…
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that…