Related papers: Optimisation of Quantum Hamiltonian Evolution: Fro…
Trotter and linear-combination-of-unitary (LCU) are two popular Hamiltonian simulation methods. We propose Hamiltonian simulation algorithms using LCU to compensate Trotter error, which enjoy both of their advantages. By adding few gates…
Local Hamiltonians of fermionic systems on a lattice can be mapped onto local qubit Hamiltonians. Maintaining the locality of the operators comes at the expense of increasing the Hilbert space with auxiliary degrees of freedom. In order to…
All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…
We numerically analyze the complexity of unitary time-evolution and precursor operators in one- and two-qubit systems using the framework of Nielsen complexity geometry. We find that, as expected, the complexities of unitary time evolution…
Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of…
Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. The existing algorithms generally approximate the time evolution operators, which may need a deep…
The efficient implementation of matrix arithmetic operations underpins the speedups of many quantum algorithms. We develop a suite of methods to perform matrix arithmetics -- with the result encoded in the off-diagonal blocks of a…
Optimal realizations of quantum technology tasks lead to the necessity of a detailed analytical study of the behavior of a $d$-level quantum system (qudit) under a time-dependent Hamiltonian. In the present article, we introduce a new…
The framework of this thesis is fault-tolerant quantum algorithms. Grover's algorithm and quantum walks are described in Chapter 2. We start by highlighting the central role that rotations play in quantum algorithms, explaining Grover's,…
Recently we developed a local and constructive algorithm based on Lie algebraic methods for compressing Trotterized evolution under Hamiltonians that can be mapped to free fermions. The compression algorithm yields a circuit which scales…
With the growing interest in quantum machine learning, the perceptron -- a fundamental building block in traditional machine learning -- has emerged as a valuable model for exploring quantum advantages. Two quantum perceptron algorithms…
Simulating Hamiltonian dynamics is one of the most fundamental and significant tasks for characterising quantum materials. Recently, a series of quantum algorithms employing block-encoding of Hamiltonians have succeeded in providing…
Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain…
Simulating the dynamics of open quantum systems is a crucial task in quantum computing, offering wide-ranging applications but remaining computationally challenging. In this paper, we propose two quantum algorithms for simulating the…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
We consider the problem of learning the evolution operator for the time-dependent Schr\"{o}dinger equation, where the Hamiltonian may vary with time. Existing neural network-based surrogates often ignore fundamental properties of the…
For the description of quantum evolution, the use of a manifestly time-dependent quantum Hamiltonian $\mathfrak{h}(t) =\mathfrak{h}^\dagger(t)$ is shown equivalent to the work with its simplified, time-independent alternative $G\neq…
Adiabatic quantum optimization is a procedure to solve a vast class of optimization problems by slowly changing the Hamiltonian of a quantum system. The evolution time necessary for the algorithm to be successful scales inversely with the…
Continuous-time quantum walks and adiabatic quantum evolution are two general techniques for quantum computing, both of which are described by Hamiltonians that govern their evolutions by Schr\"odinger's equation. In the former, the…
Hamiltonian simulation is a promising application for quantum computers to achieve a quantum advantage. We present classical algorithms based on tensor network methods to optimize quantum circuits for this task. We show that, compared to…