Related papers: A fast algorithm for approximating the ground stat…
Under suitable assumptions, the algorithms in [Lin, Tong, Quantum 2020] can estimate the ground state energy and prepare the ground state of a quantum Hamiltonian with near-optimal query complexities. However, this is based on a block…
Recent progress in quantum computing is paving the way for the realization of early fault-tolerant quantum computers. To maximize the utility of these devices, it is important to develop quantum algorithms that match their capabilities and…
This thesis deals with the problematics of the scalability of fault-tolerant quantum computing. This question is studied under the angle of estimating the resources needed to set up such computers. What we call a resource is, in principle,…
It is exponentially hard to simulate quantum systems by classical algorithms, while quantum computer could in principle solve this problem polynomially. We demonstrate such an quantum-simulation algorithm on our NMR system to simulate an…
Under suitable assumptions, the quantum phase estimation (QPE) algorithm is able to achieve Heisenberg-limited precision scaling in estimating the ground state energy. However, QPE requires a large number of ancilla qubits and large circuit…
We introduce the concept of strong quantum speedup. We prove that approximating the ground state energy of an instance of the time-independent Schr\"odinger equation, with $d$ degrees of freedom, $d$ large, enjoys strong exponential quantum…
Finding eigenstates of a given many-body Hamiltonian is a long-standing challenge due to the perceived computational complexity. Leveraging on the hardware of a quantum computer accommodating the exponential growth of the Hilbert space size…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
Accurately solving the Schr\"odinger equation remains a central challenge in computational physics, chemistry, and materials science. Here, we propose an alternative eigenvalue problem based on a system's autocorrelation function, avoiding…
We present a novel method for improving the quantum simulation of the ground state energy of molecules. We perform a pre-processing step classically, which reduces the dimensionality of the problem by generating a custom mapping which…
Predicting properties across system parameters is an important task in quantum physics, with applications ranging from molecular dynamics to variational quantum algorithms. Recently, provably efficient algorithms to solve this task for…
This thesis investigates sampling-based quantum algorithms for electronic ground state energy estimation, focusing on Quantum-Selected Configuration Interaction (QSCI) and Sample-Based Quantum Diagonalization (SQD) as near-term alternatives…
Quantum chemistry is envisioned as an early and disruptive application for quantum computers. Yet, closer scrutiny of the proposed algorithms shows that there are considerable difficulties along the way. Here, we propose two criteria for…
Developing methods to solve nuclear many-body problems with quantum computers is an imperative pursuit within the nuclear physics community. Here, we introduce a quantum algorithm to accurately and precisely compute the ground state of…
Quantum computing leverages the quantum resources of superposition and entanglement to efficiently solve computational problems considered intractable for classical computers. Examples include calculating molecular and nuclear structure,…
Estimating ground state energies of many-body Hamiltonians is a central task in many areas of quantum physics. In this work, we give quantum algorithms which, given any $k$-body Hamiltonian $H$, compute an estimate for the ground state…
In this work, we present a quantum algorithm for ground-state energy calculations of periodic solids on error-corrected quantum computers. The algorithm is based on the sparse qubitization approach in second quantization and developed for…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
We propose a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. Once the Ansatz has been decided, the quantum part of the algorithm involves the calculation of two overlap…
Quantum Phase Estimation (QPE), the quantum algorithm for estimating eigenvalues of a given Hermitian matrix and preparing its eigenvectors, is considered the most promising approach to finding the ground states and their energies of…