Related papers: Quantum algorithm for ground state energy estimati…
A major thrust in quantum algorithm development over the past decade has been the search for the quantum algorithms that will deliver practical quantum advantage first. Today's quantum computers - and even early fault-tolerant quantum…
Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We…
Significant effort in applied quantum computing has been devoted to the problem of ground state energy estimation for molecules and materials. Yet, for many applications of practical value, additional properties of the ground state must be…
Estimating the ground state energy of a multiparticle system with relative error $\e$ using deterministic classical algorithms has cost that grows exponentially with the number of particles. The problem depends on a number of state…
We propose a general-purpose quantum algorithm for preparing ground states of quantum Hamiltonians from a given trial state. The algorithm is based on techniques recently developed in the context of solving the quantum linear systems…
We develop a phase estimation method with a distinct feature: its maximal runtime (which determines the circuit depth) is $\delta/\epsilon$, where $\epsilon$ is the target precision, and the preconstant $\delta$ can be arbitrarily close to…
Quantum phase estimation (QPE) serves as a building block of many different quantum algorithms and finds important applications in computational chemistry problems. Despite the rapid development of quantum hardware, experimental…
We consider the question of how correlated the system hardness is between classical algorithms of electronic structure theory in ground state estimation and quantum algorithms. To define the system hardness for classical algorithms we…
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…
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…
Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…
We compare several quantum phase estimation (QPE) protocols intended for early fault-tolerant quantum computers (EFTQCs) in the context of models of their implementations on a surface code architecture. We estimate the logical and physical…
The hope of the quantum computing field is that quantum architectures are able to scale up and realize fault-tolerant quantum computing. Due to engineering challenges, such ''cheap'' error correction may be decades away. In the meantime, we…
In the lead up to fault tolerance, the utility of quantum computing will be determined by how adequately the effects of noise can be circumvented in quantum algorithms. Hybrid quantum-classical algorithms such as the variational quantum…
The energy gap is calculated for the ground state quantum computer circuit, which was recently proposed by Mizel et.al. When implementing a quantum algorithm by Hamiltonians containing only pairwise interaction, the inverse of energy gap…
We investigate the feasibility of early fault-tolerant quantum algorithms focusing on ground-state energy estimation problems. In particular, we examine the computation of the cumulative distribution function (CDF) of the spectral measure…
As quantum computing technology improves and quantum computers with a small but non-trivial number of N > 100 qubits appear feasible in the near future the question of possible applications of small quantum computers gains importance. One…
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…
Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available,…
Quantum simulation of molecular electronic structure is one of the most promising applications of quantum computing. However, achieving chemically accurate predictions for strongly correlated systems requires quantum phase estimation (QPE)…