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We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine…
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…
The goal of digital quantum simulation is to approximate the dynamics of a given target Hamiltonian via a sequence of quantum gates, a procedure known as Trotterization. The quality of this approximation can be controlled by the so called…
We consider simulating quantum systems on digital quantum computers. We show that the performance of quantum simulation can be improved by simultaneously exploiting commutativity of the target Hamiltonian, sparsity of interactions, and…
A projective measurement of energy (PME) on a quantum system is a quantum measurement, determined by the Hamiltonian of the system. PME protocols exist when the Hamiltonian is given in advance. Unknown Hamiltonians can be identified by…
Quantum Phase Estimation (QPE) routines are known to fail probabilistically even with perfect gates and input states. This effect stems from an incompatibility of finite-sized quantum registers to capture a phase within QPE with phase…
It has been demonstrated that the critical point of the phase transition in scalar quantum field theory with a quartic interaction in one space dimension can be approximated via a Gaussian Effective Potential (GEP). We discuss how this…
Quantum Imaginary-Time Evolution (QITE) is a powerful method for preparing ground states on quantum hardware. However, executing QITE has costly measurement budgets for general Hamiltonians. Both fidelity and computational cost are strongly…
Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical tradeoff between improved accuracy for finer…
Quantum phase estimation (QPE) is a cornerstone of quantum algorithms designed to estimate the eigenvalues of a unitary operator. QPE is typically implemented through two paradigms with distinct circuit structures: quantum Fourier…
Quantum optimization algorithms offer a promising route to finding the ground states of target Hamiltonians on near-term quantum devices. None the less, it remains necessary to limit the evolution time and circuit depth as much as possible,…
As fully fault-tolerant quantum computers capable of solving useful problems remain a distant goal, we anticipate an era of "early fault tolerance" where limited error correction is available. We propose a framework for designing early…
Distributed quantum computation is the key to high volume computation in the NISQ era. This investigation explores the key aspects necessary for the construction of a quantum network by numerically simulating the execution of the…
Eigenvalue estimation is a central problem for demonstrating quantum advantage, yet its implementation on digital quantum computers remains limited by circuit depth and operational overhead. We present an analog quantum phase estimation…
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…
In this study, we employed a quantum computer to solve a low-energy effective Hamiltonian for spin defects in diamond (so-called NV centre) and wurtzite-type aluminium nitride, which are anticipated to be qubits. The probabilistic…
This paper is concerned with the phase estimation algorithm in quantum computing algorithms, especially the scenarios where (1) the input vector is not an eigenvector; (2) the unitary operator is not exactly implemented; (3) random…
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…
Quantum computing promises transformative impacts in simulating Hamiltonian dynamics, essential for studying physical systems inaccessible by classical computing. However, existing compilation techniques for Hamiltonian simulation, in…
We investigate the sampling efficiency for the simulations of quantum many-body systems at finite temperatures when initial sampling states are generated by applying Trotter gates to random phase product states (RPPSs). We restrict the…