arXiv subjects

Joey Bonitati

Publications and source records attributed to Joey Bonitati.

4 recordsLinked to original sources

arXiv2024

Eigenstate Preparation on Quantum Computers

This thesis investigates quantum algorithms for eigenstate preparation, with a focus on solving eigenvalue problems such as the Schrodinger equation by utilizing near-term quantum computing devices. These problems are ubiquitous in several scientific fields, but more accurate solutions are specifically needed as a prerequisite for many quantum simulation tasks. To address this, we establish three methods in detail: quantum adiabatic evolution with optimal control, the Rodeo Algorithm, and the Variational Rodeo Algorithm. The first method explored is adiabatic evolution, a technique that prepares quantum states by simulating a quantum system that evolves slowly over time. The adiabatic theorem can be used to ensure that the system remains in an eigenstate throughout the process, but its implementation can often be infeasible on current quantum computing hardware. We employ a unique approach using optimal control to create custom gate operations for superconducting qubits and demonstrate the algorithm on a two-qubit IBM cloud quantum computing device. We then explore an alternative to adiabatic evolution, the Rodeo Algorithm, which offers a different approach to eigenstate preparation by using a controlled quantum evolution that selectively filters out undesired components in the wave function stored on a quantum register. We show results suggesting that this method can be effective in preparing eigenstates, but its practicality is predicated on the preparation of an initial state that has significant overlap with the desired eigenstate. To address this, we introduce the novel Variational Rodeo Algorithm, which replaces the initialization step with dynamic optimization of quantum circuit parameters to increase the success probability of the Rodeo Algorithm. The added flexibility compensates for instances in which the original algorithm can be unsuccessful, allowing for better scalability.

quant-ph↗

arXiv2021

Demonstration of the Rodeo Algorithm on a Quantum Computer

The rodeo algorithm is an efficient algorithm for eigenstate preparation and eigenvalue estimation for any observable on a quantum computer. This makes it a promising tool for studying the spectrum and structure of atomic nuclei as well as other fields of quantum many-body physics. The only requirement is that the initial state has sufficient overlap probability with the desired eigenstate. While it is exponentially faster than well-known algorithms such as phase estimation and adiabatic evolution for eigenstate preparation, it has yet to be implemented on an actual quantum device. In this work, we apply the rodeo algorithm to determine the energy levels of a random one-qubit Hamiltonian, resulting in a relative error of $0.08\%$ using mid-circuit measurements on the IBM Q device Casablanca. This surpasses the accuracy of directly-prepared eigenvector expectation values using the same quantum device. We take advantage of the high-accuracy energy determination and use the Hellmann-Feynman theorem to compute eigenvector expectation values for a different random one-qubit observable. For the Hellmann-Feynman calculations, we find a relative error of $0.7\%$. We conclude by discussing possible future applications of the rodeo algorithm for multi-qubit Hamiltonians.

quant-ph↗

arXiv2021

Rodeo Algorithm for Quantum Computing

We present a stochastic quantum computing algorithm that can prepare any eigenvector of a quantum Hamiltonian within a selected energy interval $[E-ε, E+ε]$. In order to reduce the spectral weight of all other eigenvectors by a suppression factor $δ$, the required computational effort scales as $O[|\log δ|/(p ε)]$, where $p$ is the squared overlap of the initial state with the target eigenvector. The method, which we call the rodeo algorithm, uses auxiliary qubits to control the time evolution of the Hamiltonian minus some tunable parameter $E$. With each auxiliary qubit measurement, the amplitudes of the eigenvectors are multiplied by a stochastic factor that depends on the proximity of their energy to $E$. In this manner, we converge to the target eigenvector with exponential accuracy in the number of measurements. In addition to preparing eigenvectors, the method can also compute the full spectrum of the Hamiltonian. We illustrate the performance with several examples. For energy eigenvalue determination with error $ε$, the computational scaling is $O[(\log ε)^2/(p ε)]$. For eigenstate preparation, the computational scaling is $O(\log Δ/p)$, where $Δ$ is the magnitude of the orthogonal component of the residual vector. The speed for eigenstate preparation is exponentially faster than that for phase estimation or adiabatic evolution.

quant-ph↗

arXiv2020

Projected Cooling Algorithm for Quantum Computation

In the current era of noisy quantum devices, there is a need for quantum algorithms that are efficient and robust against noise. Towards this end, we introduce the projected cooling algorithm for quantum computation. The projected cooling algorithm is able to construct the localized ground state of any Hamiltonian with a translationally-invariant kinetic energy and interactions that vanish at large distances. The term "localized" refers to localization in position space. The method can be viewed as the quantum analog of evaporative cooling. We start with an initial state with support over a compact region of a large volume. We then drive the excited quantum states to disperse and measure the remaining portion of the wave function left behind. For the nontrivial examples we consider here, the improvement over other methods is substantial. The only additional resource required is performing the operations in a volume significantly larger than the size of the localized state. These characteristics make the projected cooling algorithm a promising tool for calculations of self-bound systems such as atomic nuclei.

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