jsaroni/qhack2023_feynmanprodigies

QHack2023_Feynman prodigies

Introduction

We are trying to find the ground state of BeH2, so it is worth knowing more about its physical chemistry. In the formation of BeH2, the 2s orbital of beryllium and the 1s orbitals of both hydrogen atoms combine to form two molecular orbitals: a bonding molecular orbital and an antibonding molecular orbital. The molecule is linear, with a bond angle of 180 degrees, and the two hydrogen atoms occupy the antibonding molecular orbital. The task is to find the ground state energy of the molecule. H|Φ〉 = EG |Φ〉 (1) Knowing the ground state energy of a molecule can help predict its reactivity, chemical stability, and spectroscopic properties. With this motivation, we employ different VQE (variational quantum eigensolver) methods. VQE stands for Variational Quantum Eigensolver, which is a quantum algorithm designed to estimate the ground state energy of a quantum system using quantum computers. The goal of VQE is to find the lowest energy state of a molecule, which is important for understanding its chemical properties and behavior. The algorithm starts with an initial guess for the wave function of the molecule and then uses a classical optimizer to adjust the parameters of the wave function to minimize the energy. The adjusted wave function is then sent to the quantum computer, which calculates the energy of the wave function. This process is repeated iteratively, with the classical optimizer updating the wave function parameters and the quantum computer calculating the energy until the energy converges to the ground state energy of the molecule. We have the vanilla flavor VQE [3] method; then we explore the Tetris Adaptive VQE [4], and we finally worked with the Adaptive VQE [5, 6] method, which gave us the best results.

Circuit knitting

Circuit knitting is a technique in quantum computing that involves combining multiple quantum circuits into a larger, more complex circuit. The idea behind circuit knitting is to use smaller, more specialized circuits as building blocks, which can be combined and stitched together to create larger, more powerful circuits for solving complex problems. Overall, circuit knitting is a powerful technique in quantum computing that can help researchers tackle some of the most challenging problems in the field. It is a testament to the versatility and modularity of quantum circuits, and it has the potential to enable new breakthroughs in quantum technology.

Entanglement forging

Entanglement forging refers to a hypothetical process in which two parties can create a shared quantum state without actually having access to an entangled pair of qubits. This is accomplished through a combination of quan- tum operations and classical communication and would represent a significant breakthrough in the field of quantum information processing. The basic idea behind entanglement forging is to start with two separable qubits (i.e., qubits that are not entangled with each other) and then use a series of quantum gates and measurements to create a new state that is entangled. Entanglement forging takes a generic circuit that operates on the combined system of the spin-up and spin-down halves and splits it into smaller circuits that only operate on one half at a time. In other words, the entanglement forging technique takes a circuit operating on 2N qubits and separates that circuit into two N-qubit halves.

Zero Noise Extrapolation

Zero noise extrapolation (ZNE) is a technique in quantum computing that can improve the accuracy of quantum al- gorithms by extrapolating the results of noisy quantum circuits to the limit of zero noise. In a noisy quantum circuit, the presence of unwanted noise can cause errors in the computation, which can reduce the accuracy of the results. ZNE aims to mitigate this problem by extrapolating the noisy results to the limit of zero noise, where the true value of the computation can be obtained without any errors. One advantage of the ZNE technique is that it can be applied to any quantum algorithm, regardless of its specific structure or purpose. Moreover, ZNE can be combined with other noise mitigation techniques, such as error correction and error suppression, to further improve the accuracy and reliability of quantum computations.

Twirled Readout Error eXtinction

TREX (Twirled Readout Error eXtinction) is an error mitigation technique in quantum computing that combines twirled readout with excitations to improve the accuracy of quantum measurements. The twirled readout is a tech- nique that involves applying a random unitary transformation to the final state of a quantum circuit before measuring it. The idea behind this technique is to randomly rotate the state space in a way that cancels out certain types of noise, such as systematic errors in the measurement process. TREX has been shown to be effective in a variety of quantum computing applications, including quantum chemistry simulations, optimization problems, and machine learning tasks. It is a promising technique for overcoming the limitations of noisy, near-term quantum devices and enabling the development of more accurate and reliable quantum algorithms.