Quantum computational chemistry

Abstract

One of the most promising suggested applications of quantum computing is solving classically intractable chemistry problems. This may help to answer unresolved questions about phenomena like: high temperature superconductivity, solid-state physics, transition metal catalysis, or certain biochemical reactions. In turn, this increased understanding may help us to refine, and perhaps even one day design, new compounds of scientific and industrial importance. However, building a sufficiently large quantum computer will be a difficult scientific challenge. As a result, developments that enable these problems to be tackled with fewer quantum resources should be considered very important. Driven by this potential utility, quantum computational chemistry is rapidly emerging as an interdisciplinary field requiring knowledge of both quantum computing and computational chemistry. This review provides a comprehensive introduction to both computational chemistry and quantum computing, bridging the current knowledge gap. We review the major developments in this area, with a particular focus on near-term quantum computation. Illustrations of key methods are provided, explicitly demonstrating how to map chemical problems onto a quantum computer, and solve them. We conclude with an outlook for this nascent field.

Theory of analytical energy derivatives for the variational quantum eigensolver

“…Equation 14is converted to the form of Eq. (13) by, for example, Jordan-Wigner or Braviy-Kitaev transformation [37,38]. Note that because we always work in the second quantization formalism, the effect of the change of the molecular orbital corresponding to the change of molecular geometry is totally absorbed in the coefficients h(x).…”

Mermin's inequalities of multiple qubits with orthogonal measurements onIBMQ 53‐qubit system

“…Quantum correlation of measurements for an entangled system always exists even the subsystems of entangled states are physically separated far away. This entanglement provides a possibility to study the information of all entangled states simultaneously and gives a superior advantage of quantum computation than classical computation 3 …”

Efficient two-electron ansatz for benchmarking quantum chemistry on a quantum computer

“…Quantum computers possess a natural affinity for quantum simulation and can transform exponentially scaling problems into polynomial ones [1][2][3]. Quantum supremacy, the ability of a quantum computer to surpass its classical counterpart on a designated task with lower asymptotic scaling, is potentially realizable for the simulation of quantum many-electron systems [4,5]. Work over the previous decade has been towards this goal with a focus on calculating the energy of small molecules and exploring strategies to leverage emerging quantum technologies, especially those designed to correct or mitigate quantum errors [6][7][8].…”

“…For a quantum algorithm to exhibit quantum supremacy, obtaining the solution classically will be impractical except for cases that are close to the classical limits of feasibility [4,5]. For some problems such as prime factorization, the solution can be quickly verified, but for many-body quantum systems this is not the case [18][19][20][21][22].…”