What the foundations of quantum computer science teach us about chemistry

Abstract

With the rapid development of quantum technology, one of the leading applications that has been identified is the simulation of chemistry. Interestingly, even before full scale quantum computers are available, quantum computer science has exhibited a remarkable string of results that directly impact what is possible in a chemical simulation with any computer. Some of these results even impact our understanding of chemistry in the real world. In this Perspective, we take the position that direct chemical simulation is best understood as a digital experiment. While on the one hand, this clarifies the power of quantum computers to extend our reach, it also shows us the limitations of taking such an approach too directly. Leveraging results that quantum computers cannot outpace the physical world, we build to the controversial stance that some chemical problems are best viewed as problems for which no algorithm can deliver their solution, in general, known in computer science as undecidable problems. This has implications for the predictive power of thermodynamic models and topics such as the ergodic hypothesis. However, we argue that this Perspective is not defeatist but rather helps shed light on the success of existing chemical models such as transition state theory, molecular orbital theory, and thermodynamics as models that benefit from data. We contextualize recent results, showing that data-augmented models are a more powerful rote simulation. These results help us appreciate the success of traditional chemical theory and anticipate new models learned from experimental data. Not only can quantum computers provide data for such models, but they can also extend the class and power of models that utilize data in fundamental ways. These discussions culminate in speculation on new ways for quantum computing and chemistry to interact and our perspective on the eventual roles of quantum computers in the future of chemistry.

Grid-based methods for chemistry simulations on a quantum computer

“…We test known quantum techniques and others that we introduce, covering all key aspects of quantum simulation: state preparation, Hamiltonian simulation, and the extraction of physical observables. Thus, we characterize the resources needed to realize a “digital experiment” of quantum molecular dynamics ( 18 ) on early fault-tolerant quantum computers.…”

“…This approach involves representing wave functions over a grid of points; thus, the method explicitly encodes features such as particle symmetry (unlike the conventional second-quantized formulation). We select this approach as it is appealingly intuitive, but moreover, first-quantized simulation is anticipated by many researchers to offer the optimal resource scaling for complex and interesting molecules ( 9 , 11 , 18 ); some have even suggested that first-quantized simulation can efficiently encode both nuclear and electronic degrees of freedom on an equal footing, potentially addressing the gap in simulating non–Born-Oppenheimer processes in modern chemical physics ( 5 ).…”

Quantum information processing with superconducting circuits: a perspective

“…The VQE scales badly for large molecules (due to repeated measurements/tomography to form the expectation value of the Hamiltonian, Ĥ . Nevertheless, the VQE is the common approach for small molecules with present NISQ QPUs [115][116][117][118]. The phase-estimation algorithm (PEA) scales better, but involves much deeper circuits, puts much higher demands on the coherence time of the q-register, and needs advanced QEC.…”

“…For an overview of applications to chemistry, see reviews [116][117][118] and specific applications [45,72,73,114,[119][120][121][122][123][124][125][126][127][128][129][130][131].…”