How will quantum computers provide an industrially relevant computational advantage in quantum chemistry?

Abstract

Numerous reports claim that quantum advantage, which should emerge as a direct consequence of the advent of quantum computers, will herald a new era of chemical research because it will enable scientists to perform the kinds of quantum chemical simulations that have not been possible before. Such simulations on quantum computers, promising a significantly greater accuracy and speed, are projected to exert a great impact on the way we can probe reality, predict the outcomes of chemical experiments, and even drive design of drugs, catalysts, and materials. In this work we review the current status of quantum hardware and algorithm theory and examine whether such popular claims about quantum advantage are really going to be transformative. We go over subtle complications of quantum chemical research that tend to be overlooked in discussions involving quantum computers. We estimate quantum computer resources that will be required for performing calculations on quantum computers with chemical accuracy for several types of molecules. In particular, we directly compare the resources and timings associated with classical and quantum computers for the molecules H2 for increasing basis set sizes, and Cr2 for a variety of complete active spaces (CAS) within the scope of the CASCI and CASSCF methods. The results obtained for the chromium dimer enable us to estimate the size of the active space at which computations of non-dynamic correlation on a quantum computer should take less time than analogous computations on a classical computer. The transition point should occur at around 19 ≤ N ≤ 34, for CAS of the type (N, N ), under the assumption of the much-researched surface code. This is significantly smaller than the active spaces discussed in the context of quantum advantage in prior publications. Using this result, we speculate on the types of chemical applications for which the use of quantum computers would be both beneficial and relevant to industrial applications in the short term.

Simulating the electronic structure of spin defects on quantum computers

“…For example, the quantum phase estimation (QPE) [15] algorithm has been proven to be exponentially faster in finding eigenvalues of unitary operators than any available algorithm on a classical computer [69][70][71]. However, calculations using QPE are still impractical in the absence of error correction and require quantum resources that exceed the current capability of NISQ hardware [72]. An alternative algorithm to QPE is the variational quantum eigensolver (VQE) [73], which allows one to use shallower circuits than QPE and hence to perform calculations on non fault-tolerant quantum computers [74].…”

Quantum Biotechnology

“…Such control could be used to transfer quantum states between light and biomolecular systems [25], and therefore to form the basis of a class of robust room temperature technologies for quantum computing, communication and sensing [21,25]. Quantum computers allow molecular simulations that go beyond what is possible with quantum chemistry [26,27]. These fully-quantum simulations are predicted to allow faster, more accurate simulations of large molecules [27,28], and could therefore play an important role in the design of future pharmaceuticals, artificial enzymes and energy harvesting systems.…”

“…Quantum computers allow molecular simulations that go beyond what is possible with quantum chemistry [26,27]. These fully-quantum simulations are predicted to allow faster, more accurate simulations of large molecules [27,28], and could therefore play an important role in the design of future pharmaceuticals, artificial enzymes and energy harvesting systems.…”

“…Beyond these new technologies, a further exciting prospect for progress in understanding the scope of quantum effects in biology is the rapid development of large-scale quantum computers [9]. While the range of practical problems that these quantum computers will be capable of addressing in the near future remains relatively limited , quantum simulations of molecular dynamics are one area they appear quite naturally suited to [314,27,315,28]. Here, they are able to address a fundamental problem in quantum chemistry calculations: the necessity to make approximations to avoid the exponential scale-up in complexity of computing the properties of quantum systems as their size increases [26].…”

“…This provides the prospect to better understand both how quantum effects influence the behaviour of biomolecules, and how to engineer these effects in artificial molecules. Quantum computers have already be used to simulate a range of small molecules (see summary in [27]), but larger, more fault-tolerant computers are expected to be required to simulate molecules relevant to biotechnology [27,315] (see Fig. 7 b)).…”