Quantum simulation is a major focus of quantum computing research due to the goal of solving classically-intractable problems in predicting the behavior of complex quantum systems across a broad spectrum of applications, including material science and drug discovery. To get there, key challenges need to be overcome:
It is important to note that none of these challenges are insurmountable. All of these solutions are believed to be achievable. The potential of quantum simulation is within reach.
Although there are different approaches to take, analog quantum simulation is the most promising. An engineered quantum system, typically consisting of an array of ultracold atoms, mimics a target quantum system. This system can then be precisely controlled to reproduce the desired behaviors and interactions. Although digital quantum simulation also uses quantum systems, it does so to solve equations, not mimic behaviors, and requires a level or fault tolerance that does not yet exist. Other methods require classical computation, and face the very challenges that are fueling research into quantum computers.
Recent research can shine a light on the limits of what is currently possible, as well as offer a glimpse of what might be coming next.
“Nature isn’t classical […] and if you want to make a simulation of Nature, you’d better make it quantum mechanical, and by golly it’s a wonderful problem because it doesn’t look so easy. […] I want to talk about the possibility that there is to be an exact simulation, that the computer will do exactly the same as nature.” (emphasis in original)
– Richard P. Feynman, International Journal of Theoretical Physics, Vol 21, Nos. 6/7, 1982
For a deeper overview than can be presented here, a video titled A review of Harvard and QuEra quantum simulation results with neutral atoms reviews several recently-published results that were obtained using neutral-atom machines. The 58:10 presentation, dated March 28, 2023, includes a review by three QuEra researchers, with a following Q&A period.
The most commonly cited challenges to quantum simulation, as well as quantum computation, are noise and decoherence, scalability to large numbers of qubits, high-error operations, developing efficient algorithms, mapping problems to available hardware, optimizing parameters with classical machine learning algorithms, prioritizing quantum systems to simulate, validating simulations in the absence of comparisons, allocating quantum and classical processing, reducing estimated resource requirements, and achieving computational advantages that can withstand classical challenges.
In the paper The inherent problem in quantum simulations — and how to tackle it, Jukka Knuutinen and Dr. Ljubomir Budinski of Quanscient address a more fundamental problem. Quantum mechanics is natively linear, but many of the problems that need to be solved involve non-linear equations. One approach they identify is to linearize (Carleman linearization) those equations and then solve those linear equations, but information loss can cause inaccuracy. Another approach they identify is the lattice Boltzmann method (LBM), a computational fluid dynamics (CFD) solver, which divides the problem into independent computational points. Parallelization allows significant computational speed-ups, but quantum-unsolvable non-linear terms remain. The elimination of non-linear terms and some hybrid quantum-classical approaches are hypothetical or not well tested.
Attempts to overcome these challenges take many forms. The most notable ones include the classical optimization of parameterized quantum circuits, classical algorithms for approximating solutions, quantum error correction (QEC) codes for gate-based quantum algorithms, evolving quantum systems through adiabatic quantum computing, tensor network techniques such as Matrix Product States (MPS), quantum-inspired classical algorithms, hybrid classical-quantum algorithms, task-specific software frameworks and libraries, and task-specific algorithms.
In the article Scientists double the size of quantum simulations with entanglement forging, Robert Davis of IBM Research discusses a relatively new approach to effectually doubling the size of the systems that can be studied. An IBM team calculated the ground state energy of a 10-spin-orbital water molecule using only 5 qubits, halving the traditional qubit requirement. Whereas one qubit per feature is normally needed, the team was able to classically “cut” the problem into equal-sized groups and then classically “knit” the results together. The team identified weak entanglement, the limited entanglement between spin-up and spin-down orbitals, and divided the problem there. In principle, this approach can be applied to other problems and even to strong correlations, although the latter is considerably more challenging.