A new technique developed by scientists at North Carolina State University (NC State) allows quantum computers to quantify the thermodynamic properties of systems by evaluating the zeros of the partition function.
Image Credit: North Carolina State University.
We’ve illustrated a new way to get at thermodynamic properties of a system, such as free energy, entropy, and other properties that are too complex to currently be measured via traditional or quantum computing. By calculating partition function zeros we are on the way to solving the problem of scaling to larger numbers of qubits when trying to calculate free energies and entropies in a given system.
Lex Kemper, Study Corresponding Author and Associate Professor of Physics, North Carolina State University
In general, quantum computers are used to analyze complex systems, thanks to their potential to deal with large computations beyond the reach of traditional computers. But certain issues like quantifying the thermodynamics or free energy in a system (which involves assessing its entropy) are still considered too big to be efficiently handled by these computers.
A partition function explains the statistical properties of a system in thermodynamic equilibrium. The entire energy, free energy, entropy, or pressure of a system could be mathematically expressed with respect to the partition function or its derivatives.
Kemper and his collaborators utilized a quantum computer to quantify the partition function zeros, instead of the entropy, of a spin model as it is tuned over a transition in phase.
Our method skips the part where we calculate the entropy in favor of looking at the partition function. That’s because the partition function is a generating function–a function that you can perform operations on to get at other thermodynamic information such as the internal energy and the entropy.
Lex Kemper, Study Corresponding Author and Associate Professor of Physics, North Carolina State University
“We measure the partition function by determining where it is zero. Once you know all the zeros of a function, you know the whole function. Since the zeros lie in the complex plane, we used a mapping between having a complex magnetic field and time evolution to find them,” added Kemper.
The partition function on both a standard and a trapped ion quantum computer was evaluated by the scientists in the laboratory of Norbert Linke at the University of Maryland. The outcomes obtained from both were relatively good.
This is a way to use a quantum computer to get at all the thermodynamic properties of a system without necessitating huge numbers of quantum computations.
Lex Kemper, Study Corresponding Author and Associate Professor of Physics, North Carolina State University
The study was financially supported by the Department of Energy (grant DE-SC0019469). The study’s first author Akhil Francis is a graduate student at NC State. Norbert Linke and Chris Monroe from the University of Maryland, Jim Freericks from Georgetown University, and Sonika Johri from IonQ were also part of the study.
Journal Reference:
Francis, A., et al. (2021) Many-body thermodynamics on quantum computers via partition function zeros. Science Advances. doi.org/10.1126/sciadv.abf2447.