Fermionic tensor machine learning for quantum chemistry

An apparatus, or a system comprising a plurality of apparatuses, wherein each apparatus comprises at least one processor and at least one memory, the at least one memory storing instructions that, upon execution by the at least one processor, cause the apparatus or system to:

• process a predetermined machine learning routine in the form of a tensor network that defines layers of tensors in the routine, the routine being adapted for a regression problem of fermionic systems that are molecules or chemical reactions, the routine being processed such that:
• each tensor of the tensor network of the predetermined machine learning routine is converted into a parity preserving tensor;
• and
• a sign swap tensor is introduced in the tensor network at each crossing of legs of different tensors in the tensor network of the predetermined machine learning routine, thereby implementing anticommutation fermionic operator;
• input a first many-body problem modeling a first fermionic system in the processed predetermined machine learning routine, the first fermionic system being a molecule or a chemical reaction;
• and
• output from the processed predetermined machine learning routine at least one parameter for the first fermionic system after having inputted the first many-body problem, the at least one parameter being inferred by the processed predetermined machine learning routine.

A non-transitory computer-readable storage medium storing a computer program which, when the program is executed by at least one computing device, cause the at least one computing device to at least carry out the following:

• process a predetermined machine learning routine in the form of a tensor network that defines layers of tensors in the routine, the routine being adapted for a regression problem of fermionic systems that are molecules or chemical reactions, the routine being processed such that:
• each tensor of the tensor network of the predetermined machine learning routine is converted into a parity preserving tensor;
• and
• a sign swap tensor is introduced in the tensor network at each crossing of legs of different tensors in the tensor network of the predetermined machine learning routine, thereby implementing anticommutation fermionic operator;
• input a first many-body problem modeling a first fermionic system in the processed predetermined machine learning routine, the first fermionic system being a molecule or a chemical reaction;
• and
• output from the processed predetermined machine learning routine at least one parameter for the first fermionic system after having inputted the first many-body problem, the at least one parameter being inferred by the processed predetermined machine learning routine.