Efficient Variational Generation of Thermofield Double States on a Superconducting Quantum Processor: Theory (Part 1)

Thermofield double (TFD) states are entangled pure states between two systems which yield a thermal state when one of the systems is traced out [1]. TFD state generation on larger qubit systems is relevant for studying the finite-temperature phase diagram of condensed matter systems. We implement a quantum-classical hybrid variational optimization algorithm to efficiently generate TFD states of the tranverse-field Ising chain. Unlike Variational Quantum Eigensolvers with a cost function that is known a priori, the success of our optimization hinges on choosing the best cost function which can generate the desired TFD state. Here, we discuss the benefits and drawbacks of various cost functions that can be used for the optimization, and show how our constructed cost function yields excellent agreement across the full temperature range.

[1] Zhu et al., arXiv/1906.02699, 2019 (https://arxiv.org/abs/1906.02699)