Quantum Dynamical Emulation

The imaginary time evolution of a quantum system allows one to access many vital quantities, including ground and thermal states. While our capacity to perform simulations of quantum systems is expected to be greatly increased by quantum computing, the present paradigm of quantum-circuit models restricts quantum algorithms to the implementation of unitary gates. This means that imaginary time evolution cannot be directly implemented in a quantum circuit. Consequently, the many simulation techniques predicated on imaginary time evolution cannot be imported into a quantum algorithmic setting. In this talk I will address this by introducing the concept of quantum dynamical emulation, a constructive method for mapping the solutions of non­unitary dynamics to a weighted set of unitary operations (the latter of which can be implemented in a quantum circuit). This allows for the derivation of a new correspondence between real and imaginary time, termed Imaginary Time Quantum Dynamical Emulation (ITQDE). Using ITQDE it is possible to not only to infer ground and thermal states, but also to resolve information about the complete Hamiltonian spectrum. From this a quantum algorithm for computing the spectra of quantum systems is developed, and its utility is demonstrated both through numerical simulation and quantum hardware implementations. Finally, I will highlight some of the broader connections of ITQDE to thermodynamics, and how it might be employed in this context.