All quantum spectra in one shot

Determining the properties of the excitations in quantum many-body systems is a fundamental problem across almost all sciences. For instance, quantum excited states underpin new states of matter, support biological processes such as vision, or determine optoelectronic properties of photovoltaic devices. Yet, while ground-state properties can be determined by rather accurate computational methods, there remains a need for theoretical and computational developments to target excited states efficiently. Inspired by the duplication of the Hilbert space used to study black-hole entanglement and the electronic pairing of conventional superconductivity, we have recently developed a new variational scheme to compute the full spectrum of a quantum many-body Hamiltonian, rather than only its ground or the lowest-excited states. An important feature of our proposed scheme is that these spectra can be computed in a one-shot calculation. The scheme thus provides a novel variational platform for excited-state physics. Since our approach is suitable for efficient implementation on quantum computers, we believe this "variational quantum diagonalizer" has the potential to enable unprecedented calculations of excited-state processes of quantum many-body systems. To test the accuracy of the method, in this talk I will show an explicit calculation for a Fermi-Hubbard Hamiltonian, based on a unitary coupled-cluster ansatz.