Spectral functions on a quantum computer through system-environment interaction

Spectral functions measured with angle-resolved photoemission spectroscopy (ARPES) provide key insight to elucidate the band structure of materials. Comparison with theory requires computing dynamical one-point functions in some equilibrium state, which can be classically challenging. Their measurement on quantum computers poses multiple problems and comes with a large sampling overhead when standard techniques are used. We introduce an efficient way of measuring spectral functions on a quantum computer by directly modeling the interaction of the system with the environment involved in ARPES experiments. We develop quantum circuits whose local expectation values are proportional to the spectral function $A(k,\omega)$ for all momentum $k$ and a specific chosen frequency $\omega$. Although coming with a qubit and two-qubit gate overhead, our approach requires $O(N)$ times less sampling than previous approaches, translating into a factor $O(N)$ faster in runtime, and is particularly adapted to ion-trap quantum computers. The algorithm requires to implement a fermionic Fourier transform (FFT). We write out an efficient gate decomposition for generic radix-$n$ FFT and benchmark it on hardware for radix-$3$ on $27$ qubits. We finally demonstrate our algorithm on a Quantinuum System Model H2 ion-trap system, computing the spectral function on a one-dimensional system of $27$ sites, using $54$ qubits.