Efficient Quantum Tomography for Quantum Simulations of Field Theories

Certain computational problems in physics are estimated to require more computational resources than next-generation Exascale computing hardware will provide. Notable examples are the sign problem in fermionic systems, and real-time dynamics. The sign problem has prevented lattice QCD predictions for properties of dense matter, as well as the evolution of strongly-interacting medium after heavy-ion collisions. Quantum computing has the promise of speeding up certain tasks exponentially. However, modern quantum devices are limited by noise accumulation resulting from the application of imperfect quantum operations, setting a limit on the depth of the circuits that can be implemented. Some of these restrictions could be largely curtailed if scalable quantum tomography algorithms were available. We propose a new algorithm based on quantum interference that allows for quantum tomography of a pure n-qubit state at the cost of an additional n+1 qubits. As a relevant application of this algorithm, we demonstrate how the real-time evolution of few-site 1D QED can be extended far beyond what is possible on current devices. We also find the ground and excited states of the theory with the use of extended adiabatic state preparation enabled by IQT.