Method for simulating and evaluating an electronic system
Quantum mechanical systems, such as for instance electronic states in molecules or solid bodies, can be simulated using quantum computers. However, at present quantum computers only provide a limited quantity of qubits for the calculation. This deficiency is attributable to unsolved problems in connection with inherent noise and scalability, with the result that quantum computers currently only enable simulations of small quantum systems. A method simulates and evaluates an electronic system with a continuous spectral density on the basis of the interruption of the quantum simulation by measurements. The quantum simulation is interrupted to read the qubits, the qubit measurements are stored in a classical parity register and restored to the qubits, and the simulation is continued after the restore.
1 . A method for simulating and evaluating an electronic system having a continuous spectral density, the method comprising:
generating a continuous spectral function in a quantum simulation of an electronic cluster-bath model using a quantum computer having a plurality of qubits, wherein features of the electronic system are simulated on individual qubits and read from the qubits;
wherein the quantum simulation is interrupted to read the qubits, the qubit measurements are stored in a classical parity register and restored to the qubits, and the simulation is continued after the restore;
wherein the simulation of the electronic system comprises an accurate simulation of a cluster, as well as a simulation of a bath and an electron hopping interaction according to a mean-field approach for describing electron-electron correlations in the modeled electronic system; and
wherein the reading of the qubits occurs in a Trotter step which iteratively carries out the steps of:
applying a time evolution operation U QC (dt,R) taking into account parities stored in the parity register R;
exchanging excitation states between a respective bath qubit and an auxiliary gubit assigned to said bath qubit;
measuring a state of the auxiliary gubit;
changing an associated parity R→R+1 (mod2) if an initial state of the auxiliary qubit and the measured state of the auxiliary qubit do not match; and
setting an initial state of the auxiliary gubit to 0 with a probability ρ − and to 1 with a probability ρ + , and returning to the first step.
2 . The method according to claim 1 , wherein sharp, spectral peaks of states of the qubits of the quantum computer associated with the bath are broadened to Lorentzian functions, thereby controlling a broadening of the peaks.
3 . The method according to claim 1 , wherein the auxiliary qubit is initialized to state 1.
4 . The method according to claim 1 , wherein the parity R is changed only if the auxiliary qubit is measured in state 0.
5 . The method according to claim 1 , wherein auxiliary qubits are uniquely assigned to a plurality of bath qubits and a plurality of auxiliary qubits are read in parallel.
6 . The method according to claim 1 , wherein the antisymmetry of the fermionic wave function is taken into account by coding using the Jordan-Wigner decomposition.