Algorithm Prioritization

Many real life problems are combinatorial and solving them has actual practical applications. An intrinsic feature of these problems is that they can be formulated as minimization or maximization problems, i.e. with a cost function. At the same time finding the lowest energy of a physical system, represented by a cost Hamiltonian, is also a minimization problem. Due to this intimate relation, problems described with a cost function (QUBO) or a cost Hamiltonian (Ising) could be solved by simulating the process of finding their minimum energy. This lowest energy should encode the solution to our problem.

Tensor networks are factorizations of very large tensors into networks of smaller tensors, with applications in applied mathematics, chemistry, physics, machine learning, and many other fields.

Choose a set of states S that will be used to construct the training data. For each state it but be efficient to calculate the expectation value of X. For each state evaluate the exact expectation value with a classical computer and the noisy expectation value with a quantum computer. Generate training data set using both noisy and exact expectation values. Use this ansatz with the fitted parameters to predict noise-free observable of arbitrary quantum states.

Accreditation protocol: use M+1 circuit with M trap circuits, and 1 target circuit to be mitigated. Choose those runs where the noise is smaller than a threshold.

Prepare a ground state, take projective measurements. Then translate the wavefunction of the quantum device into a neural quantum state. Pass the trained wavefunction to Variational Monte Carlo algorithm. Postprocess the wavefunction, find the minimal energy, return the mitigated wavefunction.

Represent the ideal circuit as a quasi-probabilistic mixture of noisy ones.

Express the probability to have errors as Poisson distribution (exponential form). Build an exponential function between expectation values of different error rates to find the ideal expectation value.

Express the expectation value of an observable as a sum of the noiseless expectation value and the series sum of some noise parameters. The idea is to increase the noise, calculate the Exp value each time and use Richardson extrapolation to find the noiseless exp value.

Research & development to see if there can be improvements over classical methods.

Research & development to see if there can be improvements over classical methods.