Simulating Majorana zero modes on a noisy quantum processor

Abstract

The simulation of systems of interacting fermions is one of the most anticipated applications of quantum computers. The most interesting simulations will require a fault-tolerant quantum computer, and building such a device remains a long-term goal. However, the capabilities of existing noisy quantum processors have steadily improved, sparking an interest in running simulations that, while not necessarily classically intractable, may serve as device benchmarks and help elucidate the challenges to achieving practical applications on near-term devices. Systems of non-interacting fermions are ideally suited to serve these purposes. While they display rich physics and generate highly entangled states when simulated on a quantum processor, their classical tractability enables experimental results to be verified even at large system sizes that would typically defy classical simulation. In this work, we use a noisy superconducting quantum processor to prepare Majorana zero modes as eigenstates of the Kitaev chain Hamiltonian, a model of non-interacting fermions. Our work builds on previous experiments with non-interacting fermionic systems. Previous work demonstrated error mitigation techniques applicable to the special case of Slater determinants. Here, we show how to extend these techniques to the case of general fermionic Gaussian states, and demonstrate them by preparing Majorana zero modes on systems of up to 7 qubits.

Characterization of variational quantum algorithms using free fermions

“…Beyond elucidating the current knowledge on the interplay between symmetry and optimization, and furthering the understing on the overparameterized regime of optimization, our work can serve as the basis for a benchmarking scheme for the implementation of variational algorithms in quantum computers. These have already been performed using free states such as, e.g., Majorana zero modes [87] or the ground state of the Ising model [16]; this scheme could potentially be leveraged into error correcting methods [12]. Moreover, it provides a framework to better understand the theory behind the preparation of free states using variational algorithms, already studied in models such as the Ising model [22,41], the Kitaev model in the exactly solvable limit [45], or the cluster model [70].…”

Machine learning on quantum experimental data toward solving quantum many-body problems

“…2b. To reduce errors, apart from diverse error mitigation methods (Dynamical Decoupling, Pauli twirling, McWeeny purification) 34,35 , we implemented a parity measurement by recompiling the circuit. Further information is provided in the Supplementary Information Note 3.…”