November 2021 Meeting: Noise Resilient Quantum Circuits; Simulating Large PEPs Tensor Networks on Small Quantum Devices

Discussion Leaders: Prof. Isaac Kim (UCD Computer Science) and Dr. Ian MacCormack (University of Chicago)

November 17th, 2021

MacCormack Summary

Simulating Large PEPs Tensor Networks on Small Quantum Devices

We systematically map low-bond-dimension PEPs tensor networks to quantum circuits. By measuring and reusing qubits, we demonstrate that a simulation of an $N \times M$ square-lattice PEPs network, for arbitrary $M$, of bond dimension $2$ can be performed using $N+2$ qubits. We employ this approach to calculate the values of a long-range loop observable in the topological Wen plaquette model by mapping a $3\times 3$ PEPs tensor network to a 5-qubit quantum circuit and executing it on the Honeywell System Model H1-1 trapped-ion device. We find that, for this system size, the noisy observable values are sufficient for diagnosing topological vs. trivial order, as the Wen model is perturbed by a magnetic field term in the Hamiltonian. Our results serve as a proof-of-concept of the utility of the measure-and-reuse approach for simulating large two-dimensional quantum systems on small quantum devices

Relevant Journal Paper:

Kim Summary

Noise-resilient quantum circuits

Quantum computers are good at simulating physical properties of many-body quantum systems, but near-term quantum computers are expected to be noisy. Therefore, it is important to identify quantum computational tasks that exhibit a natural resilience against noise. I will discuss several interesting quantum circuit families which possess such robustness. Surprisingly, these circuits can perform useful tasks, such as approximating ground state properties of interacting quantum many-body systems.