Title: Variational quantum simulation of imaginary time evolution and its applications
Speaker: Xiao Yuan
Abstract: Imaginary time evolution is a powerful tool for studying quantum systems. While it is conceptually simple to simulate with a classical computer, the time and memory requirements scale exponentially with the system size. Conversely, quantum computers can efficiently simulate quantum systems, but non-unitary imaginary time evolution is incompatible with unitary quantum circuits. Here, we propose a hybrid, variational algorithm for simulating imaginary time evolution on a quantum computer. We use this algorithm to find the ground state energy of many-particle Hamiltonians; specifically those of the Hydrogen molecule and Lithium Hydride. Our algorithm finds the ground state with high probability, outperforming the variational quantum eigensolver. Our method can also be applied to general optimisation problems, Gibbs state preparation, and quantum machine learning. As our algorithm is hybrid, suitable for error mitigation methods, and can exploit shallow quantum circuits, it can be implemented with current quantum computers.
Title: Quantum error correction and error threshold simulation
Speaker: Zhenyu Cai
Abstract: Due to uncontrolled interaction with the environment and imperfect quantum control, qubits can never be perfect. The error rate achievable by current quantum hardware is far below what we need to achieve quantum supremacy. To reduce the effective error rate of the qubits, we use quantum error correction to encode the information of one qubit into many qubits. For a given error correction code to be effective, the error rate of the quantum hardware needs to be below a certain threshold. The error threshold is highly dependent on the exact quantum hardware and its error model. In this talk, we will introduce the basic concepts in quantum error correction and how to do simulation to obtain the error threshold for a given quantum error correction code and hardware.
Title: Practical Quantum Error Mitigation for Near-Future Applications
Speaker: Suguru Endo
Abstract: It is vital to minimise the impact of errors for near-future quantum devices that will lack the resources for full fault tolerance. Two quantum error mitigation (QEM) techniques have been introduced recently, namely error extrapolation and quasi-probability decomposition. To enable practical implementation of these ideas, here we account for the inevitable imperfections in the experimentalist's knowledge of the error model itself. We describe a protocol for systematically measuring the effect of errors so as to design efficient QEM circuits. We find that the effect of localised Markovian errors can be fully eliminated by inserting or replacing some gates with certain single-qubit Clifford gates and measurements. Finally, having introduced an exponential variant of the extrapolation method we contrast the QEM techniques using exact numerical simulation in the context of a 'SWAP test' circuit. Our optimised methods dramatically reduce the circuit's output error without increasing the qubit count or time requirements.