Many-body physics meets quantum computation

Quantum computers are built directly from units that follow the laws of quantum mechanics. This allows them to perform computational tasks that are intractable on classical computers. There is an intricate interplay between the fields of quantum computing and many-body physics. First of all, we may gain a better understanding of quantum many-body systems by simulating them on quantum computers. We contribute towards this goal by designing and testing an explicit method for the quantum simulation of the Heisenberg anti-ferromagnet on the kagome lattice. Conversely, as quantum computers are scaled up, they themselves become many-body systems. Hence, we may gain a better understanding of quantum computers by using analytical techniques from many-body physics. We do so by studying the system-size dependence of the decoherence rate in the single-reservoir pure dephasing model. We determine the conditions under which this dependence scales quadratically, rather than linearly with the number of qubits. This difference in system-size staling is especially important for quantum computers with many qubits. Additionally, we study the effects that perturbations of the register-bath interaction have on decoherence-free subspaces. We find that a linear response to these perturbations is not a property of decoherence-free subspaces but is in fact generic for any register subspace. We derive a concise formula for the quadratic, leading order response. This formula can be used to identify the situations where decoherence-free subspaces work well in practice.