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In this thesis, we address the additional challenges for quantum simulations posed by particles which are fermionic in nature, namely those caused by the nonlocal fermionic statistics. In particular, we study the encodings of fermionic degrees of freedom into the qubits of a quantum computer. We focus on finding a scheme which minimizes the resources required to execute a simulation and investigate the ability to mitigate errors in noisy near-term quantum simulation experiments. We finally present an algebraic theory of such encodings which clarifies their mathematical structure and facilitates devising algorithms for generating new encodings tailored to a specific task.

We then turn to the study of a specific class of algorithms for studying quantum many-body systems, called tensor network algorithms. We focus on the multiscale entanglement renormalization ansatz, a tensor network structure well-suited to studying systems at critical points. In particular, we investigate an instance of this tensor network structure that takes the form of an isometric quantum circuit that can be naturally executed on a quantum computer. We study the accuracy scaling with the required computational resources. We also uncover new emergent structures that provide new insights into the entanglement renormalization and can be leveraged to accelerate numerical computations.

Graduate Advisor: Professor James D. Whitfield

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Meeting ID: 917 2327 2082
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