Quantum error mitigation and autonomous correction using dissipative engineering and coupling techniques

Abstract

Realizations of quantum computing devices have progressed significantly, with each choice of architecture possessing advantages and disadvantages. Superconducting qubits are able to perform very fast gates, and benefit from standard manufacturing, but they suffer from very short coherence times compared to other architectures like trapped ions or spin qubits. This presents one of the greatest challenges towards achieving fault-tolerant quantum computing with superconducting architectures---improving coherence times. To that end, considerable research has been devoted to engineering qubits with longer lifetimes. Likewise, several error correction protocols have been introduced to provide a route towards fault-tolerance using noisy qubits, where a logical qubit is encoded in a collective state of many physical qubits, using stabilizer operations to detect and correct single qubit errors, thereby prolonging the logical state lifetime. However, the quantum resources required for the thousands of logical qubits needed for a factorization algorithm can be on the order of tens of millions of physical qubits for realistic error rates using surface codes. This would also require an immense amount of resources for the classical post-processing and decoding, a challenge for which there has not been a well established solution. The work in this thesis focuses on the implementation of logical qubits with autonomous error correction using dissipative engineering, in which high-coherence qubit devices are stabilized by coupling to lossy ancilla. The systems studied here have the advantage that a logical manifold can be encoded with a much smaller number of physical qubits compared to more traditional digital error correction codes, thus are called small logical qubits. This thesis presents results on improving autonomous error correction using numerically optimized pulse shaping for time parameterized coupling strength in different small logical qubits. It also presents results on a proposed scheme for error mitigation for the implementation of two-qubit gates---a dominant source of error in NISQ algorithms. Lastly, this thesis presents ongoing work with the simulation of dissipative engineering for variational quantum algorithms to improve algorithm performance.