[Colloquium] Jonathan Baker MS Presentation/Oct 18, 2021

[meganwoodward at uchicago.edu]

This is an announcement of Jonathan Baker's MS Presentation
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Candidate: Jonathan Baker

Date: Monday, October 18, 2021

Time: 11:30 am CST

Remote Location: https://uchicago.zoom.us/j/91550902790?pwd=clE0WGc1TFhZUGl5Uk1CMkt5cGRXQT09

M.S. Paper Title: Intermediate Qudits for Quantum Computing

Abstract: Quantum computation is typically expressed as a two-level binary abstraction using qubits. However, many systems are not intrinsically binary and have access to many more energy levels that can be used as logical states. Full translation from one radix to another (for example binary to ternary) offers constant advantage, and clever usage can offer even more. Many quantum algorithms make use of extra ancillary bits which are used to store temporary information. In some cases, providing asymptotic improvements in the depth of circuit decompositions, highlighting an important space-time trade-off in quantum programs. By using additional space, we can reduce the total execution time of the program. When programs are time-limited, for example by prohibitive coherence times, it is critical to decompose circuits to minimize depth. This requires that we maintain a delicate balance between using ancilla that limit the total size of programs when a large portion of qubits must be reserved. 

To make use of limited resources in quantum hardware sooner, an alternative approach is to reduce the number of ancilla requirements by making use of qudit states. I will survey our work in this area. First is the decomposition of the generalized Toffoli gate. The most efficient decompositions use many ancilla to temporarily store the ANDs between pairs of inputs, recursively. Rather than using a full extra qubit, we temporarily allow our qubits to access the 2 state and store those results locally. The qubits temporarily access this additional space but are guaranteed to return to being only a superposition of the lowest two states. With temporary use of qutrits we can obtain the same asymptotic depth and gate count as the most efficient decomposition that uses ancilla without using any ancilla. While effective, this strategy has fairly narrow uses and requires hand optimization. Second, is a decomposition of reversible arithmetic circuits. This strategy relies on the generation of the required ancilla in-place via short encoding circuits to obtain efficient depth, the best-known depth for decompositions with ancilla. I will conclude with some current work in this area. 

Advisors: Fred Chong

Committee Members: Hank Hoffmann, Fred Chong, Kenneth Brown, and Ali Javadi-Abhari