Optimizing Models of Hybrid Quantum/Classical Computation [PDF] (2024)

Quantum computers promise a substantial speedup for many computational tasks which are intractable even for state-of-the-art classical supercomputers. However, experimental implementations of quantum devices are still in their infancy and the current small prototypes are several years away from the desired goal: large-scale, fault-tolerant quantum computers. Hence, it makes sense to wonder: How can one best exploit the currently available technology to achieve the quantum advantage regime in the near term? In recent years, hybrid quantum-classical computation has emerged as an interesting proposition to address precisely this question.

In this thesis, we investigate practical ways in which hybrid strategies can be exploited to optimize the use of the available quantum resources and enable enhanced computation. We study and improve recent hybrid computational models and turn theoretical proposals into practical, software enabled solutions to be implemented in current (or near-term) quantum devices.

Specifically, we focus on Pauli-based computation (PBC), a universal quantum computing model wherein the computation is driven by an adaptive sequence of compatible, multi-qubit Pauli measurements. In chapter 3, we leverage this model to accomplish two distinct tasks. The first is circuit compilation wherein we take a Clifford+T quantum circuit with n qubits and t T gates and transform it into adaptive Clifford circuits that often require fewer gates and/or depth and, under certain circumstances, even fewer qubits. With respect to prior work, our schemes reduce the number of quantum gates of the final circuits to O(t²) (from a previous O(t³/ log t) scaling) and space/timetrade-offs are discussed which lead to a reduction of the depth from O(t log t) to O(t) within our schemes, at the cost of t additional auxiliary qubits. The second task consists of using PBC to extend an available quantum memory by k “virtual qubits” at the expense of a sampling complexity exponential in k. By using a smarter sampling strategy, we managed to improve this sampling complexity from a prior 2ᴼ⁽ᵏ⁾ scaling to O(2⁰⋅⁷³⁷⁴ᵏ). As hinted on above, besides these theoretical contributions, we also wrote Python code to carry out each of these tasks and used it to provide numerical evidence of the usefulness of PBC. In chapter 4, we further show that this model generalizes to odd-primedimensional qudits while retaining its appealing features. Intriguingly, hybrid computation appears to become increasingly more costly as the qudit’s dimension increases.

PBC is a measurement-based quantum computation model that uses measurements on a separable, magic input state to implement the desired computation. The formulation of this model rests on the magic-state injection of special, single-qubit, magic states. In chapter 5, we change gears slightly and turn to the study of states that are both magic and entangled. We focus on a specific (infinite) family of states that we call “star cat states” and provide circuit gadgets that can be used to inject them into any quantum circuit. Afterward, we study whether these states can lead to speedups in classical simulation using stabilizer-rank-based techniques or be exploited for quantum resource reduction in actual quantum computation. While we provide some evidence for a negative outcome to the former, the latter seems to have an affirmative answer. In particular, in some instances, star cat states seem to allow for implementations with fewer qubits albeit at the expense of an increased number of two-qubit entangling gates.