Quantum encodings in spin systems and harmonic oscillators

By Stephen D. Bartlett, H. Guise, Barry C. Sanders. 2001

161 citations recorded by the source corpus.

We show that higher-dimensional versions of qubits, or qudits, can be encoded into spin systems and into harmonic oscillators, yielding important advantages for quantum computation. Whereas qubit-based quantum computationis adequate for analyses of quantum vs classical computation, in practice qubits are often realized in higher-dimensional systems by truncating all but two levels, thereby reducing the size of the precious Hilbert space. We develop natural qudit gates for universal quantum computation, and exploit the entire accessible Hilbert space. Mathematically, we give representations of the generalized Pauli group for qudits in coupled spin systems and harmonic oscillators, and include analyses of the qubit and the infinite-dimensional limits.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/765ef4cc7552d03bf37e9b49b6354c50a22a0368

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz (2017, background): “2 and References [36, 37] for a review of qudit operators, including the generalized Pauli operators X̆ and Z̆.”
Qudits and High-Dimensional Quantum Computing (2020, methodology): “The qudit-based quantum computing system can be implemented on various physical platforms such as photonic systems [60, 106]; continuous spin systems [2, 11]; ion trap [91]; nuclear magnetic resonance [48, 62] and molecular magnets [99].”