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Abstract Most existing quantum algorithms are discovered accidentally or adapted from classical algorithms, and there is the need for a systematic theory to understand and design quantum circuits. Here we develop a unitary dependence theory to characterize the behaviors of quantum circuits and states in terms of how quantum gates manipulate qubits and determine their measurement probabilities. Compared to the conventional entanglement description of quantum circuits and states, the unitary dependence picture offers more practical information on the measurement and manipulation of qubits, easier generalization to many-qubit systems, and better robustness upon partitioning of the system. The unitary dependence theory can be applied to systematically understand existing quantum circuits and design new quantum algorithms.
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On the design of molecular excitonic circuits for quantum computing: the universal quantum gates
This manuscript presents a strategy for controlling the transformation of excitonic states through the design of circuits made up of coupled organic dye molecules. Specifically, we show how unitary transformation matrices can be mapped to the Hamiltonians of physical systems of dye molecules with specified geometric and chemical properties. The evolution of these systems over specific time scales encodes the action of the unitary transformation. We identify bounds on the complexity of the transformations that can be represented by these circuits and on the optoelectronic properties of the dye molecules that comprise them. We formalize this strategy and apply it to determine the excitonic circuits of the four universal quantum logic gates: NOT, Hadamard, π/8 and CNOT. We discuss the properties of these circuits and how their performance is expected to be influenced by the presence of environmental noise.
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- Award ID(s):
- 1839155
- PAR ID:
- 10176089
- Date Published:
- Journal Name:
- Physical Chemistry Chemical Physics
- Volume:
- 22
- Issue:
- 5
- ISSN:
- 1463-9076
- Page Range / eLocation ID:
- 3048 to 3057
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/C9CP05625D
