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Bulletin of the American Physical Society

Simplified mixed-state encoding for quantum computation with continuous-variable systems

Kevin Marshall, Daniel F. V. James, Alexandru Paler, Hoi-Kwan Lau

Published Mar 7, 2019• 0 citations
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Quantum Computation and Information Using Continuous Variables

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Recent development of mixed-state encoding (MSE) allows pure-state logical information to be encoded by a bosonic (continuous-variable) system in mixed physical state. Despite interest due to its counterintuitiveness, the utility of the current MSE scheme is limited due to several operational drawbacks, namely redundant information carrier, probabilistic initialization, and requirement of discrete-variable measurement. In this work, we present a simplified MSE that does not suffer from any of these drawbacks. Specifically, our protocol encodes each qubit by only one mixed-state bosonic mode and the logical basis can be deterministically initialized from thermal equilibrium. All logical operations of this encoding can be performed with continuous-variable interaction and measurement only. Without the necessity of ground-state cooling, our proposal could broaden the set of candidate systems for implementing quantum computers and reduce the reliance on demanding refrigerating facility for current quantum computing architectures. Additionally, our protocol can enhance the noise tolerance of logical qubit even if the system can be efficiently cooled.
One limitation of the quantum computing capability of a continuous-variable system is determined by our ability to cool it to the ground state, because pure logical states, in which we accurately encode quantum information, are conventionally pure physical states that are constructed from the ground state. In this work, we present an alternative quantum computing formalism that encodes logical quantum information in mixed physical states. We introduce a class of mixed-state protocols that are based on a parity encoding, and propose an implementation of the universal logic gates by using realistic hybrid interactions. When compared with the conventional pure-state protocols, our formalism could relax the necessity, and hence the systemic requirements, of cooling. Additionally, the mixed-state protocols are inherently resilient to a wider class of noise processes and reduce the fundamental energy consumption in initialization. Our work broadens the range of candidates for continuous-variable quantum computers.
Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal quantum computation with a fixed set of operations but arbitrary encoding. By storing a qubit in the parity of two or four qumodes, all computing processes can be implemented by basis state preparations, continuous-variable exponential-swap operations, and swap tests. Our formalism inherits the advantages that the quantum information is decoupled from collective noise, and logical qubits with different encodings can be brought to interact without decoding. We also propose a possible implementation of the required operations by using interactions that are available in a variety of continuous-variable systems. Our work separates the "hardware" problem of engineering quantum-computing-universal interactions, from the "software" problem of designing encodings for specific purposes. The development of quantum computer architecture could hence be simplified.