Abstract
We gather and examine in detail gate decomposition techniques for continuous-variable quantum computers and also introduce some new techniques which expand on these methods. Both exact and approximate decomposition methods are studied and gate counts are compared for some common operations. While each having distinct advantages, we find that exact decompositions have lower gate counts whereas approximate techniques can cover decompositions for all continuous-variable operations but require significant circuit depth for a modest precision.
Highlights
For a quantum computer to be able to execute an algorithm, often defined by a product of high-level unitary transformations [1,2,3,4,5,6], the operations of the algorithm must be translated into the small set of logical gates directly built into the hardware
Other results have been discovered which strengthen decomposition techniques in qubit systems by allowing for less logical gates to be needed, or the resulting decomposition to be of a greater precision. These techniques are used for single-qubit operations [16,17,18,19] as well as general multi-qubit operations [6]. In this manuscript we focus on gate decomposition techniques for continuous-variable (CV) quantum computers, which have not been as extensively studied
To potentially avoid the cost of repeating gates for greater precision, exact decomposition methods can be used as we show
Summary
For a quantum computer to be able to execute an algorithm, often defined by a product of high-level unitary transformations [1,2,3,4,5,6], the operations of the algorithm must be translated into the small set of logical gates directly built into the hardware. The problem of finding optimal ways to decompose an arbitrary gate into a product of gates from a given universal set is precisely the focus of this manuscript The study of this problem finds application when continuous degrees of freedom are used to encode error-correctable qubits, since the logical operations of the logical qubits need to be executed as continuous-variable gates [24,25,26,27].
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