A polynomial-time classical decision algorithm exactly characterizes which multivariable Laurent polynomial pairs are realizable by M-QSP and supplies a constructive implementation when the answer is yes.
Lloyd, Science 273, 1073 (1996), publisher: American Association for the Advancement of Science
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Polynomial time constructive decision algorithm for multivariable quantum signal processing
A polynomial-time classical decision algorithm exactly characterizes which multivariable Laurent polynomial pairs are realizable by M-QSP and supplies a constructive implementation when the answer is yes.