Complete set of circuit equations for stabilizer quantum mechanics

The ZX-calculus is complete for stabilizer quantum mechanics

The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics (QM), meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound, i.e. any equality that can be derived graphically can also be derived using matr...

Optimized Aaronson-Gottesman stabilizer circuit simulation through quantum circuit transformations

In this paper we improve the layered implementation of arbitrary stabilizer circuits introduced by Aaronson and Gottesman in Phys. Rev. A 70(052328), 2004. In particular, we reduce their 11-stage computation -H-C-P-C-P-C-H-P-C-P-Cinto an 8-stage computation of the form -H-CCZ-P-H-P-CZ-C-. We show arguments in support of using -CZstages over the -Cstages: not only the use of -CZstages allows a s...

The ZX calculus is incomplete for non-stabilizer quantum mechanics

Shorter stabilizer circuits via Bruhat decomposition and quantum circuit transformations

In this paper we improve the layered implementation of arbitrary stabilizer circuits introduced by Aaronson and Gottesman in Phys. Rev. A 70(052328), 2004: to implement a general stabilizer circuit, we reduce their 11-stage computation -HC-P-C-P-C-H-P-C-P-Cover the gate set consisting of Hadamard, Controlled-NOT, and Phase gates, into a 7-stage computation of the form -C-CZ-P-H-P-CZ-C-. We show...

circuit modeling of quantum well heterostructure biopolar phototransistor مدل سازی مداری qw-hbpt

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