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The realization for a faulty T gate by a faulty T measurement, which is usually used in the fault-tolerant preparation for magic states.
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Magic states have been widely studied in recent years as resource states that help quantum computers achieve fault-tolerant universal quantum computing. The fault-tolerant quantum computing requires fault-tolerant implementation of a set of universal logical gates. Stabilizer code, as a commonly used error correcting code with good properties, can...
Citations
... For example, separable states correspond with measure-prepare (also known as entanglementbreaking) channels under the isomorphism [42], and this correspondence is at the centre of the resource theory of entanglement [11,14,61] and the ongoing pursuit to quantify entanglement-a problem with applications in all of quantum physics. What is more, in the field of quantum computation Choi's isomorphism underlies the widely used protocol of gate teleportation [31], which in conjunction with magic state distillation [12,50] forms one of the main architectures for fault-tolerant universal quantum computation [55]. ...
... Since the Choi-Jamiołkowski isomorphism is a basic tool across quantum information theory, we expect the techniques used here to be useful for and to shed light on various other results in the field. For instance, the change from a kinematical to a dynamical perspective is leveraged in the protocol of gate teleportation, a central ingredient to fault-tolerant quantum computation [31,55]. What is more, in relativity theory the distinction between kinematics and dynamics becomes even less clear-cut, and it has been suggested that the Choi-Jamiołkowski isomorphism might be more than a useful mathematical gadget, but rather that it hints at a deep symmetry between kinematics and dynamics in fundamental physics [54]. ...
The Choi–Jamiołkowski isomorphism is an essential component in every quantum information theorist’s toolkit: it allows to identify linear maps between two quantum systems with linear operators on the composite system. Here, we analyse this widely used gadget from a new perspective. Namely, we explicitly distinguish between its kinematical and dynamical properties, that is, we study the isomorphism on two different levels: Jordan algebras and the different C∗ -algebras they arise from, which are distinguished by their order of composition. A number of important and novel insights stem from our analysis. We find that Choi’s theorem, which asserts that Choi’s version of the isomorphism (Choi 1975 Lin. Alg. Appl. 10 285) further maps the positive cone of completely positive linear maps (such as quantum channels) to the cone of positive linear operators (such as quantum states) on the composite system, crucially depends on the dynamical structure in C∗ -algebras. We explain in detail how this dependence gives rise to the mismatch between the basis-dependence of Choi’s version of the isomorphism, and the basis-independent version by Jamiołkowski (1972 Rep. Math. Phys. 3 275). We then overcome this subtle but pervasive issue in a number of ways: first, we prove a version of Choi’s theorem for Jamiołkowski’s isomorphism, second, we define a basis-independent variant of Choi’s isomorphism and, third, by making explicit the dynamical distinction between Jordan and C∗ -algebras, we combine the different variants of the isomorphism into a unified description, that subsumes their individual features. We also embed and interpret our results in the graphical calculus of categorical quantum mechanics.
