The wave-function description of the electromagnetic field

For an arbitrary electromagnetic field, we define a prepotential $S$, which is a complex-valued function of spacetime. The prepotential is a modification of the two scalar potential functions introduced by E. T. Whittaker. The prepotential is Lorentz covariant under a spin half representation. For a moving charge and any observer, we obtain a complex dimensionless scalar. The prepotential is a function of this dimensionless scalar. The prepotential $S$ of an arbitrary electromagnetic field is described as an integral over the charges generating the field. The Faraday vector at each point may be derived from $S$ by a convolution of the differential operator with the alpha matrices of Dirac. Some explicit examples will be calculated. We also present the Maxwell equations for the prepotential

Syndrome Measurement Strategies for the [[7,1,3]] Code

Quantum error correction (QEC) entails the encoding of quantum information into a QEC code space, measuring error syndromes to properly locate and identify errors, and, if necessary, applying a proper recovery operation. Here we compare three syndrome measurement protocols for the [[7,1,3]] QEC code: Shor states, Steane states, and one ancilla qubit by simulating the implementation of 50 logical gates with the syndrome measurements interspersed between the gates at different intervals. We then compare the fidelities for the different syndrome measurement types. Our simulations show that the optimal syndrome measurement strategy is generally not to apply syndrome measurements after every gate but depends on the details of the error environment. Our simulations also allow a quantum computer programmer to weigh computational accuracy versus resource consumption (time and number of qubits) for a particular error environment. In addition, we show that applying syndrome measurements that are unnecessary from the standpoint of quantum fault tolerance may be helpful in achieving better accuracy or in lowering resource consumption. Finally, our simulations demonstrate that the single-qubit non-fault tolerant syndrome measurement strategy achieves comparable fidelity to those that are fault tolerant.Comment: 14 pages, 9 composite figures, to be published in Quantum Information Processin