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Concept# Quantum state

Summary

In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a quantum mechanical prediction for the system represented by the state. Knowledge of the quantum state together with the quantum mechanical rules for the system's evolution in time exhausts all that can be known about a quantum system.
Quantum states may be defined in different ways for different kinds of systems or problems. Two broad categories are

- wave functions describing quantum systems using position or momentum variables, and
- the more abstract vector quantum states. Historical, educational, and application-focused problems typically feature wave functions; modern professional physics uses the abstract vector states. In both categories, quantum states divide into pure versus mixed states, or into coherent states and incoherent states. Categories with special p

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We explore the connection between the transfer matrix formalism and discrete complex analysis approach to the two dimensional Ising model. We construct a discrete analytic continuation matrix, analyze its spectrum and establish a direct connection with the critical Ising transfer matrix. We show that the lattice fermion operators of the transfer matrix formalism satisfy, as operators, discrete holomorphicity, and we show that their correlation functions are Ising parafermionic observables. We extend these correspondences also to outside the critical point. We show that critical Ising correlations can be computed with operators on discrete Cauchy data spaces, which encode the geometry and operator insertions in a manner analogous to the quantum states in the transfer matrix formalism.

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Combined microwave-optical pump-probe methods are emerging to study the quantum state of spin qubit centers and the charge dynamics in semiconductors. A major hindrance is the limited bandwidth of microwave irradiation/detection circuitry which can be overcome with the use of broadband coplanar waveguides (CPWs). The development and performance characterization of two spectrometers is presented as follows: an optically detected magnetic resonance spectrometer (ODMR) and a microwave-detected photoconductivity measurement. In the first method, light serves as detection and microwaves excite the investigated medium, whereas in the second, the roles are interchanged. The performance is demonstrated by measuring ODMR maps on the nitrogen-vacancy (NV) center in diamond and time-resolved photoconductivity in p-doped silicon. The results demonstrate both an efficient coupling of the microwave irradiation to the samples as well as an excellent sensitivity for minute changes in sample conductivity.

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We report the experimental nondemolition measurement of coherence, predictability and concurrence on a system of two qubits. The quantum circuits proposed by De Melo et al. (Phys Rev Lett 98(25):250501, 2007) are implemented on IBM Q (superconducting circuit) and IonQ (trapped ion) quantum computers. Three criteria are used to compare the performance of the different machines on this task: measurement accuracy, nondemolition of the observable, and quantum state preparation. We find that the IonQ quantum computer provides constant state fidelity through the nondemolition process, outperforming IBM Q systems on which the fidelity consequently drops after the measurement. Our study compares the current performance of these two technologies at different stages of the nondemolition measurement of bipartite complementarity.