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arXiv:0912.0230

Contradiction between assumption on superposition of flux-qubit states and the law of angular momentum conservation

А. В. Никулов

Published Dec 1, 2009• 1 citation
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Abstract

Superconducting loop interrupted by one or three Josephson junctions is considered in many publications as a possible quantum bit, flux qubit, which can be used for creation of quantum computer. But the assumption on superposition of two macroscopically distinct quantum states of superconducting loop contradict to the fundamental law of angular momentum conservation and the universally recognized quantum formalism. Numerous publications devoted to the flux qubit testify to an inadequate interpretation by many authors of paradoxical nature of superposition principle and the subject of quantum description.

DOI
10.48550/arxiv.0912.0230

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Superconducting loop interrupted by one or three Josephson junctions is considered in many publications as a possible quantum bit, flux qubit, which can be used for creation of quantum computer. But the assumption on superposition of two macroscopically distinct quantum states of superconducting loop contradict to the fundamental law of angular momentum conservation and the universally recognized quantum formalism. Numerous publications devoted to the flux qubit testify to an inadequate interpretation by many authors of paradoxical nature of superposition principle and the subject of quantum description.
The confidence of many authors in the possibility to use superconducting loop interrupted by Josephson junctions as a basis for quantum bit, flux qubit, presumes the assumption on superposition of two macroscopically distinct quantum states with macroscopically different angular momentum. The contradiction of this assumption with macroscopic realism and the conservation law must call the numerous publications about flux qubit in question. These publications uncover misunderstanding by many modern physicists of the essence of the superposition principle. The Einstein - Podolsky - Rosen (EPR) correlation or entanglement, introduced in 1935 by opponents of the Copenhagen interpretation in order to reveal the contradiction of this principle with realism, has provided a basis of the idea of quantum computation. The problem of the EPR correlation has emerged thanks to philosophical controversy between the creators of the quantum theory about the subject of its description. Therefore it is impossible to solve correctly the problem of quantum computer creation without the insight into the essence of this philosophical controversy. The total neglect of the philosophical problems of quantum foundation results to concrete mistakes, the example of which are the publications about flux qubit. In order to prevent such mistakes in the future the philosophical questions about the essence of superposition and entanglement and about the subject of quantum description are considered.
Flux qubits, small superconducting loops interrupted by Josephson junctions, are successful realizations of quantum coherence for macroscopic variables. Superconductivity in these loops is carried by ∼106\sim 10^6∼106 -- 101010^{10}1010 electrons, which has been interpreted as suggesting that coherent superpositions of such current states are macroscopic superpositions analogous to Schrödinger's cat. We provide a full microscopic analysis of such qubits, from which the macroscopic quantum description can be derived. This reveals that the number of microscopic constituents participating in superposition states for experimentally accessible flux qubits is surprisingly but not trivially small. The combination of this relatively small size with large differences between macroscopic observables in the two branches is seen to result from the Fermi statistics of the electrons and the large disparity between the values of superfluid and Fermi velocity in these systems.
Multiple and single measurements of quantum states of mesoscopic superconducting loops are carried out in order to investigate a possibility of macroscopic quantum superposition and of creation of a superconductor quantum register. Asymmetric superconducting rings are used in order to be convinced that single measurement gives result corresponding to one of permitted states and multiple one gives an average value on these states. We have measured magnetic dependencies of resistance, rectified voltage and critical current on these rings. The observed quantum oscillations of the resistance and the rectified voltage, corresponding to multiple measurement of quantum states, give evidence of two permitted states at the magnetic flux inside the ring divisible by half of the flux quantum. But the observed quantum oscillations of the critical current, corresponding to single measurement, not only does not confirm these two quantum states, but are in a direct contradiction with the observed oscillations of the resistance. It is assumed that the observed contradiction between the results of measurements made on the same ring can testify to violation of the principle of realism on the mesoscopic level that is a necessary condition for an opportunity of creation of a quantum computer.
The idea of the quantum computation is based on paradoxical principles of quantum physics superposition and entanglement of quantum states. This idea looks well-founded on the microscopic level in spite of the absence of an universally recognized interpretation of these paradoxical principles since they were corroborated over and over again by reliable experiments on the microscopic level. But the technology can not be able in the near future to work on the microscopic level. Therefore macroscopic quantum phenomenon-superconductivity is very attractive for the realization of the idea of quantum computer. It is shown in the present paper that a chain of superconducting loops can be only possible quantum register. The proposals by some authors to provide the EPR correlation with help of a classical interaction witness the misunderstanding of the entanglement essence. The problem of the possibility of superposition of macroscopically distinct states is considered.
Superconducting circuits containing Josephson junctions have previously been shown to exist in superpositions of states of electric charge and of superconducting phase. This superposition manifests itself in so-called Rabi oscillations between the two energy levels produced by the superposition. In his Perspective, Clarke highlights the report of Chiorescu et al. , who demonstrate that a superconducting ring containing three Josephson junctions also exhibits Rabi oscillations, and thus exists in a superposition of magnetic flux states. The experiments are elegant demonstrations of coherence in superconducting circuits, and are potentially of interest as quantum bits in a future computer.