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arXiv:quant-ph/9912123 · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Multilevel quantum particle as a few virtual qubits materialization

A. R. Kessel, Vladimir L. Ermakov

Published Jan 14, 2000• 2 citations
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Abstract

A conception of virtual quantum information bit - virtual qubit - is introduced. It is shown by means of virtual qubit representation that four states of a single quantum particle is enough for implementation of full set of the gates, which is necessary for creation an arbitrary algorithm for a quantum computer. The physical nature and mutual disposition of four working states is of no significance provided the existence of the suitable selection rules for the particle interaction with the external electromagnetic field pulses.

DOI
10.1117/12.375307

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A conception of virtual quantum information bit - virtual qubit - is introduced. It is shown by means of virtual qubit representation that four states of a single quantum particle is enough for implementation of full set of the gates, which is necessary for creation an arbitrary algorithm for a quantum computer. The physical nature and mutual disposition of four working states is of no significance provided the existence of the suitable selection rules for the particle interaction with the external electromagnetic field pulses.
The possibility of using multilevel quantum systems with a discrete nonequidistant spectrum for the physical implementation of a universal collection of quantum gates, which is required for constructing an arbitrary algorithm for a quantum computer, is studied on the basis of the proposed virtual-spin formalism. It is shown that such a set of gates, including two-qubit gates, can be constructed on a single spin-3/2 nucleus. The assertion that three-qubit gates can also be realized on a single spin-7/2 quantum particle is substantiated.
A virtual spin formalism is suggested to demonstrate that a single quantum particle possessing eight suitable discrete energy levels can be used for storing three information qubits and organizing on them a universal set of logical operations that are necessary for constructing an arbitrary quantum algorithm. The formalism can be practically implemented on a nuclear spin 7/2 subjected to resonance rf pulses. A single-pulse realization is found for all quantum gates of a universal set, including a three-qubit gate.
One qubit is mapped to two level system in the standard model of quantum computation: a typical example is a spin-1/2 system. Further progress requires the use of network of multilevel quantum systems of different physical origin in solids: optical levels, large or strong interacting spins etc. We propose virtual qubit formalism and show how the quantum objects state space can be used as a basis for multiqubit information recording and processing in a quantum computer. It is suggested to map the qubits into solid state NMR spin system collective states instead of the state of the individual spin. Such an approach introduces the stable computational basis without any additional actions and allows to obtain the universal set of quantum gates, which operation time is determined only by the RF pulses.
We show that virtual particles, despite being unobservable, can be described by quantum operators which can be interpreted under certain conditions as valid qubit quantum states. For a single virtual fermion, we prove that such a state is a separable mixed two-qubit state with a well-defined finite temperature. For spin-1 virtual bosons, we find them to be associated with four-qubit operators which can be interpreted as quantum states for some gauges. We also study the creation of virtual pairs of fermions, where the pair is shown to be associated with an entangled four-qubit operator, and show the corresponding quantum circuit. Finally, we prove that renormalization does not structurally affect these results. These findings represent interesting connections between quantum field theory, quantum information, and quantum thermodynamics.
A qubit, or quantum bit, is conventionally defined as "a physical system for storing information that is capable of existing in either of two quantum states or in a superposition of both". In this paper, we examine the simple question of whether two distinct levels, each consisting of multiply degenerate sub-states, could serve as a practical quantum bit. We explore this idea using a well-characterized atomic system of the kind employed in several quantum computing implementations. We approximate the atom as a two-level system without degeneracy lifting in the magnetic quantum number while using the angular momentum addition rules to select the desired state transition. We find that, in the continuous presence of the field, the atom still undergoes Rabi oscillations, which are suitable for quantum gate construction. In addition, we compute the average fidelity in quantum gate performance for a single degenerate atom and postulate the required form of two-atom interaction to construct a controlled Z gate.
Schemes of experimental realization of the main two-qubit processors for quantum computers and the Deutsch-Jozsa algorithm are derived in virtual spin representation. The results are applicable for every four quantum states allowing the required properties for quantum processor implementation if for qubit encoding, virtual spin representation is used. A four-dimensional Hilbert space of nuclear spin 3/23/23/2 is considered in detail for this aim.