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arXiv:2510.04880 · Physical Review A

Creating qubit states with degenerate two-level systems

Zhuoran Bao, Daniel F. V. James

Published Mar 17, 2026• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/n284-bpds

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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.
We propose a mechanism for single- and double-qubit state manipulations in quantum computation with an inseparable double-qubit structure. The principle is based on manipulating the degeneracy of the four energy levels. The degeneracy of levels is allowed to be fourfold, doubly degenerate in pairs and nondegenerate, and these configurations are tuned by two coupling parameters. The quantum gate operations are performed at the nondegenerate whereas the data are stored in the degenerate configurations. The fact that the center of the four energy levels is invariant at all parameter values is exploited, and this particularly increases the performance of the controlled operations. A particular realization of the proposed mechanism is suggested by using the recently proposed inductively coupled rf superconducting quantum interference device loops in the macroscopic quantum tunneling regime where the energy eigenlevels are directly connected with the measurable flux states. This very fact also allows precise read-in and read-out operations by measurement of the flux which can also be done by existing techniques. That other physical realizations of the mechanism than that examined here are likely to exist is also discussed briefly.
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Quantum gates are fundamental in Quantum computing for their role in manipulating elementary information carriers referred to as quantum bits. In this paper, a theoretical scheme for realizing a quantum Hadamard and a quantum controlled-NOT logic gates operations in the anti-Jaynes-Cummings interaction process is provided. Standard Hadamard operation for a specified initial atomic state is achieved by setting a specific sum frequency and photon number in the normalized anti-Jaynes-Cummings qubit state transition operation with the interaction component of the anti-Jaynes-Cummings Hamiltonian generating the state transitions. The quantum controlled-NOT logic gate is realized when a single atomic qubit defined in a two-dimensional Hilbert space is the control qubit and two non-degenerate and orthogonal polarized cavities defined in a two-dimensional Hilbert space make the target qubit. With precise choice of interaction time in the anti-Jaynes-Cummings qubit state transition operations defined in the anti-Jaynes-Cummings sub-space spanned by normalized but non-orthogonal basic qubit state vectors, ideal unit probabilities of success in the quantum controlled-NOT operations is determined.
A two-level quantum system is the building block of a quantum computer. This pair of quantum states defines the computational unit of a quantum computer, and it is called a quantum bit or qubit in analogy to the bit that is the binary unit of a classical computer. The spin of a single electron naturally defines such a two-level quantum system. A quantum dot can be tuned to the single-electron regime, and an array of singly occupied quantum dots provides a multi-qubit register. This thesis describes the multielectron encoding of a spin qubit using a pair or a trio of quantum dots, and it analyzes the coherence properties and manipulation protocols of this system. The singlet-triplet qubit, coded using the singlet state and the spinless triplet state of a pair of singly occupied quantum dots, can be controlled all electrically when applying voltages to gates close to the quantum dot structure. Rapid, subnanosecond modifications of the double quantum dot's charge configuration have been realized successfully. A small magnetic field gradient across the double quantum dot enables universal qubit control. Two modifications of the normal singlet-triplet encoding are introduced. (1) The six-electron configuration of a double quantum dot encodes a singlet-triplet qubit in the same way as for the two-electron double quantum dot. Two electrons at each quantum dot are irrelevant for the qubit manipulations because they are paired in a singlet state; the remaining two electrons encode the qubit. The qubit's wave function is immune to charge noise at moderate out-of-plane magnetic fields. (2) A singlet-triplet qubit encoded using two quantum dots of different sizes has an orbital state degeneracy of the singlet state and the spinless triplet state at finite out-of-plane magnetic fields. Spin-orbit interactions lift this state degeneracy, while the magnitude of the state coupling is determined by the size difference of the QDs. This setup enables the manipulations of singlet-triplet qubits without the need for magnetic field gradients. Finally, two-qubit gates between singlet-triplet qubits are proposed that use mediated exchange interactions via one quantum state. These operations are well controlled and highly noise insensitive. Orbital interactions alone can control spin qubits coded in a three electron Hilbert space. For example, the exchange-only qubit is encoded using three singly occupied quantum dots. The exchange interactions of two quantum dot pairs need to be modified to manipulate this qubit. The noise sensitivity of the exchange-only qubit is discussed. Alternatively, a three-electron qubit at a double quantum dot can be operated when single electrons are transferred between the quantum dots. Fast, subnanosecond manipulations of the double quantum dot's charge configuration are required to realize single-qubit gates. A novel two-qubit pulse gate for the three-electron double quantum dot qubit is proposed.
We present a new robust decoupling scheme suitable for levels with either half-integer or integer angular momentum states. Through continuous dynamical decoupling techniques, we create a protected qubit subspace, utilizing a multistate qubit construction. Remarkably, the multistate system can also be composed of multiple substates within a single level. Our scheme can be realized with state-of-the-art experimental setups and thus has immediate applications for quantum information science. While the scheme is general and relevant for a multitude of solid-state and atomic systems, we analyze its performance for the case composed of trapped ions. Explicitly, we show how single qubit gates and an ensemble coupling to a cavity mode can be implemented efficiently. The scheme predicts a coherence time of ∼1 s, as compared to typically a few milliseconds for the bare states.
A three state Hamiltonian with a degenerate ground state is shown to exhibit the property of generating quantum gates for fixed values of the energy parameters just by using the ability of this quantum system to evolve in time yielding suitable sets of quantum probabilities. A method is presented, based on the conventional rules of quantum mechanics, for obtaining several gates without changing the system configuration, i.e. just by adjusting the times in which the interaction is switched on and off. The mathematical rules for generating such a set of gates are completely defined and described in this work. The corresponding physical implementation should involve fast Rabi pulses and very precise switches of the kind proposed in quantum geometric computation.