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arXiv:cond-mat/0203038

Quantum Computation with Aharonov-Bohm Qubits

A. Barone, Tugrul Hakioglu, I. O. Kulik

Published Mar 2, 2002• 4 citations
arXivHTMLPDF

Abstract

We analyze the posibility of employing the mesoscopic-nanoscopic ring of a normal metal in a doubly degenerate persistent current state with a third auxihilary level and in the presence of the Aharonov-Bohm flux equal to the half of the normal flux quantum $\hbar c/e$ as a qubit. The auxiliary level can be effectively used for all fundamental quantum logic gate (qu-gate) operations which includes the initialization, phase rotation, bit flip and the Hadamard transformation as well as the double-qubit controlled operations (conditional bit flip). We suggest a tentative realization of the mechanism as either the mesoscopic structure of three quantum dots coherently coupled by mesoscopic tunnelling in crossed magnetic and electric fields, or as a nanoscopic structure of triple anionic vacancy (similar to $F_3$ centers in alkali halides) with one trapped electron in one spin projection state.

DOI
10.48550/arxiv.cond-mat/0203038

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We analyze the posibility of employing the mesoscopic-nanoscopic ring of a normal metal in a doubly degenerate persistent current state with a third auxihilary level and in the presence of the Aharonov-Bohm flux equal to the half of the normal flux quantum ℏc/e\hbar c/eℏc/e as a qubit. The auxiliary level can be effectively used for all fundamental quantum logic gate (qu-gate) operations which includes the initialization, phase rotation, bit flip and the Hadamard transformation as well as the double-qubit controlled operations (conditional bit flip). We suggest a tentative realization of the mechanism as either the mesoscopic structure of three quantum dots coherently coupled by mesoscopic tunnelling in crossed magnetic and electric fields, or as a nanoscopic structure of triple anionic vacancy (similar to F3F_3F3​ centers in alkali halides) with one trapped electron in one spin projection state.
We analyze the dynamics of a ground state two-level system built on the spatial distribution of the system wave function and designed to be well-separated from the remainder of the state space. With a total of two operative electrons on a planar array of quantum dots coupled capacitively to a set of external voltage gates, the system is modeled using an extended Hubbard Hamiltonian. The voltage dependence of the low-energy singlet and triplet states is analyzed, respectively, using the Feshbach formalism. Coherent operation of the array is studied with respect to single quantum bit operations. One quantum gate is implemented via voltage controls, while for the necessary second quantum gate, a uniform external magnetic field is introduced. The Aharonov-Bohm phases on the closed loop tunnel connections in the array are used to effectively suppress the tunneling, despite a constant tunneling amplitude in the structure. This allows one to completely stall the qubit in any arbitrary quantum superposition, providing full control of this interesting quantum system.
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.
Quantum computation using electron spins in three-coupled dots of different sizes is proposed. By using photon-assisted tunnelling, Coulomb blockade and spin rotation of electrons, logic gates are realized by static and rotational magnetic fields and resonant optical pulses. The two-bit CNOT is numerically demonstrated by the time evolution of the density matrix. In addition, the Hamiltonian is described using pseudo-spin representation and the phase change during the gate operation is discussed.
Quantum devices and computers will need operational units in different architectural configurations for their functioning. The unit should be a simple "quantum toy," an easy to handle superposition state. Here such a novel unit of quantum mechanical flux state (or persistent current) in a conducting ring with three ferromagnetic quantum dots is presented. The state is labeled by the two directions of the persistent current, which is driven by the spin chirality of the dots, and is controlled by the spin (the spin Josephson effect). It is demonstrated that by the use of two connected rings, one can carry out unitary transformations on the input flux state by controlling one spin in one of the rings, enabling us to prepare superposition states. The flux is shown to be a quantum operation gate, and may be useful in quantum computing.
A single electron spin in a double quantum dot in a magnetic field is considered in terms of a four-level system. By describing the electron motion between the potential minima via spin-conserving tunneling and spin flip caused by a spin–orbit coupling, we inversely engineer faster-than-adiabatic state manipulation operations based on the geometry of four-dimensional rotations. In particular, we show how to transport a qubit among the quantum dots performing simultaneously required spin rotations.