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Journal of Physics Conference Series

Scheme for Bell state measurement in a g-factor engineered double dot

Nobuhiko Yokoshi, Hiroshi Imamura, Hideo Kosaka

Published Jan 1, 2010• 0 citations
Publisher

Abstract

We proposed a possible protocol for Bell state measurements of spin qubits in a double quantum dot (QD). Our scheme consists of Pauli spin blockade measurements and biaxial electron spin resonance. It is assumed that the two QDs here are designed so that the Land? g-factors satisfy g1 = ?g2 with the use of g-factor engineering. The opposite sign of the g-factors cancel the average of the Zeeman fields on the two QDs, and enable us to swap three spin-triplet states for a spin-singlet state sequentially. We showed that it is possible to implement the full Bell state measurement by the sequential spin-to-charge conversions in the QD-based spin qubits.

DOI
10.1088/1742-6596/200/11/112012

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We proposed a possible protocol for Bell state measurements of spin qubits in a double quantum dot (QD). Our scheme consists of Pauli spin blockade measurements and biaxial electron spin resonance. It is assumed that the two QDs here are designed so that the Land? g-factors satisfy g1 = ?g2 with the use of g-factor engineering. The opposite sign of the g-factors cancel the average of the Zeeman fields on the two QDs, and enable us to swap three spin-triplet states for a spin-singlet state sequentially. We showed that it is possible to implement the full Bell state measurement by the sequential spin-to-charge conversions in the QD-based spin qubits.
We propose a scheme for full Bell state measurement of spin qubits in a double quantum dot. Our scheme consists of Pauli spin-blockade measurements and biaxial electron-spin resonance. In order to eliminate the average of the Zeeman fields, the double quantum dot is designed so that the Land\'e ggg-factors of first and second dots satisfy ${g}_{1}=\ensuremath{-}{g}_{2}$ with the use of ggg-factor engineering. Thus, we can swap one of the three spin-triplet states for the spin-singlet state without disturbing the other states. Our study shows that the sequential spin-to-charge conversions enable us to implement the full Bell state measurement of electron-spin qubits.
We propose a protocol and physical implementation for partial Bell-state measurements of Fermionic qubits, allowing for deterministic quantum computing in solid-state systems without the need for two-qubit gates. Our scheme consists of two spin qubits in a double quantum dot where the two dots have different Zeeman splittings and resonant tunneling between the dots is only allowed when the spins are antiparallel. This converts spin parity into charge information by means of a projective measurement and can be implemented with established technologies. This measurement-based qubit scheme greatly simplifies the experimental realization of scalable quantum computers in electronic nanostructures.
We present a scheme for full quantum state tomography tailored for two spin qubits in a double quantum dot. A set of 15 quantum states allows to determine the density matrix in this two-qubit space by projective measurement. In this paper, we choose a set gained from mutually unbiased bases. We determine how those 15 projections can be represented by charge measurements after a spin-to-charge conversion and the application of quantum gates. The quantum gates include exchange-based gates as well as rotations by electron spin resonance (ESR). We assume the experimental realization of ESR operations to be more difficult than the exchange gate operation with respect to fidelity and speed. Therefore it is an important result that the ESR gates can be limited to a $\ensuremath{\pi}/2$ rotation for one of the electron spins per measurement.
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.
Measurement-based quantum computing (MBQC) promises an alternative approach to quantum computation that has natural compatibility with error-correction codes at the cost of a polynomial increase in physical qubits. MBQC implementations have previously focused on photonic systems where two-qubit gates are difficult. On the other hand, semiconductor spin qubit systems offer fast two-qubit gates via the exchange interaction. To explore the benefits of MBQC on spin systems, two hybrid measurement-exchange schemes for full qubit control with semiconductor double-quantum-dot spin qubits are considered. Protocol 1 fully realizes the cluster-state approach to MBQC but requires singlet-triplet qubits in a magnetic field gradient. Protocol 2 implements a direct measurement-based replacement for more traditional gate-based encoded operations, without need for magnetic field gradients. Both protocols demonstrate full single- and two-qubit control through a combination of interqubit and intraqubit exchange and measurement onto the singlet-triplet basis. We show that both schemes suppress individual qubit spin-state leakage errors and offer fast gate times, up to known phase and Pauli corrections.
We propose a quantum computation architecture of double-dot molecules, where the qubit is encoded in the molecule two-electron spin states. By arranging the two dots inside each molecule perpendicular to the qubit scaling line, the interactions between neighboring qubits are largely simplified and the scaling to the multiqubit system becomes straightforward. As an Ising-model effective interaction can be expediently switched on and off between any two neighboring molecules by adjusting the potential offset between the two dots, universal two-qubit gates can be implemented without requiring time-dependent control of the tunnel coupling between the dots. A Bell-state measurement scheme for qubit encoded in double-dot singlet and triplet states is also proposed for quantum molecules arranged in this way.