Demonstration of Entanglement of Electrostatically Coupled Singlet-Triplet Qubits

Abstract

Quantum computers have the potential to solve certain interesting problems significantly faster than classical computers. To exploit the power of a quantum computation it is necessary to perform interqubit operations and generate entangled states. Spin qubits are a promising candidate for implementing a quantum processor due to their potential for scalability and miniaturization. However, their weak interactions with the environment, which leads to their long coherence times, makes inter-qubit operations challenging. We perform a controlled two-qubit operation between singlet-triplet qubits using a dynamically decoupled sequence that maintains the two-qubit coupling while decoupling each qubit from its fluctuating environment. Using state tomography we measure the full density matrix of the system and determine the concurrence and the fidelity of the generated state, providing proof of entanglement.Singlet-triplet (S-T 0 ) qubits, a particular realization of spin qubits [1][2][3][4][5][6][7], store quantum information in the joint spin state of two electrons [8][9][10]. The basis states for the S-T 0 qubit can be constructed from the eigenstates of a single electron spin, | ↑〉 and | ↓〉. We choose |S〉 = The qubit can then be described as a two level system with a representation on a Bloch sphere shown in Fig. 1a Universal quantum control is achieved using two physically distinct operations that drive rotations around the x and z-axes of the Bloch sphere [11]. Rotations around the z-axis of the Bloch sphere are driven by the exchange splitting, J , between |S〉 and |T 0 〉, and rotations around the x-axis are driven by a magnetic field gradient, ∆B z between the electrons.We implement the S-T 0 qubit by confining two electrons to a double quantum dot (QD) in a two dimensional electron gas (2DEG) located 91nm below the surface of a GaAs-AlGaAs heterostructure. We deposit local top gates using standard electron beam lithography techniques in order to locally deplete the 2DEG and form the QDs. We operate between the states (0,2) and (1,1) where (n L ,n R ) describes the state with n L (n R ) electrons in the left (right) QD. The |S〉 and |T 0 〉 states, the logical subspace for the qubit, are isolated by applying an external magnetic field of B =700mT in the plane of the device such that the Zeeman splitting makes T + = | ↑↑〉, and T − = | ↓↓〉 energetically inaccessible. The exchange splitting, J , is a function of the difference in energy, , between the levels of the left and right QDs. Pulsed DC electric fields rapidly change , allowing us to switch J on, which drives rotations around the z-axis. When J is off the qubit precesses around the x-axis due to a fixed ∆B z , which is stabilized to ∆B z/2π =30MHz by operating the qubit as a feedback loop between interations of the experiment [12]. Dephasing of the qubit rotations reflects fluctuations in the magnitude of the two control axes, J and ∆B , caused by electrical noise and variation in the magnetic field gradient, respectively. The qubit is rapidly (<50ns) i...

Consequences of Spin-Orbit Coupling at the Single Hole Level: Spin-Flip Tunneling and the Anisotropic g Factor

“…Such an interface is a central element in quantum sensors and quantum repeaters [6,7], but could also be used to simplify the layout of multi-qubit gated devices [8]. An intermediate step in the transfer of the photon polarization state onto the state of the spin involves generation of an electron-hole pair.…”

Maximizing the purity of a qubit evolving in an anisotropic environment

“…[49][50][51] Such electrical control has recently been demonstrated for hole spins in III-V nanowire quantum dots, 52 and coherence times have now been measured for hole spins in Ge-Si core-shell nanowire quantum dots. 53 The very recent achievement of the few-hole regime in lateral gated double-dot devices, 54 suggests that previous highly successful measurements performed for electron spins [55][56][57][58][59][60] can now be performed for hole spins, which show promise for much longer coherence times. 33,35 In the rest of this paper, we introduce a general method that can be used to calculate and enhance the purity of a qubit interacting with an anisotropic environment.…”

Electron spin-flip correlations due to nuclear dynamics in driven GaAs double dots

“…The singlet (S) and S z = 0 triplet (T 0 ) states of two electrons in a double quantum dot has proven to be a promising candidate for quantum information processing [2,7,20]. The wave functions of the electrons are typi- * Electronic address: halperin@physics.harvard.edu cally spread over ∼ 100 nm and the hyperfine interaction between the electrons and their nuclear environment may include several million nuclei.…”