Limitations on the maximal level of entanglement of two singlet-triplet qubits in GaAs quantum dots

Abstract

We analyze in detail a procedure of entangling of two singlet-triplet ($S$-$T_0$) qubits operated in a regime when energy associated with the magnetic field gradient, $\Delta B_z$, is an order of magnitude smaller than the exchange energy, $J$, between singlet and triplet states [Shulman M. et al., Science 336, 202 (2012)]. We have studied theoretically a single $S$-$T_0$ qubit in free induction decay and spin echo experiments. We have obtained analytical expressions for time dependence of components of its Bloch vector for quasistatical fluctuations of $\Delta B_z$ and quasistatical or dynamical $1/f^{\beta }$-type fluctuations of $J$. We have then considered the impact of fluctuations of these parameters on the efficiency of the entangling procedure which uses an Ising-type coupling between two $S$-$T_0$ qubits. Particularly, we have obtained an analytical expression for evolution of two qubits affected by $1/f^{\beta }$-type fluctuations of $J$. This expression indicates the maximal level of entanglement that can be generated by performing the entangling procedure. Our results deliver also an evidence that in the above-mentioned experiment, the $S$-$T_0$ qubits were affected by uncorrelated $1/f^{\beta }$ charge noises.

13 pages + appendices

References in corpus (36)

• Driven coherent oscillations of a single electron spin in a quantum dot
• Coherent control of a single electron spin with electric fields
• An addressable quantum dot qubit with fault-tolerant control fidelity
• Semiconductor Spin Qubits
• Electrically driven single electron spin resonance in a slanting Zeeman field
• Demonstration of Entanglement of Electrostatically Coupled Singlet-Triplet Qubits
• How to Enhance Dephasing Time in Superconducting Qubits
• Universal control of a six-qubit quantum processor in silicon
• Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization
• Semiconductor Qubits In Practice
• Electrometry Using Coherent Exchange Oscillations in a Singlet-Triplet-Qubit
• Theory of electron spin decoherence by interacting nuclear spins in a quantum dot
• Enhancing the Coherence of a Spin Qubit by Operating it as a Feedback Loop That Controls its Nuclear Spin Bath
• Singlet-triplet decoherence due to nuclear spins in a double quantum dot
• Hyperfine-mediated gate-driven electron spin resonance
• Quantum many-body theory for electron spin decoherence in nanoscale nuclear spin baths
• Dynamic Nuclear Polarization with Single Electron Spins
• Nuclear Spins in Nanostructures
• Universal logic with encoded spin qubits in silicon
• Charge-noise spectroscopy of Si/SiGe quantum dots via dynamically-decoupled exchange oscillations
• Introduction to decoherence theory
• Measurement of Temporal Correlations of the Overhauser Field in a Double Quantum Dot
• Noise-resistant control for a spin qubit array
• Conditional operation of a spin qubit
• Reducing charge noise in quantum dots by using thin silicon quantum wells
• Electron spin as a spectrometer of nuclear spin noise and other fluctuations
• Noise-correlation spectrum for a pair of spin qubits in silicon
• Exchange-based two-qubit gate for singlet-triplet qubits
• Wavefunction considerations for the central spin decoherence problem in a nuclear spin bath
• Crosstalk error correction through dynamical decoupling of single-qubit gates in capacitively coupled singlet-triplet semiconductor spin qubits
• Dynamics of entanglement of two electron spins interacting with nuclear spin baths in quantum dots
• Decoherence of coupled electron spins via nuclear spin dynamics in quantum dots
• Simulation of 1/f charge noise affecting a quantum dot in a Si/SiGe structure
• Decoherence of two coupled singlet-triplet spin qubits
• Probing two-qubit capacitive interactions beyond bilinear regime using dual Hamiltonian parameter estimations
• Charge noise suppression in capacitively coupled singlet-triplet spin qubits under magnetic field