We propose an optimized set of quantum gates for a singlet-triplet qubit in a double quantum dot with two electrons utilizing the $S\text{\ensuremath{-}}{T}_{\ensuremath{-}}$ subspace. Qubit rotations are driven by the applied magnetic field and a field gradient provided by a micromagnet. We optimize the fidelity of this qubit as a function of the magnetic fields, taking advantage of ``sweet spots'' where the rotation frequencies are independent of the energy level detuning, providing protection against charge noise. We simulate gate operations and qubit rotations in the presence of quasistatic noise from charge and nuclear spins as well as leakage to nonqubit states. Our results show that, for silicon quantum dots, gate fidelities greater than
99 should be realizable, for rotations about two nearly orthogonal axes.
The individual confinement and two-axis qubit operations of two-electron spin qubits in a GaAs gate-defined sextuple quantum dot array with an integrated micromagnet are reported in this study. As a first step toward multiple-qubit operations, we demonstrate coherent manipulations of three singlet-triplet qubits showing underdamped Larmor and Ramsey oscillations in all double dot sites. An accurate measurement of site-dependent field gradients as well as root-mean-squared electric and magnetic noise is provided, which is followed by a discussion of the adequacy of a simple rectangular micromagnet for practical use in multiple quantum dot arrays. Current limitations and possible strategies for achieving simultaneous multi-qubit operations in extended linear arrays are also presented.
We propose an optimal set of quantum gates for a singlet-triplet qubit in a double quantum dot with two electrons utilizing the S-T− subspace. Qubit rotations are driven by the applied magnetic field and an orthogonal field gradient provided by a micromagnet. We optimize the fidelity of this qubit as a function of magnetic fields, taking advantage of “sweet spots” where the rotation frequencies are independent of the energy level detuning, providing protection against charge noise. We simulate gate operations and qubit rotations in the presence of quasistatic noise from charge and nuclear spins as well as leakage to nonqubit states, and predict that in silicon quantum dots gate fidelities greater than 99% can be achieved for two nearly-orthogonal rotation axes.
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.
Singlet-triplet qubits offer an attractive encoding for semiconductor quantum computing, combining ancilla-free readout, reduced sensitivity to common-mode noise, and baseband voltage control. However, the Zeeman energy difference
ΔEZ is typically fixed by local magnetic field gradients or
g-factor inhomogeneities, leaving the exchange interaction
J as the only dynamically tunable parameter. This always-on
ΔEZ precludes orthogonal control of the qubit's rotation axes and introduces unwanted state rotations during idling. Here we demonstrate all-electrical orthogonal control of a degenerate singlet-triplet (DST) qubit formed by two hole spins in a germanium double quantum dot. Exploiting the electrically tunable anisotropic
g-factors of the two spins, we identify a regime where both
ΔEZ and
J vanish, making the
S and
T0 states degenerate at the idle point. By applying only baseband voltage pulses, we independently control both
J and
ΔEZ, enabling fully orthogonal
Z- and
X-axis rotations. Randomized benchmarking yields an average physical single-qubit gate fidelity of 99.53\% for a gate duration of approximately 100 ns. Finally, we electrically tune the degenerate point across a wide range of magnetic field orientations, enabling operation in a regime of enhanced coherence time and offering a route towards multi-qubit scaling under a shared global magnetic field.
Abstract Quantum dots in silicon are a promising architecture for semiconductor quantum computing due to a high degree of electric control and compatibility with existing silicon fabrication processes. Although electron charge and spin are prominent methods for encoding the qubit state, valley states in silicon can also store quantum information via valley-orbit coupling with protection against charge noise. By observing coherent oscillations between valley states in a Si/SiGe double quantum dot device tuned to the two-electron charge configuration, we measure the valley energy splitting in both quantum dots individually. We further demonstrate two-axis quantum control of the valley qubit using gated pulse sequences with X and Z rotations occurring within a fast operation time of 300 ps. This control is used to completely map out the surface of the Bloch sphere in a single phase-space plot that is subsequently used for state and process tomography.