## Spin qubits

In a semiconductor quantum dot, electrons are confined into a “box” small enough that they stop behaving like electrons the bulk of a solid, and start behaving like electrons in individual atoms. In particular, the electrons occupy discrete energy levels, which, if the temperature is small compared to the level-spacing, allows the electrons to be forced into the ground state of the dot. The spin of an electron stored in a quantum dot couples weakly to its environment, making it a promising candidate for a quantum bit ( “qubit”) — a device for storing and manipulating information in quantum computers.

Current research in our group focuses on the “singlet-triplet” qubit. In this device two quantum dots, each with only one electron inside, are constructed side-by-side and tuned so that they are tunnel coupled. Information is stored in the relative spin of the two electrons, further reducing coupling of the qubit to its environment. Of the four possible relative spin states of the electrons (S, T0, T+, and T-), information is stored in the S and T0 states (the so-called ‘logical subspace’). This choice is motivated by two advantages. First, the two qubit states remain unaffected by changes in magnetic field (they are both m=0), which further decouples them from the environment.

Second, due to the Pauli Exclusion principle, while in the singlet state one electron has an orbital wavefunction hybridized between the two dots, in the triplet states both electrons are confined to separate dots. Therefore by tuning the relative chemical potentials of the two dots, we adjust the charge distribution of the singlet state and the relative energy of the singlet and triplet states. This tunable energy splitting is the key to the qubit's straightforward functioning: At very large splittings, we can reliably load singlet states through exchange with the leads. Furthermore, at this splitting, the singlet state is fully localized in one of the quantum dots, while the triplet state remains blockaded. This so called “spin to charge conversion” allows the spin state of the electron to be detected by sensing the electron occupancy of the quantum dots, which is significantly easier than measuring the spin directly and enables singleshot measurement of the qubit with 98% fidelity.. At moderate energy splittings, we can perform single qubit operations evolving around the S-T0 axis of the Bloch sphere. In a two-qubit device, at these same splittings, the difference in charge distribution between states creates a dipole-like capacitve coupling, enabling an entangling gate. By setting the charge distributions equal, we turn off the interaction, and the magnetic field gradient (discussed below) dominates, providing a second control axis of the qubit state, as is required for universal control.

As with any qubit, as the S-T0 qubit interacts with its environment, information above the relative phase between the two qubit states is lost. Once a qubit is “dephased” it behaves like a classical bit, and no longer offers the same power that a quantum bit provides. Qubits must therefore interact weakly with their environments and must allow for many manipulations before the qubit is dephased. The S-T0 qubit is a particularly attractive system for solid state quantum computing because it allows for fast electrical control of the exchange interaction and benefits from the long dephasing times of traditional spin qubits.

The hyperfine interaction between the electrons and the GaAs host nuclei lead to spin dephasing times T2* ~10ns, inhibiting the performance of the qubit. More precisely, since the electrons sit in separate quantum dots they experience slightly different nuclear fields, which evolve in time. Differences in magnetic field drive transitions between S and T0 at an unknown rate, leaving the qubit in an unknown state. Substantial progress has been made in order to mitigate this effect. Using the qubit to pump spin into the nuclei, the nuclear magnetic field is stabilized, and the nuclear bath is narrowed. Using this techniqueT2* is improved to ~200ns. Additionally, using dynamic decoupling schemes that take advantage of the slow evolution of the qubit-environment interaction (hyperfine interaction), we observe T2 ~200 µs, which allows for more than 1000 coherent quantum operations.

Using nanosecond electrical control of the confining potential in the quantum dots, we can control the exchange interaction between the two electrons, which drives transitions between the up-down and down-up states. Using our nuclear control techniques and control over the exchange interaction we demonstrate universal, coherent quantum control of this qubit, allowing for preparation of an arbitrary single qubit state. We have also demonstrated entanglement between two qubits using their capacitive coupling. This is done without the need for RF magnetic fields, which can be difficult to deliver to a small sample at 40mK.

Recently we have focused on working in the rotating frame set by the magnetic field gradient. Working in this regime offers several advantages. First, at large values of the magnetic field gradient, the resonant frequency has a weak dependence on the exchange energy, which is main source of high frequency noise in the system. Second, the use of high-fidelity composite pulses and dynamical decoupling sequences promises to become attainable in the rotating frame, which is crucial to improving gate fidelities due to the strongly non-Markovian noise baths that the qubit experiences. In the rotating frame, we have performed a two-qubit entangling gate with fidelity 90%.

Another approach we are investigating is to couple two qubits with a high-impedance electromagnetic resonator. This method would allow us to increase the distance between qubits while simultaneously increasing their coupling. Separating the qubits is crucial to making the system scalable, because it decreases the DC coupling between them, which has made tuning challenging, and allows for 2D arrays of qubits necessary for surface codes.

Check out some of our research below!

A cartoon of the energy diagram for the singlet-triplet qubit. At the far left, the quantum dots have the same chemical potential, so there is no exchange energy, so the magnetic field gradient between the dots dominates the splitting. As the detuning (epsilon) between the dots increases, the exchange energy increases, causing the drive to rotate to towards the z-axis.

We require nanosecond control over the environment of a spin qubit in order to manipulate its state. Here is a sample on a board design to deliver both low frequency and high frequency voltages to the qubit