# 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. 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, it allows us to read the state of our qubit using “spin blockade.” Spin Blockade is a process in which we attempt to bring the two electrons into the same dot: the singlet, which is an antisymmetric wave function, can have both electrons occupy the orbital ground state, while the triplet, which is a symmetric wave function, would need to have one electron in the first orbital excited state, and therefore remains with one electron in each dot. 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.

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. This is done without the need for RF magnetic fields, which can be difficult to deliver to a small sample at 40mK.

Ongoing research focuses on multi-qubit experiments with the S-T0 qubit, in particular, the demonstration of a high fidelity entangled state, in which two qubits are correlated more than a classical mixture of bits can be. All quantum computing schemes take advantage of entangled states, and preparation of entangled states will allow for exploration of exciting topics is quantum information and nuclear dynamics.