# Resonant Exchange Qubits

Encoding information using quantum bits—which can be maintained in a superposition of states—is at the heart of quantum computing. Superposition states offer the advantage of massive parallelism compared to conventional computing using digital bits---which can assume only one value at a time.

Unfortunately, qubits are fragile; they dissipate in the face of interactions with their environment. A new JQI semiconductor-based qubit design ably addresses this issue of qubit robustness. Unlike previous semiconductor qubit setups, the new device has no need of external, changing magnetic fields. This permits greater control over the qubit.

The enhanced mastery results in new reliability for processing quantum information in semiconductor qubits. Furthermore, the necessary control features---voltages applied to nanometer-scale electrodes---are directly compatible with existing transistor-based devices. The research was carried out by scientists at JQI, Harvard, the Niels Bohr Institute at the University of Copenhagen, and the University of California at Santa Barbara. The results are published in two papers---one theoretical, one experimental---in the journal *Physical Review Letters*.

This new approach expands upon efforts to use individual electron spins which point “up” or “down” to form a natural qubit (Read about "Qubit Design" in Gallery, above). Instead of using a single electron the researchers used three electrons, confined in a three adjacent quantum dots. Advances in fabricating arrays quantum dots have opened new possibilities for realizing robust qubits. In the last few years, scientists have demonstrated control of multiple electrons and their associated spin in such triple quantum dots (Read about "Triple Quantum Dots" in Gallery, above). Quantum dots now have many of the essential characteristics needed for quantum computing but decoherence and stability remains an outstanding issue.

Why is using three electrons better than using one? In the case of a single electron trapped in quantum dots, the qubit is made using the two possible orientations of an intrinsic angular momentum called spin. The spin is free to point “up (aligned)” or “down (anti-aligned)” with respect to a magnetic field. Here, flipping the state of the qubit required a large, rapidly oscillating magnetic field. Fast changes in magnetic fields, however, give rise to oscillating electric fields---this is exactly what happens in electric generators. This method presents a challenge, because such additional changing electric fields will fundamentally and dynamically modify the qubit system. It is therefore better to exert control over qubits solely with electric fields, eliminating the oscillating magnetic fields.

The researchers do exactly this. They find a way to use an electric field rather than a magnetic field to flip the qubit from 1 to 0 (or vice versa). While single electron spin transitions require a magnetic field (magnetic resonance-think, MRI technology), if one adds electrons to the system and constructs the energy levels based on combinations of three-spin orientations, the magnetic interaction is longer be necessary.

JQI scientist Jacob Taylor explains further why using three electrons is better than one: "Amazingly, when the three electrons are in constant, weak contact, their interaction hides their individual features from the outside world. This is, in essence, why the three-spin design protects quantum information so well. Furthermore, even though the information is protected, a well designed 'tickling' of the device at just the right frequency has a dramatic effect on the information, as demonstrated by the quantum gates shown in the experiment."

These joint few-electron states have been studied previously and are called singlet-triplet qubit (graphical explanation in Gallery). However, while the changing magnetic fields were removed in previous works, the proposed logic gates relied on varying the tunneling rate in multiple steps, a cumbersome process that is susceptible to additional noise on the control electrodes.

These two new papers in Physical Review Letters report improvements and simplifications in qubit construction and particularly in qubit manipulation. Instead of requiring sequential changes in the tunneling, qubit manipulation is carried out directly, allowing for easy, control of the qubit around two axes. The levels are separated in energy by microwave frequencies (GHz) and can be addressed with oscillating electric fields. Additionally, by adjusting the electrode voltages, the qubit levels are made to be far in energy from other states.

Once the researchers establish the electrode voltages, they proceed to the business of performing logic operations using resonant microwaves. What does this mean? The resonant exchange qubit, as the author’s refer to it, is embedded in a crystal awash with all pesky environmental that can endanger the integrity of qubits---phonons, other electrons, and interactions with the atoms that compose the crystal. And yet, as a home for qubits, this environment is actually pretty stable. How stable? The experiments showed a coherence time of 20 microseconds. This is about 10,000 times longer than their reported gate time, which is good news for scaling up both number of qubits and gates.

The JQI theory paper that accompanies the paper devoted to experimental results proposes a way of elaborating on the basic resonant-exchange qubit design to accommodate two-qubit-logic gates. Jake Taylor "Working from a few simple concepts, this new approach to using electron spins seems obvious in retrospect. I'm particularly gratified with the ease of implementation. With this new design, we are getting fast, good, cheap quantum bits in an approach that promises enormous economies of scale. But the two-qubit gate---crucial for the future success of this approach---is the big, open experimental challenge. I'm very curious to see which method ends up working the best in practice."

Charles Marcus, leader of the Niels Bohr Institute contingent for this experiment, agrees that the resonant exchange qubit represents a workable format for reliable qubits. He gives Taylor credit in this way: "The idea for the resonant exchange qubit came from Jake, developed, I imagine, sitting with Jim Medford in the lab, next to the cryostat. Jake is the only full-time theorist I know who can run a dilution refrigerator. I think his creativity is stimulated by the thumping sound of vacuum pumps. With the resonant exchange qubit, I see a big step forward for spin qubits. Challenges remain, but I can now see a clear forward path."

*Written by Phillip F. Schewe and Emily Edwards*

*Phys. Rev. Lett.*,

**111**, 050502 (2013)

*Phys. Rev. Lett.*,

**111**, 050501 (2013)