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Controlling Decoherence

Diagram by Wayne Witzel of CMTC shows qubit electron (center) surrounded and affected by random nuclear spins of atoms in the material’s lattice.

To scientists seeking a basis for future quantum information processing, there is no more urgent or vexing problem than delaying the onset of “decoherence” – the collapse of delicate, but essential, quantum states.

The ability to store and manipulate information of any kind requires a dependable medium with which to record data and perform operations. In a conventional computer, where data exist as binary digits (“bits”) with only two values (0 or 1),that function is performed by electrical charges in memory chips, magnetic spots on disks or tiny holes on CDs. In quantum computing, however, the key element is not a bit, but a more complex and exotic entity: a quantum bit, or “qubit.”

Thanks to the nature of quantum mechanics, quantum objects can be in a combination, or “superposition,” of states at the same time. So a qubit can be a 0, a 1, or a combination of both simultaneously.

Qubits can take many physical forms, such as trapped ions, neutral atoms, photons, superconducting devices and more. In each case, the great advantage is that qubits can be used to perform certain kinds of operations exponentially faster than conventional digital computers.

The disadvantage, at least at present, is that the qubit’s superposition of states is extremely fragile. Once the qubit is prepared in the desired condition, any contact with the environment can destroy that condition -- a process called “decoherence.”

If simple physical contact were the only threat to the qubit’s condition, however, the problem would be much simpler. But it is in the nature of quantum systems that objects interfere with, and are affected by, the state of other objects whether they are in immediate contact or not. That is, the qubit’s state is “coupled” to its environment and hence vulnerable.

For example, if a qubit is embodied in the “spin” direction of an electron -- which is in a “coherent” superposiiton of both “up” and “down” -- that condition can be degraded by the influence of the spins of atoms that are quite far away, forcing the electron to collapse into decoherence.

Worse yet, that process can happen very rapidly, sometimes within nanoseconds.

So in addition to shielding their qubits in high vacuums, electromagnetic traps and ultra-cold temperatures, scientists are also in search of ways to sustain the qubit’s coherent state at least long enough to use it for information processing.

Taking the Pulse

One promising solution involves exposing the qubit to pulses of electromagnetic radiation that are fine-tuned to contain exactly the right amount of energy required to “flip” the spin of the qubit electron by 180 degrees. Repeated application of these pulses serves to attenuate the effect of the surrounding quantum objects, thus “decoupling” the qubit and protecting it from decoherence. But how many pulses -- applied in what sequence -- will produce suitably long-lasting protection for different qubit types?

At the APS March meeting, Das Sarma and members of his group at UMD’s Condensed Matter Theory Center (CMTC) presented reports on various aspects of that question. In one, Wayne Witzel showed an analysis of comparative effects of different sequences on spin decoherence in “noisy” surroundings, where spin can be affected by millions of nuclei.

Another presentation, based on work by Witzel, Benjamin Lee and Das Sarma, described how one sequence in particular (Uhrig dynamical decoupling, or UDD) -- which could produce optimal results in gallium arsenide quantum dots -- is in fact model-independent and applicable to a wide variety of conditions.

Lukasz Cywinski, Roman Lutchyn and Cody Nave, in multiple presentations, showed that coherence time in superconducting qubits could be substantially extended by carefully designed pulse sequences, and described one sequence that is optimal for “single-fluctuator” problems in superconducting qubits.

Other presentations by JQI researchers concerned a popular alternative qubit candidate: the superconducting quantum interference device, or SQUID. A SQUID consists of one or more Josephson junctions (superconducting elements separated by a very thin insulating layer) arranged in a loop. What transpires across the barrier is affected by exquisitely small changes in quantum conditions. In commercial use, SQUIDs are used to detect thefaintest magnetic fields. In the lab, they can be configured in various ways to examine quantum phenomena -- and perhaps to form the basis for practical qubits.

The work reported at the March Meeting represented a remarkable convergence of institutions and research areas, Lead author and presenter Tauno Palomaki is a Maryland graduate student working with theorists (including NIST JQI Fellow Eite Tiesinga) and with experimentalists (including UMD JQI Fellows Bob Anderson, Chris Lobb and Fred Wellstood) to examine how a two -junction or direct-current SQUID behaves when set up to serve as a qubit. Different quantum states can be prepared by cooling the SQUID to 25 milliKelvin (which brings the SQUID to the lowest-energy or ground state) and then exposing the device to microwave bursts at various frequencies.

Different frequencies cause the SQUID to make transitions from the ground state to different excited states. While all of the quantum states lead to zero voltage across the SQUID, different quantum states can be distinguished by measuring how large a current pulse is needed to cause the state to make a transition to a classical state with non-zero voltage: The lower the energy of the state, the larger the current that is needed.

To determine exactly what it takes to nudge the device out of an initial quantum state and into the voltage-producing phase, the team experimented with various levels of current and mapped out the critical tipping point at which the voltage forms after they exposed the SQUID to microwave bursts at various frequencies. Doing this allowed the researchers to precisely determine the energies of the quantum states, as well as the deleterious effects of coupling between the SQUID and nearby defects. In addition, the measurements agreed very well with a specific model for the defects, provided detailed information about the quantum mechanics of the defects, allowing the team to identify the nature of the defects and how they coupled to the SQUID.

In another presentation, Kaushik Mitra, a graduate student supervised by Lobb and Carl Williams of NIST, described a method of reducing decoherence in direct-current SQUID phase qubits.

As in the case of electron spins immersed in a “bath” of decoherence-causing effects from surrounding atoms, the sensitive SQUID is subject to noise and other perturbing effects from the environment. As a result, the time intervals between preparation of a qubit and the onset of decoherence are very short.

Mitra, Lobb and Carlos Sa de Melo showed that attaching a simple resonating circuit to the SQUID caused substantial variation in its behavior depending on the difference between the frequency of the circuit and the oscillation frequency of the qubit.

When the system was adjusted so that the two frequencies were the same, the time before decoherence hit a minimum.

But when the system was tuned such that the circuit’s frequency was about twice that of the qubit, the time to decoherence increased a hundredfold or more.

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