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Quantum Computing

Novel Entanglement States

Simultaneous entanglement of thousands of atoms

The Rey group has discovered that when reactive fermions are at "warm" micro-Kelvin temperatures, entanglement evolves naturally. When temperatures are low enough for fermions to collide and react in pairs, atoms or molecules that don't get knocked out of the experiment will be left entangled because they lose their individual identities as a result of being unable to collide. Fermions that behave this way include strontium and ytterbium, which are used in atomic clocks, and molecules such as potassium-rubidium, which are used in JILA's cold-molecule experiments.

Simultaneous entanglement evolves with atoms or molecules that can exist in one of two possible spin states. As they collide, each pair measures whether the work well together. If they do, they combine and fly out of the experiment. Soon, all the pairs that can react have done so and left the cold gas. The only ones left are the atoms or molecules that don't work well enough together to combine.

The pairs of atoms or molecules that can't combine have entered a quantum superpostion, a state in which a particle holds two different properties, such as two different spin states, at the same time. Such a steady state is very useful for measuring the passage of time in an atomic clock. 

Entanglement of mechanical motion with electrical voltage

The Konrad Lehnert group recently entangled the quantum motion of a cold (15–20 mK) vibrating drum with the quantum state of a moving electrical pulse. The motion of the cold drum was entangled with the voltage of an electrical signal as it moved away from the drum toward an amplifier. 

The group also figured out how to store half of the novel entangled state in the tiny drum. The drum then generated another electrical pulse that was entangled with the first pulse. The correlation observed between the drum motion and the signal voltage  could not be described using the mathematics of ordinary, everyday physics. Explaining entanglement requires the peculiar mathematics of quantum mechanics.

This novel entanglement scheme may be a key ingredient in the design of future quantum processors and precision instruments used to detect tiny forces currently too small to sense. It may also be a step towards testing the limits of quantum theory. 

Multidimensional quantum CT scans

The Lehnert group can create multidimensional CT scans of the quantum states of two entangled microwave fields. This development is rooted in the invention of a virtually noiseless amplifier in 2008  by researchers from JILA and NIST. The low-noise amplifier is a Josephson parametric amplifier, or JPA. In addition to having the lowest possible noise in an amplifier of this type, it also has the ability to squeeze most of the quantum fluctuations (wiggles) out of one of the two directions of a coordinate system. This capability may make it possible to use JPAs for probing the electronic states of quantum bits (qubits) of information in a quantum computer.

A major research project is underway to further this technology. The group used the amplifier to make what was essentially a one-dimensional CT scan of a hidden two-dimensional microwave field. The researchers made 35 measurements at different angles of the quantum state as it was wiggling around. Multiple precision measurements of the same quantum state yielded a full quantum picture of this microwave field—outside of a cavity.

Then the group worked to create quantum entanglement of different states of a microwave field. Quantum entanglement is a “spooky” shared quantum state called a superposition that extends across space and time. Entanglement is an essential ingredient for high-speed quantum computing, but challenging to create and maintain over time.

In 2012, the Lehnert group observed the creation of two separate, but entangled, microwave fields wiggling around inside different thin pipes. The pipes were mounted parallel to one another and 5-in apart in a laboratory apparatus. The outputs of the two pipes became entangled after their inputs were physically linked together at two separate locations in the apparatus.

Each input was a combination of a microwave field squeezed in one direction and quantum mechanical vacuum noise. A quantum vacuum is different from an ordinary, classical vacuum in that quantum particles can appear and disappear spontaneously, creating all kinds of noise in precision quantum measurements. To reduce this noise, the researchers routed part of each input into the opposite pipe.

This input mixing created identical superpositions inside each pipe of the squeezed states of the two original microwave fields, each coupled with quantum mechanical vacuum noise. At this point, the only difference between the two outputs was a 90° phase difference.

Finally, the group obtained two-dimensional CT scans of the four-dimensional quantum states spread across the two pipes. The scan was a composite picture of identical superpositions of the two-dimensional microwave fields in separate locations.

Lehnert says his group’s new method for creating entanglement across two locations greatly simplifies the process for creating and communicating entanglement in a quantum information system. For instance, it makes it possible to make a low-noise, ultraprecise measurement of the output of both pipes using only one of the two output JPAs. Because the outputs are entangled, a single measurement provides all available information about the quantum states of both pipes.

Such a low-noise measurement would not be possible if both JPAs were used in the measurement because of the constraints imposed by the Heisenberg Uncertainty Principle governing quantum systems. Measuring both outputs at the same time would add back the missing quantum noise to the system.

The Lehnert group has dubbed its new apparatus The Entanglement Factory. The group expects to use this factory for future research on quantum information devices.

Quantum Synchronization & the Classical World

Since 2008, the Murray Holland group has been studying a fascinating phenomenon known as quantum synchronization. In quantum synchronization, collections of atoms oscillating at random between their excited and ground states can become synchronized. Once synchronized, all the atoms are either in their excited or ground states at the same time. This synchronization depends on there being some form of communication, such as photons of light, between the atoms.

In 2009, the Holland group’s understanding of quantum synchronization led to a proposal for an innovative photonics quantum device to produce long-lasting phase-coherent light—like a laser. The heart of such a device would be a linear chain of neutral atoms inside an optical lattice (i.e., crystal of light). A single “lasing” photon inside the cavity would “glue” the chains of atoms together and lock them in phase as they oscillate between their ground and excited states. As a result, the atoms evolve into a coherent collective superposition of their ground and excited states. The collective superposition causes each atom to oscillate like a spring, but because all the atoms are glued together by the lasing photon, entire chains of atoms extend and contract in unison. This collective “super spring” would lose energy by emitting coherent lasing photons, which would immediately exit the laser cavity. The collective action of the spring results in the emission of far more intense coherent radiation than would occur with independent atoms. This collective emission is called superradiance.

In 2012, the Thompson group verified the predictions of the Holland group when it built and characterized the world’s first superradiant laser  [made of a million rubidium atoms (87Rb)]. Soon afterward, the Holland group began a new project to investigate the connection between photonics quantum devices based on quantum synchronization and ordinary lasers.

Superradiance is similar to synchronizations that occur in the classical world, including (1) crickets suddenly loudly chirping at the same time in the same direction, (2) fireflies emitting bright bursts of light as their behavior gets synchronized, (3) metronomes on a piece of balsa wood that first swing randomly, then become synchronized, and (4) people who once walked in sync over London’s Millennium Bridge, a particularly flexible bridge, before the bridge was closed and fixed so it wouldn’t oscillate when crowds crossed over it.

Such classical synchronous couplings are under study by Juan Restrepo, assistant professor of applied mathematics at the University of Colorado. In 2012, Restrepo began a collaboration with the Holland group and the Rey theory group to investigate the connection between classical and quantum synchronization, which is currently described by semiclassical physics. The collaborators are exploring simple models to describe quantum synchronization as they look for the best way to analyze its connection to similar phenomena in the everyday world.

The collaboration to better understand synchronization in the quantum and classical worlds could pay big dividends. For instance, it could lead to a better understanding of how the brain and sophisticated electronic devices work. The coupling of neuron oscillations may play an important role in how we think and process information. And, quantum synchronization may explain why some quantum electronic devices don’t always exhibit exactly the same behaviors. It may also help in the engineering of entangled states immune to decoherence, something that would be useful for quantum information processing.

An Innovative Quantum Computer

Jun Ye and Ana Maria Rey are collaborating with Professor Peter Zoller at the Universität Innsbruck and scientists at Harvard University on developing a comprehensive theoretical framework for an optical-lattice quantum computer based on alkaline earth metals such as Sr. This choice dovetails with expertise already found in the Ye experimental group. During the development of the Sr-lattice optical atomic clock, for example, the group explored many aspects of neutral Sr atoms, including their cooling, electronic transitions, and behavior in an optical lattice. This deep understanding of lattice-based neutral Sr atoms is informing the collaborative theoretical studies. Thus far the "information-processing" collaboration has proposed solutions for the key problems of storing, addressing, and transporting qubits (information encoded on the nuclear spins of Sr atoms). It has also put forward the advantages of a computer design that would use (1) local processors (i.e., quantum registers) for maintaining coherence and (2) qubit-state-controlled quantum gates for managing communications between qubits.

Storage and transport

Rey, Ye, and their colleagues have figured out how a Sr-based quantum computer could store qubits and have come up with a plan for communicating with individual atoms. They have also worked out a scheme for selecting a single atom, moving it to another location in an optical lattice to interact with another quit, and then moving it back, all under coherent control. These solutions required two specially engineered optical lattices that specifically address the interactions of the Sr atoms with the trapping laser light.

The computer’s optical lattices would be created from two separate wavelengths of red light, both of which are long lived. One wavelength (689.2 nm) has no net effect on Sr atoms in their ground state, while the other (627 nm) has no net effect on Sr atoms in their electronically excited, but metastable, state. The 689.2 nm lattice would be the qubit "transport" lattice, and the 627 nm lattice would be the qubit "storage" lattice. The storage lattice would hold the qubits in their ground state. When a specific qubit (i.e., atom) needed to be transported, it could be excited with laser light into its metastable state and loaded into the 689.2 nm transport lattice, where its motion could be precisely controlled (again with laser light).

The system works because the electronic structure of Sr atoms allows the atoms to store and hide stable, coherent information. Because Sr atoms have two valence electrons, both their ground and metastable states are minimally affected by external magnetic fields. This insensitivity means that the robust nuclear spins of Sr atoms can form long-lasting qubits. Equally importantly, a third electronically excited state has a high sensitivity to magnetic fields. That means magnetic fields could be used to select a specific atom from the transport lattice for operations!

This is where the precision Sr atomic clock laser comes into the picture. The clock laser makes it possible to precisely detect, measure, or manipulate atoms in both the storage and transport lattices. The beauty of this laser is that it can accurately address one or more individual frequencies encoded on the qubits in the storage lattice, and, with the help of the third electronic state, transfer only those particular qubits into the transport lattice.

Coherence

Rey’s quantum computer theory offers a novel solution for maintaining coherence in an information-processing device. Rather than constantly monitoring and attempting to keep all the atoms in the computer resonantly coherent, her formulation would build the computer out of local processors, or quantum registers. In this formulation, each register would be a single Sr atom. However, the quantum register would consist of both the atom’s electronic transitions, which would function as communications qubits, and its nuclear spin states, which would store information. As one or more quantum registers performed the same calculation, they would need to remain coherent. However, the entire computer would not need to be in sync with them. The only circumstance in which every Sr atom (quantum register) would have to be in sync is one in which every quantum register were required for a particularly complex operation. Whether one, two, or many quantum registers were working together on a computation, the communications qubits would be responsible for maintaining coherence. This task is relatively simple within one atom. However, communication between two or more atoms requires a way for just the right atoms to become entangled. In other words, the computer requires quantum phase gates.

Entanglement

The new quantum computer requires entangled states for both communication and computation. Entanglement occurs when the quantum states of two or more atoms become linked together. A key challenge for Rey and Ye is the design of robust methods for not only generating entanglement between two specific atoms, but also developing methods to maintain entangled states for as long as they are required. Rey has already proposed a design that protects entangled states from local decoherence processes. She has used it for generating robust optical coherent states in optical lattices and trapped ions.

Computations

The movement of the storage and transport lattice relative to one another allows the computer to perform calculations with information retrieved by the clock laser from different parts of the storage lattice. Calculations are performed via quantum-gate operations, in which two atoms interact by becoming entangled in a single lattice site. Once the calculation is complete, the clock laser dumps the qubits back into the storage lattice.

Quantum phase gates

Quantum phase gates consist of double quantum wells, with Sr atoms on either side. Only atoms in the ground state with opposite spins can tunnel to the other side of the well and get entangled with the atom on the other side. This entanglement is only through the electronic degrees of freedom. The process doesn’t disturb the nuclear-spin linked qubits because only communications qubits (i.e., the electronic transitions) are sharing information. Thus communication between two atoms in a single lattice site does not result in the loss of any information; nor would it disturb the coherence of the computer in any way. Equally importantly, atoms not needed for a particular calculation would be unable to pass through the quantum gate.

A two-bit gate, combined with single qubit rotations, is sufficient to perform a universal quantum computation. Single qubit rotations would be controlled by precision lasers capable of detecting and changing the state of any ground-state atom. The lasers would also manage communication between atoms by rotating the nuclear spin of a ground-state atom into a spin that allows it to tunnel through a quantum gate. The ability to control communication, together with the ability to measure and control the states of individual Sr atoms, are essential ingredients in the new quantum computer theory.

Recently, Rey and her collaborators did a theoretical study of using cold polar molecules to implement a controlled-phase gate. The molecules could be in either 1D or 2D optical lattices, or they could become ordered in a crystalline structure because of long-range dipole interactions (a phenomenon known as a Wigner crystal). The two-dimensional systems appeared to offer better fidelity. Fidelity is also enhanced by the induction of a dipole moment in the ground and excited states of the molecules. So long as major sources of decoherence (i.e., nonsymmetric interactions and phonon dispersion in Wigner crystals) were adequately addressed, the system appears to be feasible for use in optical quantum-information processing.