What is quantum coherence?

We say a message is incoherent when we can’t make it out, or when it doesn’t make sense. A scribbled note, a drunken argument or a conversation taking place five tables down in a crowded cafe might all be incoherent. In general, ​“coherent” means the opposite — consistent, connected, clear.

In science, the word coherence takes on more specific, mathematical definitions, but they all get at a similar concept: Something is coherent if it can be understood, if it forms a unified whole and if those first two qualities persist.

Scientists originally developed the concept of coherence to understand and describe the wave-like behavior of light. Since then, the concept has been generalized to other systems involving waves, such as acoustic, electronic and quantum mechanical systems. 

“Coherence is a measure of how well certain systems will maintain their relationships with each other and how well we are able to predict the evolution of those systems,” said Martin Holt, a scientist at the U.S. Department of Energy’s (DOE) Argonne National Laboratory and a member of Q-NEXT, a DOE National Quantum Information Science Research Center led by Argonne. ​“Understanding and controlling coherence in quantum technologies is crucial because the relationships involved need to be very long-lived and well-understood.”

Like researchers around the globe, Q-NEXT scientists are studying and improving coherence in quantum systems for technologies such as quantum sensing and quantum computing. Once realized, these technologies will leverage coherence to perform complex calculations, take high-resolution measurements and transmit unhackable messages, potentially revolutionizing our approach to communication, cybersecurity, simulation, optimization and more.

“Understanding and controlling coherence in quantum technologies is crucial because the relationships involved need to be very long-lived and well-understood.” — Martin Holt, Argonne scientist and member of Q-NEXT 

Coherent waves

Imagine a wave, rising and falling periodically at a certain speed (frequency) and with a certain height or intensity (amplitude). Now, throw in a second wave. If the two waves are offset from each other — if they are not rising and falling together — they are said to be out of phase. It’s this phase difference that determines whether the waves will interfere to have an amplifying or canceling effect on each other, or something in between.

We see this in everyday life. Constructive interference occurs when two singers amplify each other’s voices, or when you double bounce a friend on the trampoline. Destructive interference of sound waves is the principle behind noise-cancelling headphones.

Two waves are coherent when there is a meaningful relationship between their phases or when their interference creates a well-understood pattern. In essence, coherence is a measure of how in sync the waves are with each other. There are degrees of coherence; waves can be more or less coherent with each other.

Lasers, for example, are designed to emit highly coherent light. They contain atoms that are excited with energy and, upon their decay, emit photons (particles of light) with the same frequency and phase as each other. These photons bounce off mirrors within the laser, which serve to amplify the light traveling only in a certain direction and with a certain frequency. This special interference — or coherence — between photons results in a highly focused and uniform beam of light. Sound waves can be similarly coherent, and scientists have even created sound lasers, or sasers.

Quantum coherence

In quantum mechanics, objects can be represented as either a combination of waves or particles. In principle, this applies to any object. But this way of looking at things works best when dealing with objects that are very small, like photons, other elementary particles and atoms.

Quantum objects can be described with a special type of identifier called a wavefunction. It’s sort of a wave on steroids, since it can contain an incredible amount of information within its mathematical nooks and crannies.

This is because wavefunctions are composites of waves themselves. Quantum coherence refers to the phase relationships between these waves — the ones that, together, describe the whole object. When these waves interfere in coherent ways, it gives rise to quantum superposition, a central feature of quantum mechanics that allows an object to exist in multiple states simultaneously.

Here’s where it gets uniquely quantum. The waves composing an object’s quantum wavefunction don’t correspond to physical values, like position or energy. Instead, they correspond to the likelihood of different possible ways that the state of the object could evolve — for example, the likelihood that its energy will change over time in a certain way, or the likelihood that it will spin a certain way in a certain location. Quantum coherence is an interference between these different possible future histories of the object. 

However, this interference can exist only until the system is observed or disturbed. At that point, the interference between the waves vanishes, and the superposition is lost. The object has apparently experienced only one of the possible histories.

What does it mean for possible future histories to interfere? And for the wavefunction to collapse into just one of those histories? Those are tough questions. Currently, we know more about how to use this feature of quantum mechanics than what it means for the nature of our reality.

Sensing at the quantum level

Coherence is fragile and hard to protect. Perfectly isolated quantum objects and systems can maintain coherence indefinitely, but it would be impossible to manipulate or investigate them.

As a quantum object encounters other objects or fields, it picks up random influences from each. Even the act of measuring the object necessarily introduces noise, rendering its original wavefunction difficult, if not impossible, to decipher. As a result, the information that was stored in the coherent system is lost in a process called decoherence.

But for some applications, decoherence can be an advantage.

“If you prepare an object in a certain superposition of states with a certain coherence, and you send it into an environment with unknown influences, then a change in the object’s phase relationship can provide meaningful information about the environment,” said Jennifer Dionne, a professor of materials science and radiology at Stanford University and deputy director of Q-NEXT.

Here, the quantum object itself is the sensor. Because its phase relationship is so sensitive, it responds to subtle influences from the environment in a big way. This sensitivity could enable extremely high-resolution detection and imaging. Quantum coherence allows scientists to start the sensor off in a well-understood state that will persist over time. This makes it easier to retroactively determine how that state changed and what those changes mean about the environment.

For example, Dionne’s lab is developing quantum sensors to detect force.

“We are studying how the colors of nanoparticles change when they encounter mechanical force within an organism,” Dionne said. ​“We’ve started to deploy these sensors in living organisms using worms as test subjects. As the worms’ digestive tracts apply force, quantum transitions within the nanoparticle cause it to change color, which we can read out during digestion.”

Atomic clocks and gravitational wave sensors also rely on quantum coherence for ultraprecision. Other examples of future sensing applications using quantum coherence include miniaturized magnetic resonance imaging (MRI) technologies, which could be used to scan single cells or molecules or significantly improve the resolution of whole-organism MRI scans.

Quantum coherence plays a role in biological systems, too. Scientists believe that birds use quantum coherence of proteins in their eyes to sense Earth’s magnetic field for navigation, like an internal GPS. Researchers are developing magnetic field sensors using the same principles to help humans navigate in situations where satellite-based GPS is impossible.

Wave hello to quantum computing

One coherent object can serve as a great sensor. Two or more quantum objects that are coherent with each other enable quantum computation.

The traditional, or classical, bit in a computer can exist in one of two states, 0 or 1. Thanks to quantum superposition, a quantum bit — or a qubit — can exist in a combination of the two states simultaneously. Coherence is responsible for maintaining the phase relationships, and therefore the superposition, between these states over time and space.

“In quantum computing, instead of doing operations such as addition or multiplication on classical bits, you’re performing operations on different components of the waves that make up the wavefunction,” Dionne said. ​“It’s important to maintain coherence long enough so that, as the computer performs operations, it isn’t accumulating error as the different parts of the wavefunction decohere.”

Coherence is also responsible for maintaining entanglement, a special case of superposition that is crucial for quantum computing. When quantum objects are entangled, they maintain a particular correlation between each other even if they are physically separated by large distances.

“As long as two entangled objects remain coherent with each other, you can perform an operation on one of them, and that will give you information about the other,” Dionne said.

Say you want to use a quantum computer to predict the success of a pizza party you plan to throw. First, you need to decide what factors would contribute to a successful party, such as the taste of the pizza and the number of guests. You might assign one qubit to represent the ratio of water to flour in your pizza dough, with 0 representing no water, 1 representing only water and the superposition between them representing all possible ratios. Another qubit could represent the number of people that show up, ranging from no one to everyone you invited. Perhaps a third qubit represents how likely you are to burn your food, and so on.

“You have all of these probabilities captured in clean, coherent states, and you let the system evolve over time,” Holt said. ​“If you repeat the simulation enough, you get the probability of how successful the party will be based on the factors you encoded in the wavefunctions of the entangled qubits. But the simulation keeps going only if the states are coherent.”

Because of the way information is embedded in the wavefunction, just a small number of qubits can represent very complicated, real-world problems with lots of dependencies, such as power grid optimization or finding the most energy-efficient way to distribute goods across the globe. The longer the system is coherent, the more complex the calculations can be.

Preserving quantum coherence

Holt’s work at Argonne focuses on the development of matter-based qubits, where a defect — a replaced atom or an atomic vacancy, for instance — is embedded in a material’s otherwise normal structure. Although scientists try to protect the defects from decoherence, small changes in temperature, pressure or magnetic fields can introduce noise.

Imagine you’re running at the gym, and music is playing over the speakers. You notice it’s difficult to run at your own pace rather than running to the beat of the music, and it’s ruining your flow.

“There are a couple of ways to prevent this,” Holt said. ​“You could wear earplugs so that you’re isolated from the external influence, or you could start running significantly faster or slower so that it’s easier to decouple your body’s rhythm from that of the music. Then, even if the music changes, you don’t care because you’re just that far off from it.”

To isolate qubits from noise, scientists keep quantum computers very cold — near absolute zero. They further decouple the qubits from their surroundings by designing and manipulating the states of the qubits to respond to frequencies of light or sound that their surroundings aren’t affected by.

This is difficult to achieve, and different types of qubits are easier to protect than others. So far, the longest-lived qubits are called trapped atoms, which have been shown to remain coherent for several minutes or more. However, these qubits are difficult to use for computing applications. A recent demonstration of long-lived coherence was made by Q-NEXT scientists at Argonne and the University of Chicago. The team showed that a certain semiconductor qubit — a type of qubit that is more promising for quantum computing — stayed coherent for over five seconds.

“Preventing the loss of information through decoherence is the hard part of quantum information science, and that’s why the field is called that,” Holt said. ​“It’s not just quantum science, it’s information processing using quantum coherence.” 

About Argonne’s Center for Nanoscale Materials

The Center for Nanoscale Materials is one of the five DOE Nanoscale Science Research Centers, premier national user facilities for interdisciplinary research at the nanoscale supported by the DOE Office of Science. Together the NSRCs comprise a suite of complementary facilities that provide researchers with state-of-the-art capabilities to fabricate, process, characterize and model nanoscale materials, and constitute the largest infrastructure investment of the National Nanotechnology Initiative. The NSRCs are located at DOE’s Argonne, Brookhaven, Lawrence Berkeley, Oak Ridge, Sandia and Los Alamos National Laboratories. For more information about the DOE NSRCs, please visit https://​sci​ence​.osti​.gov/​U​s​e​r​-​F​a​c​i​l​i​t​i​e​s​/​U​s​e​r​-​F​a​c​i​l​i​t​i​e​s​-​a​t​-​a​-​G​lance.

About Q-NEXT

Q-NEXT is a U.S. Department of Energy National Quantum Information Science Research Center led by Argonne National Laboratory. Q-NEXT brings together world-class researchers from national laboratories, universities and U.S. technology companies with the goal of developing the science and technology to control and distribute quantum information. Q-NEXT collaborators and institutions have established two national foundries for quantum materials and devices, develop networks of sensors and secure communications systems, establish simulation and network test beds, and train the next-generation quantum-ready workforce to ensure continued U.S. scientific and economic leadership in this rapidly advancing field. For more information, visit https://​q​-next​.org/.

Argonne National Laboratory seeks solutions to pressing national problems in science and technology by conducting leading-edge basic and applied research in virtually every scientific discipline. Argonne is managed by UChicago Argonne, LLC for the U.S. Department of Energy’s Office of Science.

The U.S. Department of Energy’s Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, visit https://​ener​gy​.gov/​s​c​ience.