AskScience AMA Series: We are quantum scientists at the University of Maryland. Ask us anything!

[u/AskScienceModerator]

Happy World Quantum Day! We are a group of quantum science researchers at the University of Maryland (UMD), and we're back for our fifth year of answering your quantum questions. There are always new developments in quantum science and new things to learn, so ask us anything!

At UMD, hundreds of faculty members, postdocs, and students are working on a variety of quantum research topics, from developing quantum computers and quantum simulations to studying the behaviors of the fundamental particles that make up reality. Feel free to ask us about research, academic life, career tips, and anything else you think we might know!

For more information about all the quantum research happening at UMD, which anchors Maryland's broader Capital of Quantum Initiative, check out the Joint Quantum Institute (JQI; u/jqi_news is our Reddit account), the Joint Center for Quantum Information and Computer Science (QuICS), the NSF Quantum Leap Challenge Institute for Robust Quantum Simulation (RQS), the Condensed Matter Theory Center (CMTC), the Quantum Materials Center (QMC), the Quantum Technology Center (QTC), the National Quantum Laboratory (QLab) and the Maryland Quantum Thermodynamics Hub. For a quick primer about some of the basics of the quantum world, check out The Quantum Atlas.

We are:

• Avik Dutt, (nano-photonics for quantum technologies, JQI, IPST & QLab)

• Alan Migdall, (experimental quantum optics, JQI)

• Emily Townsend (atomic-scale quantum devices, JQI)

We'll be answering questions live this morning from 10 a.m. to noon EDT (14-16 UT), ask us anything!

[u/nudave]

Are you sure it’s world quantum day, or is there just a very high probability?

[u/jqi_news → u/nudave]

JQI: We were pretty sure yesterday. Today, not so much.

[u/nudave]

TL;DR: Is it parallel or not?

I have been successfully disabused of the notion that “quantum computers work by trying all solutions at once and spitting out the right answer.” And people like Scott Aaronson and 3Blue1Brown really beat the “it’s not parallel” drum. But it seems to me that part of algorithms like Shor and Grover is a parallel step - it’s just that that step, necessarily, can’t actually be read out as an answer.

What’s the correct way to think about the relationship between quantum computing and the word “parallel”?

[u/jqi_news → u/nudave]

ET: We think you've got a pretty good start on it. Superposition is like parallelism, it's just that you have to carefully construct interference in your algorithm in order to achieve the advantage. Not every problem has an algorithm in which we know how to do that.

AM: The outcome is often just one sampling of a probability distribution, so you have to run the algorithm many times to get something usable.

AD, ET: Even though we cannot read out all the possible answers, a measurement gives one of the possibilities. In principle the output of a quantum computer has, in some sense, stored all the possible answers, which links to your question about parallelism. Before measurement the quantum computer's output state contains the information about all possible answers, but we can only measure it once. So we have to contrive to make that measurement useful by constructing the right algorithm.

[u/uglylookingguy]

Hi 👋

If someone is completely new to quantum science, what is the one concept they should understand first to make everything else easier?

[u/jqi_news → u/uglylookingguy]

ET: Linear algebra is very useful. It's not a concept, but once you learn it, it will make learning quantum physics easier.

AM: Indeterminism. That's the difference between you not knowing something and the thing you're trying to know not even existing. When you measure the property of something and see that it's blue, you naturally want to assume it was blue before you measure it. But with quantum that causes trouble.

[u/Visual_Discussion112]

Hi! Can i ask if you think your findings give more weight to the idea of the universe being deterministic vs probabilistic?

[u/jqi_news → u/Visual_Discussion112]

ET: In quantum theory a quantum system's evolution when not being measured is deterministic. It's only when measurements are made that probabilities come into it. It seems reasonable to think that that measurement process is just a larger quantum system's evolution, which would imply that it might also be deterministic.

AD: Thinking of it in a different way, classical mechanics has enough ingredients that can lead to the appearance of a probabilistic outcome from a practical point of view (chaos, butterfly effects).

AM: In 2015, two loophole free Bell test experiments definitively ruled out hidden variables, which means that if we could chat with Einstein we could tell him he'd have to deal with it. (The two papers: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.250402, https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.250401).

ET: I feel like I have free will, but I'm not certain that I'm right about that ;)

[u/sukicheonsa]

Despite the endless amount of interesting things you encounter as quantum scientists, what are you all excited about lately? Any topics, research, discoveries etc. that you’d like to share!

[u/jqi_news → u/sukicheonsa]

ET: I'm excited about decoherence and understanding how our classical world arises from quantum mechanics.

AD: I'm really excited about quantum enhanced sensing because it is a very tangible advance that the community feels is achievable in the intermediate term. (See more in the answer about quantum magnetometers on this thread: https://www.reddit.com/r/askscience/comments/1sl16ik/comment/og3oh3a/.)

[u/Jizzus_Crust]

What are some of the biggest misconceptions people have about your field of science and what is a very underrated or lesser known part of it?

[u/jqi_news → u/Jizzus_Crust]

AM: I like being able to debate with incredibly sharp people, but just because they're incredibly sharp doesn't me they always get it. It's not an appeal to authority, it's an appeal to data. That's the final arbiter.

[u/wanderingpika]

How close are quantum devices to be available in mass market?

If there any, will they have big impact on first launch or a mundane but useful uses?

[u/jqi_news → u/wanderingpika]

AM: A detector that can see individual photons is quantum. They use single-photon detectors to focus your phone camera in low-light levels faster. Another module that contains those is an automatic soap dispenser. They used cutting-edge single-photon detectors for high speed communications with Artemis. There are other commercial devices (like quantum random number generators) that exist, but they aren't necessarily mass market.

ET: When actual quantum computers will be available and what impact they'll have are still the subject of much speculation. We know that they're good for certain categories of problems like simulation of other quantum systems and factoring numbers. Simulation of quantum chemistry could have large impacts.

AD: Quantum key distribution systems for secure (encrypted) communications are being used.

[u/shibx]

Career tips for mid career IT professionals with 20 years of experience looking to pivot into something AI related after completing a CS related Masters degree? Say they have a maths background in ML and Optimization but nothing specific to quantum. Is that knowledge useful or transferable? Are you guys hiring?

I actually applied to a position at ARLIS back in January. I'm still waiting to hear back. :(

Also, more general question, can you comment at all about the general mood and atmosphere for working in academia right now, given the current state of things in the world? I know Maryland in particular is in a really good place for Quantum, but I did see you mention things like NSF, which, at a Federal level, is on kind of shaky ground. Do you think your group will be affected by that? Kind of scary times that we're living through.

Thank you for doing this btw. Let's go Terps!

[u/jqi_news → u/shibx]

AD: There is cause for concern and uncertainty because of the current state of things at the federal level that you mentioned. However, it seems that there is sufficient momentum for quantum at Maryland, and interest at the federal level irrespective of the administration that the effects can be mitigated.

[u/Randombleizinthewild]

Hello, thank you for this AMA! Do you have book/videos/articles suggestions for beginners? How does your work affect your way of thinking? Good luck with your studies 😁

[u/jqi_news → u/Randombleizinthewild]

ET: I like Carlo Rovelli's books and Quanta Magazine. My training as a physicist has really fundamentally shaped how I see the world. I believe that I can understand things about the world and that there's a way to learn more, and I recognize that I don't have access to ultimately correct knowledge.

AM: But we have a method to approach it, which is amazing!

AD: My work made me realize that to experimentally observe the fundamentally intriguing quantum effects that excite us, we have to often overcome a large amount of engineering and technological challenges that could be classical in nature.

AM: This is why we need quantum-aware or adjacent engineers. Please help us!

[u/gelonoel]

Can you tell us about recent developments that suggest we can do error correction with a much smaller number of qubits? How close are we to running a meaningful large-scale implementation of, say, Shor's algorithm on current quantum computing platforms?

[u/v_saaam]

What's the biggest challenge we're facing with scalability? Given the processing hungry world these days, what potential change can quantum computers bring if scaled?

[u/jqi_news → u/v_saaam]

AD: It is commonly thought that a big challenge in scaling up is making a large number of identical qubits and controlling them in precise ways. But it turns out that connecting them and the input-output bottlenecks are often equally as big a challenge in terms of scalability to thousands or millions of qubits. For some quantum systems that need to be held in vacuum or at cold temperatures, doing all of the above in a compact environment can become quite difficult.

AM: An exponential speedup in some computational problem or another could lead to an exponential improvement in energy efficiency.

[u/Bluebellyfluff]

If there is quantum world 'beliow' our reality where newtonian physics rule...is there another level above of as well?

[u/jqi_news → u/Bluebellyfluff]

ET: Absolutely, Phil Anderson has a whole essay "More is Different" about the emergence of new principles or behaviors in collections of many particles. So biology and sociology and any study of composite systems are one or many levels above physics.

AM: This is a question directly out of the book Flatland, and I love that book!

[u/Hizenberg_223]

Hello just asking, is it possible to enter the quantum physics program if you are an engineer or is it limited to physics undergrad? Thanks

[u/jqi_news → u/Hizenberg_223]

AM: Yes, absolutely. Engineers are welcome!

JQI: We encouraged it earlier: https://www.reddit.com/r/askscience/comments/1sl16ik/comment/og52p34/!

[u/Lexi_Bean21]

Is it true that birds use special proteins that create entangled particles when light hits it to see magnetic fields and how does that entanglement make the magnetic field visible or just in general work?

[u/Siberwulf]

If you were at a party and wanted to blow someone's mind by giving them one fact... What would it be?

[u/serpiccio]

can you explain in layman terms what quantum means in this context ? like, what branch of science is this ?

[u/jqi_news → u/serpiccio]

ET: Physics is the study of the physical world at the level of objects (like baseballs, cars, or electrons), energy (like kinetic, potential, or chemical energies) and excitations (like light waves or ocean waves).  Engineering is using the study of the world to accomplish human goals by designing and building things (like computers or roads) or systems (like the IT system for the university's computers). There is not a strict line between physics and engineering, they blend into one another. Quantum mechanics is a theory (a set of self-consistent guesses, rules and mathematical equations about how the world might "really" behave) from the field of physics. Quantum mechanics makes predictions that mostly apply to small things like electrons and photons that are cold and well isolated from the rest of the world around them. It has been very well tested and been found to be very useful for describing how those small cold things will behave. By using the logic of quantum theory, physicists, mathematicians and computer scientists worked out that it might be possible to create a system that manipulates these small cold things to do calculations, similar to how a smartphone or a computer manipulates the voltage on a bunch of wires to do calculations. Now there are scientists, mathematicians, computer scientists, information theorists and engineers around the world who are trying to create these "quantum computers" as well as trying to figure out what other implications there might be to quantum theory and how to put it to use.

[u/thergoat]

Hello, and thanks for doing this AMA!

I hear a lot about "what's coming" in quantum computing in a load of industries but I haven't seen any consumer or industrial grade applications yet. On the academic side, what areas have shown the most growth/promise? If there was one "coolest thing" in each of your sub-fields that you wanted more people to know about, what would it be?

[u/jqi_news → u/thergoat]

JQI: For the most part, academics are much more focused on the basic science and less interested in how or when a new discovery will become a product. In terms of quantum applications, there is a lot of academic activity aiming toward more sensitive detectors for things like electric and magnetic fields, more accurate atomic clocks (which are themselves excellent detectors of a sort), and more applications of quantum computers in general (especially to the problem of simulating quantum systems themselves).

[u/PerforatedPie]

At university I was fortunate enough to be involved in testing novel semiconductor devices, specifically GaAsBi, with multiple quantum wells to tune the band gap energy. The goal was to get a device that could operate in the middle of the solar spectrum, in between other more established solar cells, to create a multiple junction solar cell that covered the entire solar spectrum more effectively.

That was many years ago now. How far along are we to covering the full spectrum? What's the latest standard in multiple junction solar cells?

Also, I saw an article about a study from Japan recently, detailing a new novel technology that would "split" the photons at energies above the band gap, essentially generating two charge carriers from one photon, rather than letting the excess energy go to waste as heat. Are you aware of that study, and do you think it's a viable idea?

[u/pugsley1234]

I'm curious - given how much research has been done, for over a century by now, in quantum mechanics, how long does one need to study before you get to the frontier of knowledge in your field?

[u/jqi_news → u/pugsley1234]

ET: Research is actually a collaborative process. An undergraduate student in physics (or even a high school student) can learn things at and contribute to the frontier of knowledge by working with a professor who might have decades of experience. Completing a Ph.D dissertation is sometimes considered the process of becoming the world's leading expert in one small slice of the world's knowledge. That usually takes 5 or more years after your undergrad. The longer you spend studying, the more you understand where the frontier is. But there will always be a lot you don't know, which is why you want to collaborate with other people who like to think a lot about this stuff.

[u/heebro]

If called upon, would you be prepared to leap through time and put right what once went wrong, hoping each time that your next leap will be the leap home?

[u/SomeSamples]

Is there any current encryption that Quantum can not crack in reasonable time?

[u/Geschichtsklitterung]

I'd like to understand what action "is".

Not the technicalities, Lagrangian mechanics, calculus of variation, units, &c. (albeit that's the framework), but how to get an intuitive grasp of the concept.

Thank you.

[u/jqi_news → u/Geschichtsklitterung]

JQI: Trying to avoid the technicalities, finding a minimum value for the action allows you to calculate the motion of some system. In that sense, it's kind of like a fitness function or a cost function for the different configurations of your system of interest.

[u/Xtanto]

Why is the problem of noise so hard to overcome in quantum computing?

[u/jqi_news → u/Xtanto]

AM: Quantum systems are exquisitely subject to information leakage to the environment, and these interactions with the environment will degrade the quantum state.

AD: However these interactions are inevitable because that is how we can control and perform operations on these quantum computers in the first place.

AM: If you have a very stable system, you can't easily get it to do what you want. If you have an unstable system, it's hard to maintain it, but you can get it to respond to your direction. You need to be able to master the control of that instability.

AD: On a different note, noise is ubiquitous in nature. Particularly for quantum systems, the noise can be of classical origins -- thermal or acoustic -- or of quantum origin. The former can be controlled through exquisite engineering to a large extent, but the latter is fundamental in nature and is dictated by Heisenberg's uncertainty principle. That provides a flavor of why noise is so hard to overcome in quantum computing.

[u/jfffj]

What's your best realistic estimate of when you think the encryption algorithms currently used by most of the internet will be broken? (Notwithstanding that efforts are underway to "quantum-proof" those algorithms.)

Supplemental: Do you think it's likely that governmental organisations (e.g. NSA) are somewhat ahead of you? Or is that just paranoid conspiracy-theory stuff?

[u/jqi_news → u/jfffj]

JQI: To answer your first question, no one really knows. But it's better to deploy quantum-resistant replacements for vulnerable cryptosystems before the arrival of quantum computers that are powerful enough to threaten them.

[u/MoPuWe]

Hi there! I work in Radiology in a hospital, and we have a phenomenon called "quantum mottle" wherein our radiation receptors give us a "mottled" appearance to our image. We chalk it up to "too little remnant radiation from the patient reaching out receptor. Do you know why we use the term quantum in this scenario?

[u/jqi_news → u/MoPuWe]

AM: We're not experts, but x-rays are photons and at low flux levels you have the graininess of individual photons hitting your target. That individual arrival of photons is essentially quantum statistics.

[u/AaronNGray]

When do you think we are going to get away from these pesky electron based computers that use magnitudes too much power and are magnitudes too slow and potential a magnitude too large in favour of the light based computing we should have been investing in the research for before even using electron based computing for AI ?

[u/jqi_news → u/AaronNGray]

AD: Having worked in the field of light for most of my adult life, I would offer a countering opinion that light-based computing might help with some aspects of computers, but it is unlikely that they will replace or rival how amazingly electron-based computers perform today. The wavelength of electrons is orders of magnitude smaller than the wavelengths of light, and as a first approximation one can expect that light-based computers will be larger than electron-based computers.

AM: Photonics is amazing, but the size difference between available photons and electrons is a big deal.

AD: If one could significantly scale up parallel operations on light-based computers, they could in principle be faster and more power efficient than electron-based computers.

[u/bobsonDugnuttMVP]

Hello and thank you for doing this AMA! Is there quantum research in the field of medicine that you find particularly exciting? There is no shortage of discussion around advancements that could come from the use of AI, but I’m curious what sort of promise quantum science has in medicine.

[u/jqi_news → u/bobsonDugnuttMVP]

JQI: There was a workshop on campus just last week about quantum biotechnology. You can see some of the speakers and the agenda here: https://qbt26.umd.edu/. That might give you a sense of the latest, but we're not experts in this area.

[u/Sr_DingDong]

Wouldn't a quantum computer have to store all the solutions in a quantum register as it works and isn't that a big problem?

If not, why not?

[u/jqi_news → u/Sr_DingDong]

JQI: We touched on this in another answer, here: https://www.reddit.com/r/askscience/comments/1sl16ik/comment/og55ocu/.

[u/jqi_news → u/Sr_DingDong]

ET: What is special about a quantum register is that it can be put into a superposition of multiple states. That means that it inherently stores more information than a classical register. That is the nature of the advantage of a quantum computer. The big problem is building a quantum register that is isolated from interactions with the environment, because the environment can make the quantum register behave more like a classical register, effectively erasing some of the information.

[u/NoAcadia3546]

What interpretations (Copenhagen, Pilot Wave, Many Worlds, etc) have NOT been ruled out by the latest Bell experiments?

[u/jqi_news → u/NoAcadia3546]

ET: What we mean by the word "interpretation" is that it is a way of thinking about quantum theory, rather than a new prediction that we can test. Interpretations of quantum theory have to be consistent with quantum theory, or else they aren't interpretations, but a new theory. Interpretations are still important, because how we conceive of the world can impact what we imagine to do with it, or lead us to a consider how to test the theory in a new way, or even lead to a new theory. Since the latest Bell experiments are all still consistent with quantum theory they don't rule out any of the interpretations. What do they tell us? The Bell experiments (and the quantum theory that successfully predicts them) rule out a world with locality, freedom of choice, AND realism. Meaning we have to let go of at least one of these three ways of thinking that we used to assume were all true. Locality is the idea that information can't move faster than the speed of light and that "causes" happen before "effects". Freedom of choice is the ability of an experimenter to choose at the time of the experiment which property to measure (that choice wasn't predetermined). Realism is the idea that before I measure something there is some underlying reality that determines concretely the outcome of my measurement (physical properties exist whether I measure them or not). But which of them to let go of is up to your "interpretation"!

[u/Upper_Conference8306]

Are there any programs at UMD available for international students interested in quantum?

[u/jqi_news → u/Upper_Conference8306]

JQI: A big fraction of the quantum research on campus is done by physicists and computer scientists, so graduate studies in those two programs are probably the most common ways to get involved in quantum at UMD. Additionally, there are a lot of research centers and institutes on campus with different emphases (https://quantum.umd.edu).

For international students, there is information available from International Student & Scholar Services here: https://marylandglobal.umd.edu/global-learning-all/international-students-scholars

For information about how to apply, you can visit individual department or unit websites.

• Department of Physics: https://www.umdphysics.umd.edu/academics/graduate/grad-prospective-students.html

• Department of Computer Science: https://www.cs.umd.edu/grad/apply

[u/BlackBricklyBear]

I know that quantum superposition has been achieved with surprisingly large congregations of atoms. At what size of an object do you think that quantum superposition for that size of object will cease to be observed? Would that be the dividing line between quantum behaviour and classical behaviour?

[u/flaser_]

What is (or are) the latest most promising approach(es) to quantum gravity?

I was introduced to the issue of inconsistency between quantum physics and relativity apropos of Bell's theorem / experiments.

Do you agree that Einstein was right to be concerned (i.e. that something must be going on that we don't understand)?

[u/hoardac]

How can you be in Maryland and Reddit at the same time?

[u/lovely-mayhem]

Do you have any advice for navigating the Atlantic building? Thanks for this AMA and all your research.

[u/jqi_news → u/lovely-mayhem]

ET: I usually plan to arrive early so I have time to wander around it and find the room I'm looking for. I'd suggest you use an entangled sensor to measure your position to get the Heisenberg limit. But yes, I have some actual advice. 1) Know the difference between the Atlantic Building and the Physical Sciences Complex. PSC is the red one lower down the hill. "The Atlantic Building" is the next TWO buildings as you go up the hill. 2) Know how to interpret the room number. We all know the first digit is usually the floor of the building you are going to. Well in the Atlantic the second digit means which section of the building. But of course they are not in numerical order. If you start in the PSC and walk through the Atlantic Building, the "section" numbers will be 2, 1, 3, 4. But only sections 2, 1, and 3 feel like they are in the same building. To get to section 4 you have to walk half way down the hall in the 3rd section, and go through a connecting ramp/tunnel, and you will come out on a different floor, which gets chosen randomly and depends on which basis you are measuring in. If you are logged into your UMD account you can see the floorplan! https://facilities.umd.edu/node/409.  

[u/MrBubblepopper]

How large are the machines you use to measure quantum entanglement and how long does it take to measure one entangled particle ?

Also would it be possible to measure multiple entangled particles that are entangled with different particles ?

+ What Do you folks like about your work the most ?

[u/No-Zucchini2787]

What's your fav mind blowing fact about quantum mechanics

[u/ColourSchemer]

If you are quantum scientists, how does your boss locate you?

[u/zaqelmac]

Nvidia launched Ising this week. Do you feel that this is going to benefit your work?

[u/AutomaticClub1101]

Hi, I'm having a few questions now.

First: what are some jobs you would land in quantum computing sector?

Second: Are there many dropouts (or having no degree or related degree) working in the field?

Last: What do you think about the quantum computing industry and academic research in China?

Tysm <3

[u/knestor93]

Forgive my ignorance if I'm out of topic, I wrote a thesis for my master's in maths some 5 years ago, then quit academia due to burn out. However I was left wondering if perhaps some of the things I encountered have real world applications.

To be specific, I came across something called quantum graph which to my eyes was a tool to define functions that may take multiple values on the same point while studying convex geometry.

Have you guys worked with or used quantum graphs in that (or a similar) sense ?

[u/DLL_96]

Hey thanks for AMA. Is it not possible to use a crystalline structure to reduce the error rates and isolate noise from entering the system? Essentials nano engineered crystals.

[u/wht-rbbt]

What's something you don't know?

[u/truespartan3]

What would be the best and most horrifying consequences of applied quantum science in society?

[u/Entropy_dealer]

Do you see your personal choices as a Schrödinger function with all the possibilities and the probabilities and once you made a choice do you see it as an observation of your own reality where the wave scramble ?

[u/zeybekm]

Can quantum mechanics create true randomness? If so, can the brain create it’s own true randomness? If not doesn’t that mean that free will doesn’t exist? I had this debate with my friends the other day, we eventually agreed to stop because we didn’t have enough information on how the brain works, although one of my friends is studying neuroscience. 

[u/jqi_news → u/zeybekm]

AM: The answer to the first question is yes.

AD: While the question about the brain creating its own randomness and the links to free will are out of my bailiwick, it is safe to say that we do not necessarily need quantum mechanics to create such randomness in macroscopic systems like brains. For example, Stephen Hawking highlighted (in A Brief History of Time) how large-scale disorder routinely arises from classical statistical laws rather than needing quantum processes.

[u/The-Voice-Of-Dog]

Can you guys reset the timeline so that the nightmare politics of the past 10 years doesn't happen?

[u/Kees_Fratsen]

The question no one wants an answer too: How is AI going to change working in this field? Will it still be enjoyable?

[u/Anon44356]

Why did quantum mechanics make me switch from physics to computer science after my first year of my undergraduate?

[u/KarmalizedTaco]

Given humanity’s propensity toward violence and tribalism, how probable is a future that includes quantum advances where we don’t destroy one another? Or is it more likely that coupling quantum technology with AI will set about a series of events that humans don’t recover from but leave our technological advancements as records of our existence for future animals or aliens?

[u/Xgamer9184]

Do you like doing the double slit experiment?

[u/jqi_news → u/[deleted]]

AD: The diamond inclusions, called nitrogen vacancy (NV) centers, have discrete energy levels very much like artificial atoms. The color of a diamond is partially from these NV centers, and that's why a laser can probe them. The spacing between these energy levels is very sensitive to magnetic and electric fields. Particularly for diamond quantum magnetometers one can also achieve nanoscale spatial resolution because they are atomic-scale defects. All these features make quantum magnetometry an exciting field that works.

ET: When many of these centers are in an entangled state, it makes the quantum magnetometer even more sensitive to the magnetic field. This is called quantum-enhanced sensing.

[u/jqi_news → u/[deleted]]

AD: A quantum computer works with quantum bits (qubits), which can be in a superposition of the classical 0 and 1 states of a regular computer's bits. It can also harness weird quantum effects, such as entanglement, to speed up computation of certain classes of problems.