1. Institute for Quantum Computing — University of Waterloo

Institute for Quantum Computing (IQC) is one of the first and best institutes in the business. It was founded in 2002 by Raymond Laflamme and Michele Mosca. IQC is funded by the founder of BlackBerry, Mike Lazaridis. Recently, a team of researchers led by an IQC faculty member performed the first-ever simulation of baryons — fundamental quantum particles — on a quantum computer, which helps scientists to study neutron stars and the earliest moments of the universe.

Image source — Wikipedia

Here is the link to a video if you are excited to know more about IQC — Institute for Quantum Computing

2. University of California, Berkeley

Quantum computers provide exponential speedups for computational tasks such as integer factorization and the properties of quantum bits can be used to achieve secure communication. These advances have also changed our understanding of the relation between information and quantum physics, with significant implications for a broad range of subjects, including quantum phases, metrology, quantum nanosystems and measurement and control of quantum systems. The Berkeley Center for Quantum Information and Computation brings together researchers from the colleges of Chemistry, Engineering and Physical Sciences to work on fundamental issues in quantum algorithms, quantum cryptography, quantum information theory, quantum control and the experimental realization of quantum computers and quantum devices.

Here is the link to their official website — BQIC

3. University of Oxford

Oxford University is at the forefront of the UK’s efforts to build the first generation of quantum computers with world-leading performance. Quantum computing has the potential to transform areas of our lives such as healthcare, finance and security — and Oxford is a pioneering theory, technology and responsible innovation to ensure that its power will bring benefits for all of society.

The university’s own David Deutsch first described a universal quantum computer way back in 1985. The first working pure state NMR quantum computer was demonstrated at Oxford and the University of York. The university is still positioned among the top leaders in quantum science.

Want to know more about their research and achievements? Here you go — University of Oxford Quantum Computing

4. Centre for Quantum Information and Foundations — University of Cambridge

The discovery that quantum physics allows fundamentally new modes of information processing has required the existing theories of computation, information and cryptography to be superseded by their quantum generalizations. The Centre for Quantum Information and Foundations, part of the University of Cambridge, and based within the Department for Applied Maths and Theoretical Physics, conducts theoretical research into all aspects of quantum information processing, the implications of quantum computing and quantum information theory for physics, and broader foundational questions in quantum physics.

Researchers and professors at the University of Oxford and the University of Cambridge are the first to combine Natural Language Processing (NLP) with Quantum Computing. They named it Quantum Natural Language Processing (QNLP).

Image source — Wikipedia

5. Harvard Quantum Initiative — HQI

The Harvard Quantum Initiative in Science and Engineering (HQI) is a community of researchers with an intense interest in advancing the science and engineering of quantum systems and their applications. They said their mission is to help scientists and engineers explore new ways to transform quantum theory into useful systems and devices.

Today, as the ‘second quantum revolution’ starts to gain momentum, HQI brings together scientists and engineers across sectors — universities, companies, and government — to leverage quantum effects such as superposition and entanglement in ways that will profoundly impact the way information is acquired, stored, sent, and processed.

Image source — Wikipedia

6. NCCR QSIT — Quantum Center

NCCR QSIT brings together more than 30 research groups from the field of quantum science and technology in Switzerland, across disciplines, from quantum information theory to device engineering. The National Centre of Competence in Research (NCCR) on Quantum Science and Technology (QSIT) is a research initiative of the Swiss National Science Foundation (SNSF). NCCRs are designed to promote long-term research projects in areas of outstanding strategic importance for the development of science in Switzerland.

The Quantum Center sees itself in this tradition of contributing to the young field of quantum science and technology with a clear vision, coordinated efforts across disciplinary boundaries, and the flexibility to adapt to emerging directions. After the end of the last funding period of NCCR QSIT, the Quantum Center will continue several of its programs and initiatives.

7. National University of Singapore and Nanyang Technological University — Centre for Quantum Technologies

The Centre for Quantum Technologies (CQT) is a Research Centre of Excellence (RCE) in Singapore. It brings together physicists, computer scientists and engineers to do basic research on quantum physics and build devices based on quantum phenomena. The Centre was established in December 2007 with support from Singapore’s National Research Foundation and Ministry of Education. CQT is hosted by the National University of Singapore (NUS) and has staff at Nanyang Technological University (NTU).

CQT builds technologies for secure communication, quantum computing, and precision measurement. They create our software and control systems that push the boundaries of what’s possible and collaborate with industries.

Here is the link to their official website — Center for Quantum Technologies

Image source — CQT Website

8. Centre for Quantum Photonics (CQP) — University of Bristol

The Quantum Engineering Technology Labs (QET Labs) at the University of Bristol was launched in April 2015 and encompassed the activities of over 100 academics, staff, and students. They bring together Bristol’s broader quantum and related activity to maximize opportunities for new scientific discoveries that underpin engineering and technology development.

QET Labs brings together the Quantum Engineering Centre for Doctoral Training (QE-CDT), the Quantum Technology Enterprise Centre (QTEC), and the research teams of their staff and students. Working together, we aim to transform science into real concept demonstrators and entrepreneurial innovation that will be the springboard for the commercial success of quantum technologies. They primarily investigate and build photonic quantum computers.

Here is the link to their website where you can get more information about what they are doing, about the research — University of Bristol — QET Labs

9. University of Maryland, College Park — Joint Quantum Institute

The Joint Quantum Institute (JQI) is on the verge of a new technological revolution as the strange and unique properties of quantum physics become relevant and exploitable in the context of information science and technology.

The Joint Quantum Institute (JQI) is pursuing the goal through the work of leading quantum scientists from the Department of Physics of the University of Maryland (UMD), the National Institute of Standards and Technology (NIST) and the Laboratory for Physical Sciences (LPS). Each institution brings to JQI major experimental and theoretical research programs that are dedicated to the goals of controlling and exploiting quantum systems.

Image source — JQI Website

Here is the like to their website — JQI

10. LMU Munich — Quantum Applications and Research Laboratory (QAR-Lab)

In the Quantum Applications and Research Laboratory (QAR-Lab), they explore the possibilities of quantum computing for practice and develop an early quantum advantage in the areas of optimization and artificial intelligence. To do so, they are already putting use cases into practice on quantum computers such as D-Wave, Fujitsu, Rigetti, and IBM and evaluating these quantum computers, comparing architecture and performance, and using their specially developed UQO platform as middleware for architecture-independent programming.

QAR Labs are currently researching the following domains of quantum computing.

• Quantum Optimization
• Quantum Artificial Intelligence
• Quantum Software Platform (UQO)

Here is the link to their website — QAR Labs Munich

The mentioned above Research labs/Institutes/Universities are only a few. There are lots of other research institutions working rigorously in this field. Below is the link to all the universities in the world working on quantum technology —

https://quantumcomputingreport.com/universities/

1. IBM

IBM is one of the first to get into business. They were the first to put a quantum computer on the cloud which can be accessible to everyone no matter where they live on earth. IBM has recently said that ‘there were about 3 lakh registered users who run more than one billion quantum circuits on real hardware and simulators.’

In 2017, IBM was the first company to offer universal quantum computing systems via the IBM Q Network. The network now includes more than 125 organizations, including startups, research labs, and education institutions. Partners include Daimler AG, JPMorgan Chase, and ExxonMobil. All use IBM’s most advanced quantum computers to simulate new materials for batteries, model portfolios and financial risk, and simulate chemistry for new energy technologies, the company said.

It has recently announced their 121 qubit quantum computer named eagle which is really a significant milestone. (As far as we dont take error rate into consideration)

By 2023, IBM scientists will deliver a quantum computer with a 1,121-qubit processor, inside a 10-foot tall “super-fridge” that will be online and capable of delivering a Quantum Advantage — the point where certain information processing tasks can be performed more efficiently or cost effectively on a quantum computer, versus a classical one, according to the company.

Here is their roadmap for the future — Roadmap IBM Quantum

Image Source — https://www.ibm.com/quantum-computing/

2. XANADU

Xanadu is a Canadian quantum technology company with the mission to build quantum computers that are useful and available to people everywhere. Founded in 2016, Xanadu is working toward a universal quantum computer using silicon photonic hardware.

The company also provides users access to near-term quantum devices through its Xanadu Quantum Cloud (XQC) service. The company also leads the development of PennyLane, an open-source software library for quantum machine learning and application development.

Here is the link to their official website and if you are interested to learn Quantum Machine Learning don’t forget to try PennyLane

Xanadu — https://www.xanadu.ai/

PennyLane — https://www.xanadu.ai/pennylane

Image Source — https://medium.com/xanaduai

3. COLDQUANTA

ColdQuanta commercializes quantum atomics, which it said is “the next wave of the information age.” The company’s Quantum Core technology is based on ultra-cold atoms cooled to a temperature of nearly absolute zero; lasers manipulate and control the atoms with extreme precision.

The company manufactures components, instruments, and turnkey systems that address a broad spectrum of applications: quantum computing, timekeeping, navigation, radiofrequency sensors, and quantum communications. It also develops interface software.

ColdQuanta’s global customers include major commercial and defense companies; all branches of the US Department of Defense; national labs operated by the Department of Energy; NASA; NIST; and major universities.

In 2020, ColdQuanta was selected by the Defense Advanced Research Projects Agency (DARPA) to develop a scalable, cold-atom-based quantum computing hardware and software platform that can demonstrate quantum advantage on real-world problems.

Here is the link to the official page of coldquanta — https://coldquanta.com/

Image source — Google

4. ZAPATA COMPUTING

Zapata Computing empowers enterprise teams to accelerate quantum solutions and capabilities. It introduced Orquestra, an end-to-end, workflow-based toolset for quantum computing. In addition to previously available backends that include a full range of simulators and classical resources, Orquestra now integrates with Qiskit and IBM Quantum’s open quantum systems, Honeywell’s System Model, and Amazon Bracket, the company said.

The Orquestra workflow platform provides access to Honeywell’s HØ, and was designed to enable teams to compose, run, and analyze complex, quantum-enabled workflows and challenging computational solutions at scale, Zapata said. Orquestra is purpose-built for quantum machine learning, optimization, and simulation problems across industries.

Image Source — LinkedIn

Link to their software toolkit — Orquestra

Link to their official website — https://www.zapatacomputing.com/

5. AZURE QUANTUM

In collaboration with academic and research institutions around the world, Microsoft Quantum Computing performs experimental and theoretical processes to develop quantum computers, employing scholars, theorists, and physicists from mathematics, physics, and computer science. The aim is to develop our knowledge of quantum computing, as well as its implementations and integration.

As a Researcher, Student or quantum enthusiast, one can broaden their learnings through the access to the most diverse set of quantum technologies by

1. An open ecosystem, enabling you to access diverse quantum software, hardware, and solutions from Microsoft and our partners.

2. A trusted, scalable, and secure platform that will continue to adapt to our rapidly evolving quantum future.

3. Quantum impact today, with pre-built solutions that run on classical and accelerated compute resources (also referred to as optimization solutions)

Image Source — Google

Link to their official website — https://azure.microsoft.com/en-us/

6. D-WAVE

Founded in 1999, D-Wave claims to be the first company to sell a commercial quantum computer, in 2011, and the first to give developers real-time cloud access to quantum processors with Leap, its quantum cloud service.

D-Wave’s approach to quantum computing, known as quantum annealing, is best suited to optimization tasks in fields such as AI, logistics, cybersecurity, financial modeling, fault detection, materials sciences, and more. More than 250 early quantum applications have been built to date using D-Wave’s technology.

In February, D-Wave announced the launch of Leap 2, which introduced new tools and features designed to make it easier for developers to build bigger applications. In July, the company expanded access to Leap to India and Australia. In March, D-Wave opened free access to Leap for researchers working on responses to the COVID-19 pandemic. In September, the company launched Advantage, a quantum system designed for business. Advantage has more than 5,000 qubits, 15-way qubit connectivity, and an expanded hybrid solver service to run problems with up to one million variables, D-Wave said. The advantage is accessible through Leap.

Here is the link to leap — https://www.dwavesys.com/solutions-and-products/cloud-platform/

Image source — Google

7. HONEYWELL

It is one of the industry’s early leaders in quantum computing. In 2014, the company began its journey by taking part in an innovative intelligence research project to learn more about the technology. Honeywell is now heavily invested in a concept known as trapped ion quantum computing. This method makes use of ions suspended in space to relay data via their movement.

As a leading technology company, they will shape the adoption and integration of quantum information systems into the industries such as Pharma, Chemicals, Finance, Telecommunication, etc.

Trapped-ion quantum computers use numerous, individual, charged atoms (ions) to hold quantum information. Hoenywell’s systems use electromagnetic fields to hold (trap) each ion so it can be manipulated and encoded using microwave signals and lasers.

8. RIGETTI

It’s a full-stack quantum computing firm that designs and produces superconducting quantum integrated circuits, packages and deploys them in a low-temperature setting, and develops control systems to execute quantum logic operations on them. Rigetti Computing is an integrated systems company that builds quantum computers and the superconducting quantum processors that power them. Through the Quantum Cloud Services (QCS) platform, their machines can be integrated into any public, private or hybrid cloud.

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Image source — https://www.rigetti.com/

9. Cambridge Quantum Computing

Since its inception in 2014, the aim has been to positively transform the world using the power of quantum computing. Breakthroughs in drug discovery, healthcare, materials science, cybersecurity, and energy will become possible as quantum computers become more powerful. They are one of the world’s foremost quantum computing companies, delivering science-led, enterprise-driven solutions to tackle hard problems across a range of industries.

Cambridge Quantum designs, engineers and deploys algorithms and enterprise-level applications by taking cutting-edge research into solutions for solving real problems. TKET, our hardware-agnostic software development platform, and other technologies are currently utilized by an ever-growing global user base.

Image Source — https://cambridgequantum.com/

There are many more startups and companies using quantum technology all around the world, If you are curious to know more about those companies, please visit the given link below.

Public Companies — https://quantumcomputingreport.com/public-companies/

Private/Startup Companies — https://quantumcomputingreport.com/privatestartup/

Government/Non-Profit Companies — https://quantumcomputingreport.com/governmentnon-profit/

X Gate

X gate flips the state of qubit, to put simple and easy. It can also be said that X gate does the same kind of work in quantum computing that is done by the NOT gate in classical computing. The Pauli matrix of X gate can be seen below

We can see how each gate impacts the qubit on a Bloch sphere in Qiskit. Initially i.e.,before applying a particular gate to the qubit, each qubit is set to be in the state ‘0’ and this is how it looks on Bloch sphere

After applying X gate to the qubit, the state of the qubit turns out to be ‘1’, if the initial state of the qubit is ‘0’.

Here is the code snippet which when executed in Qiskit gives the above output and this also shows how X gate looks.

The code that is given below when executed gives you the Bloch sphere that is shown above

Y Gate

Y gate rotates the state vector 180 degrees around Y axis on the Bloch sphere. This rotation is always done in anti clock wise direction. The Pauli matrix of Y gate is given below

When we look at what a Y gate does on Bloch sphere(if the initial state of the qubit is 0), it seems like it does the same work as an X gate, but don’t fall into the trap. Let’s make the initial state of the qubit to a superposition of 0 and 1 (you will know more about this by the end of the article).

And this is how the state vector looks on Bloch sphere when a Y gate is applied to the above Bloch sphere code.

Here is the code to build a circuit where Y gate is applied to a single qubit

The code given below when executed gives the Bloch sphere of Y gate

Z Gate

Z gate rotates the state vector 180 degrees anti clockwise around Z axis on the Bloch sphere. The Pauli matrix of Z gate is given below

The initial state of the qubit is shown on the Bloch sphere. If you could see and analyze where state vector goes after applying Z gate to the initial state, I am sure you can understand it more clearly.

The final state of the qubit on the Bloch after applying Z gate is given below

The given below is the code to construct a circuit with Z gate applied to a single qubit

Want to look at the Bloch sphere? Here you go!!

Looks like every gate doing the same work? Don’t worry!! See every gate in the perspective of rotation around the axis, you will be fine.

If you still have doubts or got stuck anywhere, please join this course on quantum computing where you can learn from basics to advanced algorithms and get hands-on experience — Quantum Computing with Qiskit Ultimate Masterclass

H Gate or Hadamard Gate

H gate is one of the most important gates in quantum computing. It brings the two states (0 and 1) into superposition and it can be also expressed as a 90 degree rotation around Y axis followed by a 180 degree rotation around X axis. The Pauli matrix of H gate is

This how the Bloch sphere looks when a Hadamard gate(H gate) is applied to a qubit whose initial state is 0.

Please feel free to execute the code given below in Qiskit and check it out yourself.

Code to look at the Bloch sphere of the Hadamard gate (H gate)

S & S-Dagger Gates

S gate can easily expressed as the √Z-gate (90 degree rotation around Z axis). It does a quarter-turn around the Bloch sphere. It is important to note that unlike every gate introduced in this chapter so far, the S-gate is not its own inverse which is called as dagger (sdg).

The Pauli matrix of S gate and S dagger gate is given below

To see how S gate affect the qubit, let us make the initial state of the qubit as a superposition of 0 and 1 by applying a H gate. Here’s how it looks

And this is how the Bloch sphere looks after applying S gate to the H gate on the same single qubit.

Code to build a single qubit quantum circuit with S gate applied to first qubit

Code to look at the Bloch sphere and state vector of S gate

T & T-Dagger Gates

The T-gate is a very commonly used gate, As with the S-gate, the T-gate is sometimes also known as the 4√Z-gate. Even T gate has its own inverse(dagger) and the Pauli matrices of both of them are given below

To see how T gate affect the qubit, let us make the initial state of the qubit as a superposition of 0 and 1 by applying a H gate. Here’s how it looks

This is how the Bloch sphere looks after applying T gate to the qubit whose initial state is the superposition of 0 and 1.

Get hands on experience by running the code given below and build your own circuit with T gate

Code to see the Bloch sphere of T gate

Thank you so much for reading this far. Now you had an intuition on single qubit quantum gates and you know how they work and what do they do exactly do. Here is a course I would highly recommend to join to get a good knowledge in quantum computing and hands-on experience — Quantum Computing with Qiskit Ultimate Masterclass

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What if I say that ‘you are reading and not reading this at the same time? (until someones measures you)’ — Amazed? Here in this article we provide you a very good intuition on the basics of quantum computing.

1. Quantum Computing — What exactly is it?

If you haven’t heard of the word quantum computing, don’t worry! The probability of you hearing this in the next few years will almost be equal to one. Quantum Computers are wizards, they can perform magics and wonders where we fail to understand what’s happening with our naked eye. I would say classical computers are not different from quantum computers but they are completely opposite. Classical computers represent data with 0’s or 1’s (bits), for example number 2 is represented as 10 in a classical computer(binary). Whereas in quantum computers data is represented with a certain probability of 0 and a certain probability of 1, for example — 50% 0 and 50% 1(qubits or quantum bits- two level quantum system). This phenomenon is called superposition.

Superposition is the linear combination of quantum states. In our example quantum states are 0 and 1. Superposition gives parallel processing powers to a quantum computer. This means that many quantum states can simultaneously be manipulated! All quantum computers have this property inherently!

2. Why should we use quantum computers over advanced classical computers?

As we saw above, when compared to classical computers we can represent more complex data using quantum computers. Quantum computers can be used in many diverse fields such as, Machine Learning, Cryptography, Finance, Security, Drug Discovery, Chemistry, and can also help us in bringing Climate change, where classical computers fail to take a part. This means that quantum computer are not going to replace classical computers but rather be used for specialized applications. Quantum computers use the basic principles quantum mechanics to work. In our high schools we were taught that the ground state energy of a hydrogen atom is -13.6 eV, but did we ever see the practical results with our naked eye? Did we ever try to do that?

You may wonder, but yes quantum computers help us in achieving this practice and it didn’t put its limits to a simple hydrogen atom, we can also see the ground state energy of lithium hydride and some small molecules, and I am pretty sure in the near future we may discover new elements or may find some new drugs or can break an RSA encryption with advanced quantum computers!

One can learn quantum computing even if he/she doesn’t have any background of physics. Here is the link to a course where you can learn from basics of quantum computing to advanced quantum algorithms — Quantum Computing with Qiskit Ultimate Masterclass

It’s so exciting and fascinating to build a future where things work according to the rules and laws of nature. Thanks to Feynman for letting us know this. David Deutsch, Shor and many other scientists and enthusiasts are working hard to achieve “Quantum Advantage”. I also thank my parents who brought me into this era where quantum computing is growing exponentially day by day, if they didn’t I might be someone in the future who just uses a quantum computer but I would never know how they had originated and I guess now you should thank your parents too!

Take a deep breath, thank them and search on.

3. Do we need to replace classical computers with quantum computers?

To be precise we are not going to replace classical computers with quantum computers, at least not soon. Both of them have their own advantages and disadvantages, one cannot use a quantum computer at room temperature and they are very costly. Classical computers are user friendly, we can carry them wherever we want to and they are available at low prices when compared to quantum computers. So don’t fall for them when they say ‘Quantum computers are going to replace classical computers’.

Congratulations! You have made it to the end of this article and now you have a basic understanding of how quantum computers work, pretty interesting right? Now you might be wondering, what should be my next steps?

Join our social media platforms for more interactive content on quantum computing and please feel free to ask anything related to quantum! Here is the link to the course in case if you have missed the above one — Quantum Computing with Qiskit Ultimate Masterclass

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