16 Companies Developing Quantum Algorithms

Image by Gerd Altmann from Pixabay

A Background To Quantum Algorithms

It is generally regarded that 1981 was the year quantum computing first appeared to the world. The Nobel Laureate Richard Feynman, a quantum visionary, had given a seminal speech at the First Conference on the Physics of Computation, organized in collaboration with MIT and IBM. In the speech, Feynman identified that it would be impossible for a classical computer to simulate quantum mechanical processes. To do it, he proposed, a completely new kind of computer would be required, one that was aligned to the laws of quantum mechanics.

Unfortunately, a classical computer is inadequate at dealing with this as the exponential growth of data in a quantum system is far beyond its limits utilizing sub-exponential space and time complexity. A quantum computer, however —  based on a quantum system that makes use of the non-classical properties — can process exponentially large amounts of data in only polynomial time. This is the uniqueness of the system.

With such a show of computational force using quantum mechanics, there are several fields that can benefit outside the remit of Newtonian mechanics. These include, but are not exclusive to, mathematics, cryptography and information theory.

Of all the buildouts realized from quantum information theory and computation, it is a paper by professor of applied mathematics at MIT Peter Shor which is the most influential. Shor’s algorithm, first published in 1997, is an immense achievement of human intellectual power. The quantum algorithm, then, performs prime factorization of integers in polynomial time.

But what does this actually achieve?

In a word, it gives us the power to exponentially speed up and even beat the fastest of algorithms built from classical systems. As of yet, there are no known classical algorithms that can successfully factor integers into prime numbers. By using quantum algorithms like Shor’s, it is possible to do things that previously were thought impossible, like breaking public-key cryptographic systems like RSA, which rely on classical algorithms’ inability to crack them.

Since Shor’s algorithm came into being more than twenty years ago, there have been many quantum algorithms devised for use on the ever-expanding quantum computing hardware that is being developed by the likes of D-Wave Systems, Google, IBM and Microsoft.

And that, no doubt, is set to continue as we move into this next decade.

The quantum decade.

With that in mind, TQD thought it time to put out its own list of the players in the quantum computing industry that are developing quantum algorithms to service the growing ecosystem, based on the wealth of data available at The Quantum Insider (TQI), our very own data platform.

I have omitted all the large public companies, for one, though there are still several big private players represented. Why? Well, it’s always good to give the smaller fish a chance, isn’t it?

1. 1QBit


1QBit is a Canadian QC company founded in 2012 that seeks to apply computation to ML and optimization science via its hardware-agnostic software platform. And its 1Qloud™ platform — using novel quantum-inspired optimization solutions — is part of this.

This hardware-agnostic approach allows researchers, developers and data scientists to exploit the amazing power of computers inspired by quantum mechanics and state-of-the-art quantum-based algorithms without prior knowledge of “each individual hardware platform or to manage complex and expensive computing infrastructure.”

1QBit’s Graph-Based Molecular Similarity (GMS) tool will be adopted by pharmaceutical companies to perform virtual screening and assisting in drug discovery while the company’s Quantum-Inspired Hierarchical Risk Parity (QHRP) method utilizes quantum-inspired technology and advanced hardware accelerator and is just the thing for optimizing portfolios.

Have routing and scheduling headaches? 1QBit’s Advanced Routing and Scheduling Platform combines the power of quantum-inspired hardware with novel formulations to eradicate complex logistical and mobility problems and optimize production tasks etc.

2. Algorithmiq


Founded in 2020, Algorithmiq is based in Turku, Finland and focuses on complex system approaches combined with quantum algorithms to tackle computationally costly problems in drug design. Still very much in stealth mode as we speak, get ready to hear more from this company in the very near future.

3. Cambridge Quantum Computing

One of the most high-profile QC companies in the British Isles, Cambridge Quantum Computing (CQC) was founded back in 2014. Its t|ket⟩™ platform, an “architecture agnostic quantum software stack and ‘best in class’ compiler, translates machine-independent algorithms into executable circuits, optimizing for physical qubit layout whilst reducing the number of required operations.”

Along with this, CQC offers clients a suite of quantum algorithms for applications and programs.

In January of this year, the company announced its partnership with Roche. The collaboration with help design and implement noisy-intermediate-scale-quantum (NISQ) algorithms for early-stage drug discovery and development.


A Polish company established in 2016 with headquarters in Krakow, BEIT designs and implements quantum-inspired algorithms that solve all the relevant NP-complete class of problems.

BEIT’S algorithms offer solutions in vehicle routing. The startup’s QUBO Solver, on the other hand, returns optimal qubits assignment with its theoretical probability. The library for simplifying writing quantum programs in Python, called QUASAR, is available as open-source at GitHub and can be easily integrated with IBM Qiskit, Google Cirq, and OpenQASM.



CLASSIQ is an exciting QC startup from Israel. Founded in 2020, the company’s unique IP translates innovative ideas into original quantum algorithms.

So how does it do this? CLASSIQ’s platform synthesizes and analyzes any quantum circuit of your choosing. Compatible with all gate-level environments like Qiskit, Cirq and QSharp, the beauty of this platform is that it also allows the user to incorporate hardware-specific knowledge into your input, be it photonic or superconducting qubits, trapped ions and atoms or quantum dots.

6. Entropica Labs


Singapore-based Entropica Labs was established in 2018. Designing algorithms and software tools to operate on the leading cloud quantum computing platform partners IBM, Rigetti Computing and Microsoft, the startup’s hardware-driven approach guarantees ensure a “smooth integration, testing and benchmarking across models.”

7. ExaQ.ai


ExaQ.ai was founded in late 2020 and is based in Singapore and designs quantum ML algorithms and software tools. Utilizing the polyadic QML Library, ExaQ.ai trained a qmodel for the ternary classification of the Iris flower dataset on IBM quantum computers, achieving an accuracy level of classical ML.

Other offerings include The Polyadic QML Library, a Python library to define, train and deploy quantum ML models, the ManyQ quantum computer simulator optimized for ML and an early quantum ML algorithm called the Quantum Perceptron, a simulation of a two-qubit quantum computer.

8. HQS Quantum Simulations

HQS Quantum Simulations designs software for material scientists in the chemical industry and academia. Founded in Karlsruhe, Germany in 2017, HSQ uses ultra-modern, bespoke simulation software at the quantum level to evaluate the properties of molecules and materials.

9. Jij


Founded in 2018, Jij Inc is a Japanese quantum startup developing an optimization computation platform using the quantum Ising computer.

Designed to tackle optimization problems in a variety of industries and fields, Jij-X-OPT is a mechanism that includes a flexible middleware (Jij-Cloud).

10. JoS Quantum


Providing research services and the JSQ Innovation LAB to identify use cases and prototype quantum algorithms, JoS Quantum is a German startup founded in 2018.

With products ranging from EnerQuant, a project to develop solutions for models in energy markets that consist of complex optimization problems including stochastic components to a quantum algorithm for the sensitivity analysis of business risks, JoS Quantum’s Research as a Service (RaaS) focus is set to prepare the financial, insurance and energy sectors for the quantum era.

11. Ketita Labs

A spinoff from the University of Tartu, Estonia, Ketita Labs was set up in 2018 and is working on hybrid quantum-classical algorithms for near-term quantum computing. Very much in stealth mode to date, Ketita Labs is the second Finnish startup included on the list, impressive for a country of its size.

12. Phasecraft

Working on quantum modelling and simulation, this quantum software startup’s investigation into novel quantum materials is contributing to the development of superior batteries and more efficient solar cells while contributing to research simulating chemical reactions, new catalysts and the optimization of important industrial processes. For a more in-depth look at Phasecraft’s exciting IP, refer to the Insights section of the website where you can find access to the team’s research papers.

Phasecraft was founded in 2018 by professors from the University College London (UCL) and the University of Bristol.

13. QunaSys


QunaSys is a software developer founded in Japan in 2018. Having developed several important algorithms for chemical simulations, its software offering Qamuy is a powerful tool to support exploring problems facing quantum chemistry.

14. Semicyber


Based in McLean, Virginia, just across the Potomac River From Washington D.C, Semicyber develops and applies quantum algorithms to emerging technologies. The startup was founded in 2018.

15. Solid State AI

Solid State AI is a Canadian startup established in 2017. The Toronto-based company develops and deploys an ML software called AIMS (Artificial Intelligence for Manufacturing Systems) designed for advanced manufacturers to increase yields and throughput.

16. Zapata Computing


Due to the rules of the alphabet, Zapata Computing usually comes in last on every list TQD puts out, though that shouldn’t be an indication of the company’s unimportance in the sector.

Founded in 2017 and with headquarters in Boston, Zapata Computing is one of the most innovative companies in the space. Developing solutions for a whole gamut of industries that encompass chemistry, logistics, finance, oil and gas, aviation, pharmaceuticals, and materials, Zapata Computing’s state-of-the-art platform Orquestra combines a powerful software platform and open-source quantum algorithm libraries which deliver real-world advances in computational power for applications. Composing workflows in the YAML-compatible Zapata Quantum Workflow Language (ZQWL), the platform’s “wrappers” exist for open-source algorithms (e.g., from Qiskit, Cirq, and Forest).

Have we missed any out or got something wrong? If so, don’t hesitate to contact us at hello@thequantumdaily.com.

The Quantum Insider (TQI)


Just in case this list hasn’t satisfied your cravings for data on companies busy developing quantum algorithms for the market, you can pop on over to The Quantum Insider (TQI), TQD’s very own data platform. Here you can find deep and insightful information on all aspects of the QIS industry.

TQI is an invaluable resource for journalists, researchers, investors, companies, and government agencies looking to extend their knowledge of the growing quantum tech ecosystem!

James Dargan
James Dargan
James Dargan is a contributor at The Quantum Daily. His focus is on the QC startup ecosystem and he writes articles on the space that have a tone accessible to the average reader

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