How Advanced Mathematics is a Must in Quantum

Quantum Information Science(QIS), in particular, the subfield of Quantum Computing, can be very mathematical depending on where one is landing. For working on quantum algorithms, due to a lack of high-level programming abstractions, programming is still being done at the gate level. So understanding the underlying abstract mathematical structures underpinning the quantum gates, such as Lie Groups, is a must. Even when abstractions are built in the coming years, having access to advanced mathematical machinery will be vital to building nontrivial game-changing quantum algorithms. 

We offer comprehensive mathematical support services for designing, evaluating and implementing state-of-the-art projects in the following areas:

Quantum Data Encoding (QDE): Data encoding, in particular, classical-to-quantum data encoding is one of key barriers to leveraging the exponential computational power that quantum computing can bring. We live in a world where classical data is very abundant, however classical data cannot be loaded straight into a quantum computer! To run a quantum algorithm in against classical data, it needs to be enconded first into quantum state(s). There are several proposed methods for doing so, including; angle encoding, amplitude encoding, basis encoding, QRAM encoding etc.

Quantum Error Mitigation (QEM): Although NISQ hardware is becoming ever more accessible via the cloud, there are still many technical challenges before they become useful. This is because NISQ hardware is prone to errors stemming from the fact that the fundamental building blocks of quantum computers (qubits) can only perform computation over a very short period in the best NISQ hardware before breaking down (decoherence). This means that the results of the quantum computations can be more inaccurate the longer our algorithms run! Quantum error correction is not feasible for the current NISQ hardware due to the lack of a large number of qubits needed. Hence, error mitigation is a reasonable workaround that could give us the best chance to help address this problem, potentially making NISQ hardware practical for non-trivial problems. There have been quite a few QEM protocols proposed in the literature over the past few years, including; Probabilistic Error Cancellation (PEC), Zero-Noise Extrapolation (ZNE), etc.

Quantum Error Mitigation (QEC): QEM somewhat bridges the gap between the current NISQ devices and Fault-Tolerant Quantum devices for specific algorithms developed for the NISQ era (an excellent review of NISQ algorithms can be found here). However, to be able to run quantum algorithms such as the famous Shor's algorithms that are known to provide a computational advantage over classical counterparts, we'll need quantum error correction! Several quantum error correction codes have been proposed in the literature over the past few years, including the famous surface codes (see an introduction here), which provide rich connections between Algebraic Topology, Geometry and Quantum Information Science.

Quantum Machine Learning (QML): Analogous to Classical machine learning, Quantum machine learning (QML) aims to create models capable of learning from data encoded in quantum states. Hence, one can see that data encoding is critical!  There have been novel research ideas around understanding the symmetries of models' underlying datasets. This is part of a new active subfield of QML known as 'Group-Invariant Quantum Machine Learning, which exploits group-invariant models that produce invariant outputs under the action of any element of the symmetry group G associated with the dataset (more details here).

How our Approach is Different?

Firstly, we deeply understand the enormous pressure enterprise organisations face to evolve and embrace next-generation technology in an ever-growing competitive global digital market where playing catch up with competitors in terms of new technology can be very costly in the long-run. The key outcome of our Quantum consulting service is to help data-driven enterprise organisations build the mathematical capabilities that redefine their business models to stay relevant, compete, and be leaders in their core markets. Secondly, our consulting team comprises the brightest young PhD-level mathematicians who complete our tailored academia-to-industry transition program with an emphasis on Quantum technologies.  Here are some of the benefits of working with us:

• Frictionless remote collaboration with your in-house engineering leads and quantum researchers to help identify the critical mathematical gaps in your Quantum project(s).
  
• Deployment of PhD-level mathematicians to help in-house Quantum R&D teams leverage advanced branches of mathematics, such as; Abstract Algebra, Algebraic Topology, Algebraic Geometry, Functional Analysis & Measure Theory.
  
• Source and manage PhD level talent pipeline tailored to your needs and with long term retention in mind.
  
• Upskill your existing Quantum research team members with a tailored mathematical curriculum based on specifics of each R&D project.
  

Our team is ready to help your organisation transform its operations at the intersection of frontier Quantum research innovation and customer needs.  Would you like to learn how we can unlock your in-house technical talent superpowers with our collaboration while preserving your independence?

 
Get in touch with our team today!