Quantum Algorithms vs. Quantum-Inspired Algorithms

This article by Pedro Lopes originally appeared on The New Stack

Quantum computing, as a field, is very inspirational. The promise of solving hard computational problems beyond the reach of regular computers feeds our hope of deploying energy-efficient solutions to logistics problems, of speeding up and saving costs in material and drug discovery with more realistic ab-initio simulations, and better predicting the behavior of complex dynamical systems that affects everyone’s lives - including weather and financial markets.

This inspirational view drew a lot of attention and investment to the field, and the fertile ground provided expected and the unexpected opportunity for growth. Among the unexpected topics that have been growing together with the quantum computing industry is the field of quantum-inspired solutions.

But what even are these? What is their relation to quantum computing? Since quantum-inspired solutions are growing in tandem with the quantum computing industry, sometimes competing for resources, it should do well to revisit the topic and bring some clarity to the questions and provide perspective on expectations for current and future end-users.

Quantum-inspired algorithms usually refer to one of two things: (i) classical algorithms based on linear algebra methods — often methods known as tensor networks — that were developed in the recent past, or (ii) methods that attempt to use a classical computer to simulate the behavior of a quantum computer, thus making the classical machine operate algorithms that benefit from the laws of quantum mechanics that benefit real quantum computers.

Regarding (i), while the physics community has leveraged these methods to address problems in quantum mechanics since the 70s [Penrose], tensor networks have an independent origin as far back as the 80s in neuroscience. In reality, there is nothing truly quantum behind about them; they are fundamentally based on linear algebra.

For (ii), the process of emulating a quantum system falls back on the limitations of classical hardware. Emulating the full dynamics of a large quantum system classically is extremely challenging, for the same reasons why one would prefer to build a real one!

So, does this mean that quantum-inspired algorithms are bogus? Not really. These are quite novel classical algorithms, and running state-of-the-art algorithms made for state-of-the-art hardware means that real situations arise where one can achieve a better performance for problem-solving today. In other words, running decades-old software in a freshly bought classical machines is unlikely to achieve optimal execution.

This performance improvement also helps drive the friendly competition between classical and quantum methods, guaranteeing those full quantum solutions really are doing their job of challenging — and beating — classical solutions.

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Organizations should ask themselves: What do I see as my journey through the quantum landscape? If the goal is to leverage the most recent developments in computational problem-solving to address the company’s current challenges, then pushing for the adoption of quantum-inspired solutions can be a reasonable approach.

However, if the goal is to truly explore the limits of classical computation within their business and prepare for quantum disruption, then settling for quantum-inspired approaches may not be sufficient.

Even if a company's immediate goal is to find solutions for today, it does not necessarily need to limit itself to quantum-inspired solutions. The advancement of new application-specific quantum hardware, often referred to as analog quantum computers, has introduced machines with real quantum coherence and scale, with hundreds of qubits, which have already demonstrated value in specific scientific applications.

The goal of this type of hardware is to limit the breadth of applicability, favoring performant use of quantum resources for particular use cases. While gate-based machines are universal, they are limited to a few tens of qubits that can be emulated on a laptop.

The new analog quantum computers cannot be easily emulated with classical hardware, and there is ongoing debate regarding whether their success in scientific applications will translate to more general applications.

It is worth noting that we mentioned two types of quantum-inspired methods: case (i) does not necessarily bring anyone closer to quantum readiness, but a case can perhaps be made for situation (ii), where the methods being emulated are closer to what a quantum computer would perform. This means that transitioning from a quantum-inspired solution to a fully quantum solution, once quantum hardware reaches the required level, may involve a lower adaptation barrier.

Furthermore, even if, at times, these methods do not really have anything to do with the real quantum in quantum computing, these methods provide a venue for companies to really improve their solutions for problems of today, with ROI today.

This means that these methods can really contribute to bridging the development and adoption of quantum technologies through valleys of pessimism or lower investment, helping upper management keep engaged with the technology as it evolves to full maturity.

Despite the advent of quantum computing, classical computing has not stagnated. Quantum-inspired methods are but one of the new developments of classical computing that participate in the productive competition that brings both fields farther ahead. But if your aspiration is to be quantum-ready, you will probably need more than inspiration. You will need to be quantum.

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Image by Faizal Sugi from Pixabay

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