Quantum computing has come on in leaps and bounds in the last few years. Indeed, once the big technology companies like IBM, Microsoft, and Google started showing an interest, I kind of stopped keeping track. Nevertheless, research on the basic elements of quantum computing continues and is, for me, more interesting than the engineering achievements of commercial labs (which are still absolutely necessary).

In line with my interests, a group of researchers demonstrated the first quantum memristor recently. This may be a critical step in bringing a type of highly efficient neural network to the world of quantum computing without an eye-watering large number of quantum connections.

Memristors and adding the quantum

The concept of the memristor dates back to the 1970s, but, for a long time, it sat like a sock under your washing machine: forgotten and un-missed. The essential idea is that the current that flows through a memristor doesn’t just depend on the voltage that is applied across the terminals but also on the history of applied voltage. Physical implementations of memristors offer great promise for low-energy computing because they can be used to make energy-efficient memory.

A quantum memristor, when considered in light of quantum information, is slightly more complicated. A qubit, which stores a single bit of quantum information in its quantum state, doesn’t necessarily have a well-defined bit value. Instead of being a logical one or logical zero, it may be in a quantum superposition state. The value of the qubit is only known when we measure it—a measurement always reveals either a one or a zero. The probability of obtaining a logical one (or zero) is governed by the properties of the quantum superposition. 

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The job of a quantum computer is to gently modify these probabilities through interactions with other quantum superposition states until the results are read out.

Now, consider a memristor in this scheme. A memristor should modify the quantum state of a qubit based on the value of previous qubits. That means two things. First, the memristor has to preserve the quantum properties of a qubit (otherwise no further operations can be performed). Second, to set its own internal state, the memristor has to measure a qubit, which wipes out its properties. In some sense this means that the perfect quantum memristor cannot exist (for reference, there are theorists who are offended by the idea of the classical memristor, so this is not new territory).

Splitting the difference

Undeterred by this contradiction, researchers have managed to create a quantum memristor anyway. Let’s start with the core of the idea. Imagine you have an imperfect mirror. If you target the mirror with a single photon of light, the photon will either reflect off the mirror or be transmitted, with a probability that depends on how reflective the mirror is. Let's say you count the transmitted photons and use that number to change the reflectivity of the mirror. This effectively creates a memristor—but not a quantum memristor.

To add quantum happiness, we have to modify the experiment slightly. We replace the light source with one that sends packets that either contain a single photon or no photon (a superposition state of one or zero photons). The packets that are reflected from the mirror preserve their superposition state and can be used for future computation, while those that are transmitted are measured to modify the reflectivity of the mirror. Now we have a full quantum memristor: The probability of a future qubit being reflected by the mirror is modified by the current qubit state.

Implementing this in practice is a bit more complex, and the researchers used different photon properties than just the number of photons. However, the behavior (and the mathematical model) are the same, and the quantum memristor functioned as expected.