Quantum memristor: a memory-dependent computing unit

An abstract image intended to evoke a complex electronic processor.

Quantum computing has made leaps and bounds in recent years. Indeed, once big tech companies like IBM, Microsoft, and Google started paying attention to it, I kind of stopped following. Nevertheless, research into the basics of quantum computing continues and is, to me, more interesting than the engineering achievements of commercial labs (which are still badly needed).

In line with my interests, a group of researchers recently demonstrated the first quantum memristor. This may be a critical step in bringing a type of highly efficient neural network into the world of quantum computing without a 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 remained like a sock under your washing machine: forgotten and essential. The essential idea is that the current flowing through a memristor does not only depend on the voltage applied to the terminals but also on the the story of the applied voltage. Physical implementations of memristors hold great promise for low-power computing because they can be used to create power-efficient memory.

A quantum memristor, when viewed in light of quantum information, is slightly more complicated. A qubit, which stores a single bit of quantum information in its quantum state, does not necessarily have a well-defined bit value. Instead of being a logical one or a logical zero, it can be in a state of quantum superposition. The qubit’s value is only known when we measure it – a measurement always reveals a one or a zero. the probability to obtain a logical one (or zero) is governed by the properties of quantum superposition.

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

Now consider a memristor in this diagram. A memristor should change the quantum state of a qubit depending on the value previous qubits. This means two things. First, the memristor must preserve the quantum properties of a qubit (otherwise no other operation can be performed). Second, to define its own internal state, the memristor must measure a qubit, which erases its properties. In a 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).

Split the difference

Undeterred by this contradiction, the researchers still managed to create a quantum memristor. Let’s start with the heart of the idea. Imagine you have an imperfect mirror. If you aim a single photon of light at the mirror, 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 transmitted photons and use that number to change the reflectivity of the mirror. This does indeed create a memristor, but not a quantum memristor.

To add quantum bliss, we need to tweak the experience slightly. We replace the light source with one that sends out packets that contain either a single photon or no photons (a superposition state of one or zero photons). Packets that are reflected by the mirror retain their superposition state and can be used for future calculations, while those that are transmitted are measured to change the reflectivity of the mirror. We now have a complete quantum memristor: the probability that a future qubit will be reflected by the mirror is modified by the fluent qubit state.

Implementing this in practice is a bit more complex, and researchers have used different photon properties than just photon counts. However, the behavior (and mathematical model) is the same and the quantum memristor worked as expected.