Quantum computing has emerged by leaps and bounds in the past few years. In fact, once big tech companies like IBM, Microsoft, and Google started showing interest, they kind of stopped being tracked. However, research continues on the basic elements of quantum computing and is, to me, more interesting than the engineering achievements of commercial laboratories (which are still absolutely necessary).

In line with my interests, a group of researchers recently demonstrated the first quantum memristor. This could be a crucial step in bringing a kind of highly efficient neural network into the realm of quantum computing without a large number of quantum connections.

## Memristors and Quantum Addition

The concept of the memristor dates back to the 1970s, but has long remained like a sock under a washing machine: forgotten and not missed. The basic idea is that the current flowing through the memristor depends not only on the voltage applied across the terminals but also on the *Date* of applied voltage. Physical applications of memristors offer great promise for low-power computing because they can be used to make energy-efficient memory.

A quantum memristor, when viewed in light of quantum information, is a bit more complex. 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 a rational number being one or a rational zero, it may be in a state of quantum superposition. The value of a qubit is only known when we measure it – the measurement always reveals either a one or a zero. The *Probably* Getting 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 so that the results can be read.

Now, think of a memristor in this scheme. The memristor must modify the quantum state of the qubit based on *the value* of the previous qubits. This means two things. First, the memristor must preserve the quantum properties of the qubit (otherwise no further operations can be performed). Second, to determine its internal state, the memristor must measure qubits, which erases its properties. In a sense, this means that a perfect quantum memristor cannot exist (for reference, there are two theorists who resent the idea of a classical memristor, so this is not a new area).

## split the difference

This discrepancy didn’t deter the researchers, they were able to create a quantum memristor anyway. Let’s start with the essence of the idea. Imagine you have an imperfect mirror. If you target the mirror with a single photon of light, the photon will either be reflected off the mirror or transmitted, with a probability that depends on the extent of the mirror’s reflection. Suppose you count the photons sent and use this number to change the reflection of the mirror. This effectively creates a memristor – but not a quantum memristor.

To add quantitative happiness, we have to modify the experience a little. We replace the light source with one that sends beams containing either a single photon or no photon (a superposition state of a single photon or zero). Beams reflected from the mirror retain their superposition state and can be used for future calculations, while beams that are sent are measured to modulate the reflection of the mirror. Now we have a complete quantum memory: the probability of a future qubit reflection by the mirror is modulated by *Stream* Qubit country.

Implementing this in practice is a bit more complicated, 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 worked as expected.

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