# ‘Quantum Memory’ Proves Exponentially Powerful

## Introduction

It’s not easy to study quantum systems — collections of particles that follow the counterintuitive rules of quantum mechanics. Heisenberg’s uncertainty principle, a cornerstone of quantum theory, says it’s impossible to simultaneously measure a particle’s exact position and its speed — pretty important information for understanding what’s going on.

In order to study, say, a particular collection of electrons, researchers have to be clever about it. They might take a box of electrons, poke at it in various ways, then take a snapshot of what it looks like at the end. In doing so, they hope to reconstruct the internal quantum dynamics at work.

But there’s a catch: They can’t measure all the system’s properties at the same time. So they iterate. They’ll start with their system, poke, then measure. Then they’ll do it again. Every iteration, they’ll measure some new set of properties. Build together enough snapshots, and machine learning algorithms can help reconstruct the full properties of the original system — or at least get really close.

This is a tedious process. But in theory, quantum computers could help. These machines, which work according to quantum rules, have the potential to be much better than ordinary computers at modeling the workings of quantum systems. They can also store information not in classic binary memory, but in a more complex form called quantum memory. This allows for far richer and more accurate descriptions of particles. It also means that the computer could keep multiple copies of a quantum state in its working memory.

A few years ago, a team based at the California Institute of Technology demonstrated that certain algorithms that use quantum memory require exponentially fewer snapshots than algorithms that don’t use it. Their method was a major advance, but it required a relatively large amount of quantum memory.

That’s something of a dealbreaker, because as a practical matter, quantum memory is hard to come by. A quantum computer is made of interconnected quantum bits called qubits, and qubits can be used for computation or memory but not both.

Now, two independent teams have come up with ways of getting by with far less quantum memory. In the first paper, Sitan Chen, a computer scientist at Harvard University, and his co-authors showed that just two copies of the quantum state could exponentially reduce the number of times you need to take a snapshot of your quantum system. Quantum memory, in other words, is almost always worth the investment.

“These two- or three-copy measurements, they’re more powerful than one might think,” said Richard Kueng, a computer scientist at Johannes Kepler University Linz in Austria.

To prove this, Chen and his co-authors combined information theory, an area of mathematics that studies the transmission and processing of information, with specialized techniques used in quantum error correction and classical simulations of quantum computation.

The day after this work appeared on the scientific preprint site arxiv.org, a group based at Google Quantum AI in Venice, California, posted another paper that arrived at a similar conclusion. This work focused on applications in quantum chemistry.

The combined results also speak to a more fundamental goal. For decades, the quantum computing community has been trying to establish quantum advantage — a task that quantum computers can do that a classical one would struggle with. Usually, researchers understand quantum advantage to mean that a quantum computer can do the task in far fewer steps.

The new papers show that quantum memory lets a quantum computer perform a task not necessarily with fewer steps, but with less data. As a result, researchers believe this in itself could be a way to prove quantum advantage. “It allows us to, in the more near term, already achieve that kind of quantum advantage,” said Hsin-Yuan Huang, a physicist at Google Quantum AI.

But researchers are excited about the practical benefits too, as the new results make it easier for researchers to understand complex quantum systems.

“We’re edging closer to things people would really want to measure in these physical systems,” said Jarrod McClean, a computer scientist at Google Quantum AI.