Even noisy quantum computers may soon have the potential to provide a quantum advantage over classical methods for some condensed matter problems.

Matters’ constituent particles can interact in a variety of ways based on their intrinsic properties. These interactions manifest themselves as materials with properties that serve functions in every aspect of our lives — whether solid, liquid, or gas. Some interactions between particles, however, can give rise to exotic properties and phases of matter, like superconductivity or ferromagnetism. Condensed matter physicists study how inter-particle interactions give rise to these interesting behaviors. And the physics of these interactions is described by the laws of quantum mechanics, which was one of the first motivations for building and simulating them on a quantum computer.

Condensed matter physics has important implications for our understanding of nature and the development of new technologies. Advances made by condensed matter physicists have led to seminal inventions, like the development of the transistor, and the building blocks of IBM Quantum processors’ superconducting qubits with Josephson junctions.

Given the importance of furthering our understanding of matter, we’re excited that IBM Quantum systems make ideal laboratories to study condensed matter physics. And while condensed matter physicists often must rely on large collaborations or costly hardware to run their experiments, our cloud-based quantum processors enable users to make potentially groundbreaking advances in condensed matter physics with little more than their laptop and a user account with IBM Quantum.

## Spinning up real world condensed matter physics research

In fact, a small team of researchers employing even today’s noisy quantum computers can make a valuable impact. An active area studied by condensed matter physicists is the dynamics of interacting spin systems. Spin is a crucial property of elementary particles that could be described by the clockwise or counter-clockwise spinning of toy tops, but with a quantum take.

The two states of a quantum bit form a natural analogue to the “up” and “down” spins, and interactions between spins can be easily toggled by our systems’ control pulses. The connectivity of our qubits therefore allows users to naturally simulate the dynamics of spin lattices, and explore how the collective behavior of spins change under the influence of external forces.

For example, a paper by researchers at the Autonomous University of Madrid (UAM)^{1} simulates the dynamics of a one-dimensional Ising model — essentially, a line of particles in one of the two spin states that could interact only with their neighbors — in the presence of external magnetic fields both parallel and perpendicular to the system. They recreated this system on the *ibmq_paris* system’s 27-qubit processor.

Another study by researchers at Lawrence Berkeley National Laboratory^{2} simulated another canonical spin system described by the Heisenberg model

To learn more about the Heisenberg model, join this year’s IBM Quantum Open Science Prize, which asks participants to simulate a Heisenberg model Hamiltonian for a three-particle system on one of IBM Quantum’s 7-qubit systems. Register here.

*ibmq_paris*system. In each case, the teams found that they could accurately calculate relevant properties of the systems that they were studying, and could significantly enhance the quality of their simulations with error mitigation techniques, even on existing noisy processors.

Crucially, these teams were able to run their simulations without any specialized equipment; they simply had to run their quantum programs on a cloud-based IBM Quantum computing system. Dozens of papers published on the *arXiv* physics pre-print server, including our own experiments with our 27-qubit processors, have demonstrated the power of IBM Quantum processors in simulating spin dynamics. Even noisy quantum computers may soon have the potential to provide a quantum advantage over classical methods for some condensed matter problems.

## Using a quantum computer to understand phases of matter that act like a crystal in time

Other researchers are using quantum computers to study phases of matter beyond what we can create in the lab. This past May, two researchers at the University of Melbourne

Another team at the University of Melbourne recently published two research papers that detail the generation of a 27-qubit genuine multipartite entangled state and, separately, the generation of a 65-qubit bipartite entangled state. These results with IBM Quantum processors demonstrate one of the largest entangled states yet created. Read more.

^{3}on

*arXiv*— using

*ibmq_manhattan*’s and

*ibmq_brooklyn*’s 65-qubit processors to simulate a chain of 57 driven spins with nearest-neighbor interactions. The traditional crystal is a spatial crystal, such as matter composed of a lattice of atoms in a stable, preferred structure in space. The idea of the time crystal posits that perhaps there exists some phases of matter that act like a crystal in time, with states that have a periodicity in time. Physicists have been actively studying driven spin systems as a platform for the realization of such phases of matter.

Thanks to IBM Quantum’s cloud-based quantum systems, accessing hardware capable of creating powerful simulations of spin systems is as easy as signing up for an IBM Quantum account. This access provides researchers with important tools to enable ground-breaking advances so that they can push the field of condensed matter physics forward on their own. Meanwhile, members of the open source Qiskit community are constantly creating new solutions and sharing knowledge on how to get ideas off the ground.