Quantum simulation reveals the secrets of superdiffusion

Quantum computing

The research using IBM's preliminary quantum computer that includes 27 superconducting qubits signifies an important advancement in executing complex quantum transport computations. The study was recently featured in the Nature journal NPJ Quantum Information.

Quantum computing is inching closer to commercial applications. Trinity and IBM Dublin's collaborative project addresses one of the riveting fundamental questions of quantum simulation. Professor John Goold, Director of Trinity Quantum Alliance, who led the study, explains the magnitude of this accomplishment.

He said that simulating the dynamics of a complex quantum system is a daunting task for regular computers. Consider a device with 27 qubits (quantum bits): to describe this system, a conventional computer must store about 134 million coefficients in memory. As the number of qubits increases say to 300, the demands become so immense that no standard computer can handle it. Nobel-winning physicist Richard Feynman proposed the idea of using quantum systems to simulate quantum dynamics and pointed out that quantum computers could naturally describe these systems, avoiding the massive demands on conventional computers.

The research team focused on simulating spin chains, which are little connected magnets used to understand magnetism. They were exploring a model called the Heisenberg chain and were interested in how spin excitations move across the system over time. They discovered something called superdiffusion, governed by an equation usually associated with growth phenomena like the height of snow during a snowstorm or how a stain on cloth spreads. Amazingly, the same equations apply in quantum dynamics, and the team was able to verify this using a quantum computer. This was the primary achievement of their work.

A closer look at the simulation

Professor Goold elaborated on the simulation: "We explored a regime where superdiffusion occurs, governed by the Kardar-Parisi-Zhang equation. It is incredible how the same equations that describe phenomena like snow growth during a snowstorm can be applied in quantum dynamics. Our main achievement was verifying this through the quantum computer."

Programming challenges and achievements

Nathan Keenan, the IBM-Trinity predoctoral scholar, sheds light on the challenges of programming quantum computers. "The operations performed at the chip level are imperfect. You want to minimize the runtime of a program to shorten the time in which errors can affect your result," he shared.

Juan Bernabé-Moreno, Director of IBM Research UK & Ireland, voiced his enthusiasm about IBM's commitment to advancing quantum computing technology and expressed delight over the promising results of the collaboration with Trinity College Dublin.

A new era

As the world embarks on a new era of quantum simulation, Trinity's quantum physicists are leading the way, scripting the future of technology. Quantum simulation, now a central research focus, is further reinforced by the newly launched Trinity Quantum Alliance, founded and directed by Prof. John Goold.

IBM's collaboration with Trinity has once again underscored the rapidly developing landscape of quantum computation, opening new avenues and reinforcing the belief that quantum physics is not just a theoretical but a practical path to the future's technological marvels.

The study was published in the Nature journal NPJ Quantum Information

Study abstract:

Understanding how hydrodynamic behaviour emerges from the unitary evolution of the many-particle Schrödinger equation is a central goal of non-equilibrium statistical mechanics. In this work, we implement a digital simulation of the discrete time quantum dynamics of a spin-1/2 XXZ spin chain on a noisy near-term quantum device, and we extract the high temperature transport exponent at the isotropic point. We simulate the temporal decay of the relevant spin correlation function at high temperature using a pseudo-random state generated by a random circuit that is specifically tailored to the ibmq-montreal 27 qubit device. The resulting output is a spin excitation on a homogeneous background on a 21 qubit chain on the device. From the subsequent discrete time dynamics on the device we are able to extract an anomalous super-diffusive exponent consistent with the conjectured Kardar-Parisi-Zhang (KPZ) scaling at the isotropic point. Furthermore we simulate the restoration of spin diffusion with the application of an integrability breaking potential.