## AWS Quantum Computing Blog

# Realizing quantum spin liquid phase on an analog Hamiltonian Rydberg simulator

This week at re:Invent, we announced the future availability of a Rydberg-atom based quantum computer from QuEra Computing. Launching in 2022, it will introduce a new quantum computing paradigm to Amazon Braket, Analog Hamiltonian Simulation (AHS).

AHS uses programmable quantum devices to emulate the behavior of other quantum mechanical systems. Already today, researchers in academia are using such special purpose devices to study quantum mechanical phenomena and fundamental physics models that would otherwise be hard to simulate on classical computers. In this post, we introduce you to the AHS quantum computing paradigm, and the type of workloads you will be able to run on the QuEra device on Amazon Braket. To illustrate the potential of this technology, we dive into a paper published in the journal *Science*. In the experiment, conducted by researchers at Harvard, MIT, QuEra Computing, and the University of Innsbruck, and with support from AWS, a Rydberg atom AHS device is used to prepare and study the properties of an exotic quantum phase of matter, a topological spin liquid. This work constitutes the first experimental verification of this quantum effect, expanding on the decades-long theoretical research on quantum spin liquids [for a detailed review, see Zoo of quantum-topological phases of matter].

**A new type of quantum computation**

Quantum computing is a nascent technology with many facets. Researchers around the world, including our teams at the AWS Center for Quantum Computing, are pursuing the goal of building a fault-tolerant quantum computer to unlock the full potential of this technology. On the other hand, customers are using Amazon Braket, the quantum computing service of AWS, to explore near-term applications of quantum computing in chemistry, optimization, and machine learning on the current generation of Noisy Intermediate Scale Quantum (NISQ) devices. While the hunt for error corrected devices and first industry applications continues, a different type of quantum computational devices is beginning to be used in academia for scientific discovery.

In the late 2000s, quantum optics researchers invented and built the first quantum gas microscopes; a new type of experimental device that enabled physical emulation of strongly-correlated many-body systems. Due to the quantum correlations in these systems, it is difficult to make theoretical or numerical predictions on their properties or behavior. Instead of using numerical algorithms to study the underlying mathematical models, researchers created an artificial setup where individual atoms move in a periodic potential, mimicking electrons in a solid-state material. With careful tuning of the experimental parameters, they replicated the conditions described by the Hubbard model, except at a much larger scale and slower pace than in an actual material. By spreading the dynamics over orders of magnitude larger space and time, the scientists were able to directly observe spatial correlation and time evolution to understand the fundamental physical effects that govern the behavior of electrons in certain materials, such as superconducting alloys. The data produced by the quantum gas microscopes provided direct evidence of the existence and nature of the phases of matter predicted by the Hubbard model.

Since these early ideas, such analog Hamiltonian simulations have been proposed and realized on a growing number of physical platforms, including trapped ions, Rydberg atoms with individual cavity modes, and superconducting qubits.

While the implementations are different, the basic idea is the same: First, you build a system with a high degree of control over the individual constituents of the system (e.g., individual atoms) and their mutual interactions. Then you tweak your system parameters in such a way that the time evolution of your system, governed by the so-called Hamiltonian, mimics the behavior of a system of interest. Finally, after the system evolves over a period of time, you take measurements to learn about the quantum phenomena inherent to the system. Because you are studying these effects in the engineered system, you have better control of the parameters to probe the behavior in different regimes. This allows you to observe the quantum mechanical effects at the level of the individual constituents to understand the underlying physical principles in detail.

While a fully programmable AHS device has the same computational power as a digital quantum computer, today’s AHS devices trade-off programmability for useful quantum size for a specific subset of problems. This is to avoid the overhead that is invariably introduced by digital approaches through the need to break down an arbitrary problem into the gate sets supported by the device. This makes AHS devices excellent candidates for the first demonstration of a *useful quantum advantage*. This approach is exactly in the spirit of Feynman’s original idea of quantum computation, as published almost 40 years ago:

“Nature isn’t classical […] and if you want to make a simulation of Nature, you’d better make it quantum mechanical, and by golly it’s a wonderful problem because it doesn’t look so easy. […] I want to talk about the possibility that there is to be an *exact* simulation, that the computer will do *exactly* the same as nature.” (emphasis in original)

– Richard P. Feynman, International Journal of Theoretical Physics, Vol 21, Nos. 6/7, 1982

**Analog quantum simulation with Rydberg atoms**

A particularly versatile platform for this kind of quantum computing is based on Rydberg atoms. In this approach, alkaline or alkaline earth atoms are trapped in an array of laser light. Lasers are tuned to lower the ground state energy of the atoms, attracting individual atoms to the high-intensity spots of the laser field. This enables arranging the atoms in customizable 2- or 3-dimensional spatial configurations (see Fig 1). Using an additional laser to excite the outermost electrons of these atoms to states with long range interaction (called Rydberg states), one can switch the interactions between atoms on and off. By tuning the spatial configuration, the interaction patterns, and other system parameters, Rydberg systems can implement a variety of different Hamiltonians. Over the past years, they have been proposed for simulation of quantum mechanical effects in fields ranging from condensed matter physics, high-energy physics, quantum dynamics, to quantum gravity.

**Studying quantum spin liquids with a Rydberg AHS device **

In the most recent work by Semeghini et al., published in the journal *Science*, the team of multi-national researchers showed how a Rydberg AHS device can be used to prepare and study an exotic quantum phase of matter, specifically a quantum spin liquid.

Quantum spin liquids have been theoretically described many decades ago with intriguing properties such as long-range entanglement and protected states that can be used for quantum information processing. While theoretically predicted, the experimental observation of this phase of matter has been elusive. The experiment described in the paper is the first experimental observation of this quantum effect, highlighting the potential of the Rydberg platform for scientific discovery. To understand what a spin liquid is, it is helpful to start with a pair of spins with antiferromagnetic interactions. To minimize the interaction energy, spins would anti-align, creating a so-called singlet state, which is a superposition of one spin pointing up and the other one down. If a third spin is added, it is no longer possible for every pair of spins to anti-align simultaneously, a situation that is commonly referred to as *frustration*. When many spins on a plane interact with their neighbors in a way that introduces frustration throughout the entire system, such as in an edge-Kagome lattice, a curious phenomenon can emerge. Throughout the entire ensemble, spins pair up with neighbors such that every spin is part of a singlet pair (see Fig 2). The ground state of the system, known as a quantum spin liquid, is the superposition of all states that fulfill this condition.

*topological order*, is an intriguing feature that enables the storing of information that cannot be changed by making small local changes. For this reason, using the entire system as a qubit prevents local errors, such as flipping the state of one of the atoms, from modifying the stored information (see Fig 3). The researchers from Harvard, MIT, QuEra Computing Inc., and the University of Innsbruck used a programmable Rydberg AHS device to create and probe a quantum spin liquid. For this purpose, they used individually controlled neutral atoms positioned on the edges of a Kagome lattice. Rydberg atoms have the property that when one of the atoms is in the Rydberg state, none of the other nearby atoms can simultaneously be in the Rydberg state, due to the so-called Rydberg blockade mechanism. The size of the blockade radius encompasses the six nearest atoms, such that every vertex of the Kagome lattice is connected to exactly one Rydberg atom. The number of configurations satisfying this condition is exponentially increasing with the system size and corresponds to the pairing of nearby spins into singlets on the Kagome lattice.

Semeghini and her collaborators showed the preparation of a state consistent with different configurations of each vertex being paired to one nearby Rydberg excitation. Combining measurements in different bases, and using topological string operators to rule out other topologically trivial phases, they found a region of parameters where all signatures point to a coherent superposition of such configurations, consistent with a quantum spin liquid. Moreover, by introducing a hole at the center of the system, they modified the underlying topology and showed the emergence of two topological sectors. Information stored across these two sectors would be protected from local disturbances due to the global order of the spin liquid phase.

**Conclusion**

Quantum computing is a rapidly evolving field with many different technologies and approaches. In this blog post, we introduced you to the concept of analog Hamiltonian simulation, a quantum computing paradigm that uses programmable devices to directly simulate physical systems of interest. Already today, researchers are using such devices to study quantum phenomena that otherwise would be hard to simulate on classical computers. The recent paper by Semeghini et al. illustrates this point. Using a programmable Rydberg device the authors realized, for the first time, a quantum spin liquid phase and analyzed its properties experimentally, exemplifying the type of scientific discovery that is enabled by analog Hamiltonian simulation. We are excited to soon bring this technology to customers of Amazon Braket, when we launch the QuEra device in 2022. Our goal is to bring AHS out of the lab and into the hands of scientists around the world, to accelerate research into important questions that will grow the understanding of the fascinating and powerful field of quantum physics.

To learn more about how AWS is accelerating research in quantum computing, see