# Preparing and stabilizing quantum states through engineered dissipation

April 9, 2024

Xiao Mi and Dmitry Abanin, Research Scientists, Google Research, Quantum AI Team

## Quick links

A quantum computer can solve certain problems exponentially faster than a classical computer. However, current realizations of its building blocks, qubits, are plagued by errors induced by uncontrolled interactions between quantum bits (or qubits) and the environment. Such interactions introduce *dissipation*, which destroys quantum entanglement, a necessary resource in quantum algorithms, and drives a quantum processor toward trivial, classical states. This *decoherence* process introduces errors, corrupting the utility of the quantum processor. As such, environmental dissipation is the main limiting factor for the current-generation quantum processors. Paradoxically, while uncontrolled dissipation is a bane of current quantum processors, *engineered* dissipation — created with a carefully tailored environment — may in fact aid a quantum processor by steering it into a desired entangled state.

In our latest work, “Stable Quantum-Correlated Many Body States via Engineered Dissipation”, published in *Science*, we explore this counterintuitive effect of engineered dissipation. Not only does this method offer a reliable way to prepare a quantum state, but it also naturally stabilizes the state so that it survives much longer than it would without the dissipation. These experiments lay the groundwork for improved methods to prepare strongly correlated states (which may be found in e.g. magnets) in a quantum processor, which could help physicists learn about exotic quantum materials, such as high-temperature superconductors, in the future.

## Background

Before a quantum processor can run an algorithm or simulation, all of its qubits must be initialized into a known state. This process, known as quantum state preparation, is often accomplished by applying quantum operations that are coherent — that is, they do not induce any dissipation. In this work, we instead couple the qubits to an environment that is tailored in just the right way so that the qubits are steered to their desired state through dissipation.

To demonstrate how this works, we can look at one of the simplest examples, where engineered dissipation is used to “cool” a quantum system toward its lowest energy state, known as its ground state. To accomplish this, we first connect the quantum system to another, auxiliary quantum system. Next we can transfer excitations from the system of interest to the auxiliary system, then remove the excitations via engineered dissipation. The removal of excitations gradually drives the system towards its entangled ground state (see illustration below).

In the past, some groups have prepared entangled states of up to eight atoms with engineered dissipation. But more intricate, many-body entangled states have been out of reach due to environmental decoherence caused by other, undesirable dissipation channels. With our Sycamore processor, we have developed fast reset capabilities that makes the desired engineered dissipation dominant over unwanted dissipation channels.

## Experiment

In this work, we use 35 qubits of a 49-qubit Sycamore processor to emulate magnetic spins, while the 14 remaining auxiliary qubits are used to mimic the previously mentioned tailored environment. We found that over time, this tailored environment imparts a cooling effect on the spin system and steers it toward the entangled ground state of a quantum spin model known as the transverse-field Ising model. In this model, an array of spins are positioned on a lattice, with each either pointing “spin-up” or “spin-down.” Neighboring spins interact with one another, and an external magnetic field is applied perpendicular to the spin alignment. Depending on the relative strengths between the spin interactions and the applied magnetic field, the system can be ferromagnetic or paramagnetic.

We demonstrate the effect of cooling on the spins in this model through a series of experiments. First, we set up a 1D system, where a chain of our “spin” qubits are connected in a line. Throughout this chain, every few qubits are also connected to auxiliaries that act as the dissipative environment (see figure below). We found that as the cooling cycles progress, the system settles into a correlated state that resembles the ground state of the 1D transverse-field Ising model. We then connect our qubits in a two-dimensional lattice (with auxiliaries dispersed throughout; see the middle panel below) to perform a similar experiment in 2D. We find that, in this 2D system, we can create antiferromagnetic correlations between the spins so that they anti-align with their neighbors.

When we apply techniques previously developed to mitigate errors, we found that we could dissipatively prepare ground states with fidelities of 90% for an 18-qubit system. This value matches the highest achieved fidelities at comparable system sizes using unitary circuits. We also demonstrated theoretically, in the same work, that the dissipative state preparation protocol scales more favorably vs. system size in terms of preserving state fidelity. These comparisons highlight the promise of the dissipative approach. The cooling algorithm is expected to be even more advantageous for more intricate correlated states, because once the coupling to the tailored environment is engineered, then you can just “set it and forget it.” The system naturally evolves to the desired state and stays there as long as the dissipation is happening.

Finally, we demonstrated that engineered dissipation has applications to non-equilibrium quantum phenomena beyond state preparation. Here we use a 1D system of 26 qubits to emulate a Heisenberg spin chain, a paradigmatic correlated system. We drive a current through the chain by periodically resetting the spins of two auxiliary qubits at either end. We first studied transferred magnetization, whose time dependence is observed to vary strongly depending on the underlying parameters of the model, in agreement with established theory (see below). At the so-called “isotropic point,” where exact solutions of the model are unknown, the team discovered a previously unknown phenomenon. At this point, we observed that the spin current has a distinct power-law dependence with time, which indicates a form of previously unknown, anomalous diffusion for this spin model. This result highlights the increasing functionality of the quantum processor as a tool for fundamental physics discovery, where the introduction of engineered dissipation unveils quantum phenomena that have never been observed or theoretically realized.

## Conclusion

This work shows that engineered dissipation strongly enhances the functionality of quantum processors, allowing for a conceptually new approach to preparing and probing quantum-correlated states. Engineered dissipation will aid in the preparation of strongly correlated states, which give rise to new quantum phases of matter that are found in materials such as magnets. Quantum materials are considered among the most promising applications of quantum processors, yet most other protocols for correlated state preparation are severely limited by unwanted decoherence. We believe the methods demonstrated here will also enable the preparation of intricate many-body states such as quantum spin liquids, which may aid in the synthesis of high temperature superconductors or new materials for data-storage.