**Simulating quantum critical dynamics in a D-Wave quantum annealer**

By Andrew King, Director of Performance Research, D-Wave

The best examples are simple. This is especially true in quantum computing, where complexity can get out of hand pretty fast. A team of researchers at D-Wave, with collaborators from USC, Tokyo Tech, and Saitama Medical University, recently explored a quantum phase transition — a complex subject by anyone’s standards — in a very simple 1D chain of magnetic spins. Our work, published today in Nature Physics, studies quantum critical dynamics in a coherently annealed Ising chain. Here are a few things we learned along the way.

**Programmable quantum phase transitions, as ordered**

Phase transitions, such as water to ice, are commonly attributed to changes in temperature. But there is another type of phase transition — -a quantum phase transition (QPT) — -where quantum effects determine the properties of a physical system, in the absence of thermal effects. In a 1D chain, spins at the end of the simulation are either “up” or “down”, and we get “kinks” separating blocks of up spins and down spins (during the simulation, spins can be in a superposition of up and down). The density and spacing of kinks depend on, among other things, the speed and “quantumness” of the experiment. In this work we guided the programmable system of spins through a QPT and investigated the effect of varying parameters such as speed, system size, and temperature.

In the simple 1D case, we know what to expect. Behavior is qualitatively described by the “Kibble-Zurek mechanism”, a widespread phenomenon seen in both early-universe cosmology and condensed matter systems. Moreover, the quantitative details are known: dozens of papers have been published on the subject, some including closed-form equations that predict the outcome of our experiments.

This foundation gave us our first lesson: Our experimental measurements, using up to 2000 qubits, are in close agreement to these equations — -within a few percent. Confirming this in a well-understood setting is an important step on the way to simulating more exotic systems, where classical simulation is intractable and we don’t know what to expect from a quantum simulator.

This isn’t the first time phase transitions have been studied in a D-Wave processor, and it isn’t the first quantum simulation of this QPT. But this is the first QPT simulated in a D-Wave processor, and the experiments exceed previous work in terms of size, programmability, and the ability to generate long-range quantum correlations.

**Coherent quantum annealing and thermal effects**

Quantum coherence is the stock-in-trade for macroscopic quantum phenomena, including lasers, superconductors, and, of course, quantum computers. But experiments on coherence in quantum annealing — -the approach used here — -have been limited. In this research, experiment matches theory for fast experiments, indicating coherent behavior with no thermal effects from the environment. This is another important piece of evidence that we have a programmable quantum system.

When we slow down, we start to exchange energy with the environment. This leads to decoherence, and in some cases we observe “anti-Kibble-Zurek” behavior. In other cases, we see a smooth crossover to a finite-temperature quantum system, with no increase in energy. This confirms what we expected: decoherence in a quantum annealer does not bring the computation toward random output, which is the unfortunate case in gate-model quantum computing. Rather, the effects are relatively graceful, and can be reduced by controlling noise in the environment. This is a priority at D-Wave, where we are now developing both gate-model and annealing-based quantum computers.

**A foundation for “intractable” simulations**

Richard Feynman famously proposed the simulation of quantum systems via programmable realizations, and this is what we intend to do. In this work, we demonstrated the ability to accurately simulate programmable QPTs. So what’s next? Systems that are not so well understood. This includes the simulation of exotic and novel QPTs. It also includes the application of QPTs to classical optimization, where we hope to demonstrate — and understand — a computational advantage over classical methods.

*Disclaimer*: This post contains forward-looking information. Please see the disclaimer in press release.