Quantum Games Unveil New Possibilities in Phases of Matter, Study Finds

Researchers from the University of Colorado Boulder, California Institute of Technology, University of Sydney, and Quantinuum have introduced a family of multiplayer quantum games that use topologically ordered phases of matter to secure quantum advantage. Unlike previous examples, the quantum advantage in these games is robust to arbitrary local perturbations and persists away from the exactly solvable point. The team demonstrated this robustness on Quantinuum’s H11 quantum computer. The research presents a significant step forward in understanding and applying quantum phases of matter in quantum computing, opening up new possibilities for the use of quantum hardware.

What are Manybody Quantum Games and How Do They Relate to Phases of Matter?

Manybody quantum games are a new perspective on phases of matter in quantum hardware. They relate the quantum correlations inherent in phases of matter to the securing of quantum advantage at a device-oriented task. In a recent paper, a team of researchers from the University of Colorado Boulder, California Institute of Technology, University of Sydney, and Quantinuum introduced a family of multiplayer quantum games. These games use topologically ordered phases of matter as a resource, yielding quantum advantage.

Unlike previous examples, quantum advantage in these games persists away from the exactly solvable point and is robust to arbitrary local perturbations, irrespective of system size. The researchers demonstrated this robustness experimentally on Quantinuum’s H11 quantum computer. They played the game with a continuous family of randomly deformed toric code states that can be created with constant-depth circuits, leveraging mid-circuit measurements and unitary feedback.

The researchers were able to tune through a topological phase transition, witnessed by the loss of robust quantum advantage, on currently available quantum hardware. This behavior is contrasted with an analogous family of deformed GHZ states for which arbitrarily weak local perturbations destroy quantum advantage in the thermodynamic limit.

How Does the Notion of Phases of Matter Apply to Quantum Devices?

The advent of noisy intermediate-scale quantum (NISQ) devices has opened up a new frontier for manybody physics, replete with fundamental questions that remain to be fully answered. One of these questions is whether the notion of phases of matter, the foundation of condensed matter physics, can be meaningfully applied to such devices. In other words, can phases of matter be realized and identified in a robust manner on quantum hardware, and can available hardware be continuously tuned between distinct phases of matter?

Another question is whether the notion of phases of matter has any bearing on the computational power of the device in question. For example, can the correlations inherent in phases of matter be harnessed to gain quantum advantage at certain tasks? How robust are these notions to gate imperfections or to noise? Can we harness the unique features of NISQ devices, such as direct access to the manybody wave function, to design novel probes of exotic physics?

These are some of the most pressing open problems at the intersection of condensed matter physics and quantum information science, and definitive answers are only beginning to emerge.

What are Multiplayer Nonlocal Quantum Games?

One stimulating recent development examines NISQ devices and manybody quantum states through the lens of multiplayer nonlocal quantum games. These are generalizations of Bell tests to the manybody context, which take advantage of the fact that measurements made on an entangled resource state can be more correlated than any classical local hidden-variable model would permit, a property known as contextuality.

Contextuality can be applied to gain quantum advantage at a suitably designed task, whereby a set of players who are not allowed to communicate with each other are required to output appropriately correlated answers to a set of questions such that there is no classical strategy that guarantees success at this task. Armed with an appropriately contextual resource state, the players can win the game with better-than-classical probability.

Insofar as the pattern of entanglement—and hence contextuality—is a property of a quantum phase of matter, there can therefore be a tight link between phases of matter and the ability to secure quantum advantage at a given task. This notion is crystallized in the context of measurement-based quantum computation (MBQC), where the success probability for a given quantum computation can be directly related to the presence of contextuality.

How Can Topologically Ordered Phases Be Harnessed for Quantum Advantage?

Unfortunately, the only games known to provide quantum advantage throughout a phase employ symmetry-breaking phases, which are not robust to symmetry-breaking noise. This is also the only setting in which it is known how to tune across a phase transition involving a long-range-entangled phase using a finite-depth quantum circuit on available hardware.

One might have thought it would be better to employ topologically ordered phases, which are robust to arbitrary local perturbations. However, it is not known how to robustly harness the quantum correlations inherent therein to gain quantum advantage, and relatedly, it is not known how to tune across a topological phase transition using a finite-depth circuit on available hardware.

In the recent paper, the researchers introduced a family of multiplayer quantum games that harness topological order to gain robust quantum advantage and demonstrated this advantage in experiments carried out on Quantinuum’s H11 device. They also explained how one may robustly tune through a topological phase transition using a constant-depth circuit that utilizes mid-circuit measurement and feedback, which is witnessed by the presence of quantum advantage or lack thereof.

What Does This Mean for the Future of Quantum Computing?

The researchers’ work presents a significant step forward in the understanding and application of quantum phases of matter in quantum computing. By demonstrating the robustness of quantum advantage in topologically ordered phases of matter, they have opened up new possibilities for the use of quantum hardware.

The ability to tune through a topological phase transition on currently available quantum hardware is a significant achievement. It not only demonstrates the practical applicability of these theoretical concepts but also provides a new tool for exploring and exploiting the unique properties of quantum phases of matter.

Finally, the researchers’ work also raises intriguing questions for future research. For example, how can the unique features of NISQ devices be harnessed to design novel probes of exotic physics? How can the correlations inherent in phases of matter be harnessed to gain quantum advantage at certain tasks? These are some of the most pressing open problems at the intersection of condensed matter physics and quantum information science, and the researchers’ work provides a promising direction for future research.