Research

Quantum lego, tensor network and quantum error correction

Modelling quantum gravity with experiments

Overview

Our research group focuses on the interface of gravity, information, and emergent phenomena in quantum manybody systems.

Quantum mechanics and the theory of relativity are two pillars of modern physics. Their partial unification has led to important discoveries and conceptual advances. However, important inconsistencies remain to be reconciled. Quantum gravity aims to bridge these differences and unify general relativity and quantum mechanics.

Research in the past decades suggest that information plays a central role in understanding the nature of gravity; various advances were made possible by examining spacetime geometry and gravity under the lense of quantum information. Conversely, traditional concepts in gravity such as geometry and symmetry also exerts fruitful influence on quantum information science, allowing us to intuit otherwise abstract and complex quantum phenomena from a different perspective.

More specifically, we will study how space-time geometry and gravity can emerge from quantum information theoretic constructs like entanglement, complexity, and quantum error correcting codes. We will also borrow toolsets from quantum gravity and quantum manybody physics, such as tensor networks, to design useful constructs like error-correcting codes needed for fault-tolerant quantum computation. Finally, these efforts help bridge the gap between quantum gravity, which is traditionally a purely theoretical study, and experiments on quantum devices.

Quantum gravity and quantum information

With the work of Bekenstein, Hawking and many others, information made its debut in quantum gravity through our studies of black holes. These studies later led to other conceptual developments and counter-intuitive ideas where (quantum) gravity can be understood holographically.

A concrete realization of holography is the anti-de Sitter/Conformal Field theory (AdS/CFT) correspondence, which was first discovered as a consequence of non-perturbative string theory. This correspondence describes a strong-weak duality between two theories of different geometries and dimensions. This is an interesting scenario where we can study quantum gravity in a sandbox. Curiously, one can understand it as an instance where a theory of quantum gravity living in a higher dimensional bulk emerges from the lower dimensional CFT.

A key objective of this group is to understand how different aspects of spacetime and gravity can manifest themselves as emergent phenomena, both in AdS/CFT proper and in various quantum mechanical systems such as quantum error correcting codes. For instance, we study how spacetime geometry can be reconstructed from entanglement data of the CFT. Techniques and findings from quantum information allow us to probe some of the otherwise opaque consequences from string theory in a different angle and have substantially improved our understandings of space, time, and the origin of gravity. Broadly speaking, we also explore the connection between quantum codes and other important concepts in high energy theory, like gauge theory and confinement.

Quantum lego, tensor network and quantum error correction

Quantum information is fragile, and for large-scale, reliable quantum computing, one needs to be able to preserve the information as we process them. This means that our quantum computer not only has to contain a large number of qubits, but also has to be fault-tolerant. Currently, a powerful, if not the only, way is to encode quantum information in quantum error correcting codes. However, designing good codes is hard, as it involves a great many of requirements and qubits.

We study quantum codes with tensor networks, which is a graphically intuitive language that has been used to study quantum many-body systems variationally. It also enables one to understand large quantum systems far more efficiently on classical computers. It is not only good for building toy models of quantum gravity, but also good for studying quantum error correcting codes.

Quantum codes may be understood as special quantum many-body systems that enjoy a large number of symmetries. As such, it is possible to study them with a more constrained set of tensor networks methods called quantum legos. This quantum gravity-inspired approach enables us to design and analyze quantum codes more effectively. It also helps us understand them both analytically and numerically. Part of the objective will be to extend this framework for code design, as well as to optimize and analyze the new codes one creates in various ways. In particular, we study how these processes may be automated with machine learning.

We also explore the interface of tensor network with other areas of quantum information science, like quantum network, state preparation, measurement-based quantum computation, and quantum (adjacent) algorithms.

Modelling quantum gravity with experiments

Experimental efforts on quantum gravity is difficult because of the Planck scale. High energy theorists often think of this as probing an unattainably high energy in colliders. Alternatively it requires us to maintain quantum coherence on macroscopic/massive objects, for instance, in AMO experiments. Although studying quantum gravity (or even classical gravity) in our universe is hard enough with multi-billion-dollar experiments, it may be possible to learn about certain aspects of it with table-top quantum simulations.

One approach is to understand QG is to study bulk quantum gravity via the AdS/CFT correspondence by simulating holographic CFTs on a quantum computer. While we do not expect this to be achievable in the near future, one can identify different salient aspects of AdS/CFT using toy models that are constructible on near-term quantum devices. Although their small size is not enough to capture all there is in a field theory, its behaviour can already contain some new physics that is computationally infeasible to simulate using our current best classical algorithms.

We collaborate with experimentalists to implement holographic error correcting codes on near-term quantum computers. These are important toy models where one can begin to understand how simple notions of geometry or a poor man's version of gravity can emerge in complex quantum systems. We also look to probe other aspects such as quantum chaos and scrambling, which quantum gravitational systems (like black holes) are often believed to exhibit. Related topics include ground state preparation on quantum computers, which are pivotal for simulating future systems like quantum chemistry and quantum field theories. These efforts have immense impact for both fundamental science and for practical aspects of quantum computing.

Looking for more?

It is hard to capture everything we hope to do in a few bullet points. There are many more research directions that lie within the general umbrella of quantum information, high energy physics and quantum many-body systems.

For example, one can build up toy models of cosmology like our expanding universe using quantum circuits and tensor networks. Other directions include using quantum gravity inspired codes as magic state factories, quantum algorithms for quantum error correction, and to use overlapping (approximate) qubits to understand emergent gravity.

If you find any of these topics interesting, feel free to email Charles Cao at cjcao*AT*vt.edu.

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