Quantum Physics

The past decade has seen an explosion of research into resource theories—simple, quantum-information-theoretic models for constrained agents. Resource theories have provided foundational insights about thermodynamics, entanglement, and more. Yet whether resource theories can inform science outside our neighborhood of quantum information theory has been an outstanding question. I will present what is, to my knowledge, the first application of a resource theory to answer a pre-existing question in another field. Molecular switches, or photoisomers, surface across nature and technologies, from our eyes to solar-fuel cells. What probability does a switch have of switching? A general answer defies standard chemistry tools, as photoisomers are small, quantum and far from equilibrium. I will bound the switching probability by modeling a photoisomer within a thermodynamic resource theory. This work has helped pave the path for resource theories to impact science broadly.

References
• NYH and Limmer, Phys. Rev. A 101, 042116 (2020). https://journals.aps.org/pra/
abstract/10.1103/PhysRevA.101.042116
• NYH, in Eddington, Wheeler, and the Limits of Knowledge, Eds. Durham and
Rickles, Springer (2017) arXiv:1509.03873.

Zoom Link: https://pitp.zoom.us/j/99315796008?pwd=dDJBMjR2ckRmdlhtdWJZeHJuNUI1QT09

We generalize the concept of folding from surface codes to CSS codes by considering certain dualities within them. In particular, this gives a general method to implement logical operations in suitable LDPC quantum codes using transversal gates and qubit permutations only. To demonstrate our approach, we specifically consider a [[30, 8, 3]] hyperbolic quantum code called Bring's code. Further, we show that by restricting the logical subspace of Bring's code to four qubits, we can obtain the full Clifford group on that subspace.

Zoom Link: https://pitp.zoom.us/j/94852018243?pwd=RmFHM1QyNS9CK0RMRm5yUEt0MzdSZz09

The Page curve describing the radiation entropy of a unitarily evaporating black hole has recently been obtained by new calculations based on the replica trick. We analyse the discrepancy between these and Hawking's original conclusions from a quantum information theory viewpoint, using in particular the quantum de Finetti theorem. The theorem implies the existence of extra information, W, which is neither part of the black hole nor the radiation, but plays the role of a reference. The entropy obtained via the replica trick can then be identified to be the entropy S(R|W) of the radiation conditioned on the reference W, whereas Hawking's original result corresponds to the non-conditional entropy S(R). The entropy S(R|W), which mathematically is an ensemble average, gains an operational meaning in an experiment with N independently prepared black holes: for large N, it equals the regularized entropy of their joint radiation, S(R_1…R_N)/N. The discrepancy between this entropy and S(R) implies that the black holes are correlated, that is geometrically captured by the replica wormholes. In total, I will give three different interpretations of the radiation entropy calculated via the replica trick. Furthermore, I will briefly discuss the implications of ensemble interpretation in light of free probability theory, which offers the tools to deal with the effect of replica symmetry breaking in a refined calculation of the radiation entropy. (Based on the joint work (https://arxiv.org/abs/2110.14653) with Renato Renner.)

Zoom Link: https://pitp.zoom.us/j/93221648666?pwd=TkwrS0pMYjlLa090WCtCYjd0Nk9RZz09

Fracton models provide examples of novel gapped quantum phases of matter that host intrinsically immobile excitations and therefore lie beyond the conventional notion of topological order. Here, we calculate optimal error thresholds for quantum error correcting codes based on fracton models. By mapping the error-correction process for bit-flip and phase-flip noises into novel statistical models with Ising variables and random multi-body couplings, we obtain models that exhibit an unconventional subsystem symmetry instead of a more usual global symmetry. We perform large-scale parallel tempering Monte Carlo simulations to obtain disorder-temperature phase diagrams, which are then used to predict optimal error thresholds for the corresponding fracton code. Remarkably, we found that the X-cube fracton code displays a minimum error threshold (7.5%) that is much higher than 3D topological codes such as the toric code (3.3%), or the color code (1.9%). This result, together with the predicted absence of glass order at the Nishimori line, shows great potential for fracton phases to be used as quantum memory platforms. If time allows, I will also present some of our more recent progress on fractons.

Reference: arXiv:2112.05122.

Zoom Link: https://pitp.zoom.us/j/97053396111?pwd=Ny9tK295dGVacENJMzg0aHRObjZEZz09

Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state's complexity quantifies the number of computational gates required to prepare the state from a simple tensor product. The greater a state's distance from maximal complexity, or ``uncomplexity,'' the more useful the state is as input to a quantum computation. Separately, resource theories -- simple models for agents subject to constraints -- are burgeoning in quantum information theory. We unite the two domains, confirming Brown and Susskind's conjecture that a resource theory of uncomplexity can be defined. The allowed operations, fuzzy operations, are slightly random implementations of two-qubit gates chosen by an agent. We formalize two operational tasks, uncomplexity extraction and expenditure. Their optimal efficiencies depend on an entropy that we engineer to reflect complexity. We also present two monotones, uncomplexity measures that decline monotonically under fuzzy operations, in certain regimes. This work unleashes on many-body complexity the resource-theory toolkit from quantum information theory.

Zoom Link: https://pitp.zoom.us/j/96197686002?pwd=R2dPbTY3TEMxQWdESWpYeno3VDlOZz09

The sustained storage, transmission, or processing of quantum information will likely be a non-equilibrium process that requires monitoring the system and applying some form of feedback to produce fault-tolerance.  In this talk, I will discuss a class of models based on random quantum circuits with intermediate measurements that display a similar phenomenology to standard models for fault-tolerance, including the existence of a threshold, but with several helpful simplifications.  However, naïve realizations of the threshold require an exponential number of repetitions of the experiment to fully explore the output space of the intermediate measurements.  Recently, it has been proposed that this problem can be circumvented by developing efficient entanglement “decoders” that have close parallels to quantum error correction decoders.  We show how to leverage modern machine learning tools to devise a neural network decoder to detect the phase transition. We then study the complexity and scalability of this approach and discuss how it can be utilized to detect entanglement phase transitions in generic experiments.

Zoom Link: https://pitp.zoom.us/j/99123641139?pwd=VmkyR3BSNWF5bURVYmFVakp0ZkNRZz09

Many-electron problems pose some of the greatest challenges in computational science, with important applications across many fields of modern science. Fermionic quantum Monte Carlo (QMC) methods are among the most powerful approaches to these problems. However, they can be severely biased when controlling the fermionic sign problem using constraints, as is necessary for scalability. Here we propose an approach that combines constrained QMC with quantum computing tools to reduce such biases. We experimentally implement our scheme using up to 16 qubits in order to unbias constrained QMC calculations performed on chemical systems with as many as 120 orbitals. These experiments represent the largest chemistry simulations performed on quantum computers (more than doubling the size of prior electron correlation calculations), while obtaining accuracy competitive with state-of-the-art classical methods. Our results demonstrate a new paradigm of hybrid quantum-classical algorithm, surpassing the popular variational quantum eigensolver in terms of potential towards the first practical quantum advantage in ground state many-electron calculations.

The field of quantum information provides fundamental insight into central open questions in quantum thermodynamics and quantum many-body physics, such as the characterization of the influence of quantum effects on the flow of energy and information. These insights have inspired new methods for cooling physical systems at the quantum scale using tools from quantum information processing. These protocols not only provide an essentially different way to cool, but also go beyond conventional cooling techniques, bringing important applications for quantum technologies. In this talk, I will first review the basic ideas of algorithmic cooling and give analytical results for the achievable cooling limits for the conventional heat-bath version. Then, I will show how the limits can be circumvented by using quantum correlations. In one algorithm I take advantage of correlations that can be created during the rethermalization step with the heat-bath and in another I use correlations present in the initial state induced by the internal interactions of the system. Finally, I will present a recently fully characterized quantum property of quantum many-body systems, in which entanglement in low-energy eigenstates can obstruct local outgoing energy flows.

Causality is fundamental to science, but it appears in several different forms. One is relativistic causality, which is tied to a space-time structure and forbids signalling outside the future. On the other hand, causality can be defined operationally using causal models by considering the flow of information within a network of physical systems and interventions on them. From both a foundational and practical viewpoint, it is useful to establish the class of causal models that can coexist with relativistic principles such as no superluminal signalling, noting that causation and signalling are not equivalent. We develop such a general framework that allows these different notions of causality to be independently defined and for connections between them to be established. The framework first provides an operational way to model causation in the presence of cyclic, fine-tuned and non-classical causal influences. We then consider how a causal model can be embedded in a space-time structure and propose a mathematical condition (compatibility) for ensuring that the embedded causal model does not allow signalling outside the space-time future. We identify several distinct classes of causal loops that can arise in our framework, showing that compatibility with a space-time can rule out only some of them. We then demonstrate the mathematical possibility of causal loops embedded in Minkowski space-time that can be operationally detected through interventions, without leading to superluminal signalling. Our framework provides conditions for preventing superluminal signalling within arbitrary (possibly cyclic) causal models and also allows us to model causation in post-quantum theories admitting jamming correlations. Applying our framework to such scenarios, we show that post-quantumjamming can indeed lead to superluminal  signalling contrary to previous claims. Finally, this work introduces a new causal modelling concept of ``higher-order affects relations'' and several related technical results, which have applications for causal discovery in fined-tuned causal models.

The Quantum Bayesian, or QBist, interpretation regards the quantum formalism to be a tool that a single agent may adopt to help manage their expectations for the consequences of their actions. In other words, quantum theory is an addition to decision theory, and its shape, we hope, can teach us something about the nature of reality. Beyond simple consistency, an interpretation is judged by its capacity to point the way forward. In the first half of the talk, I will highlight several ways in which my collaborators and I have applied QBist intuitions to pose and solve technical questions regarding the informational structure and conceptual function of quantum theory. At the root of many of these developments is the notion of a reference measurement, the key to a probabilistic representation of quantum theory. In this setting, we can explore the boundary of the quantum reasoning structure from a uniquely QBist angle. Working with such representations grants a new perspective and inspires questions which wouldn't have occurred otherwise; as examples, we will meet downstream results concerning quantum channels, discrete quasiprobability representations, and a variant of the information-disturbance tradeoff. Most recently, I have pursued ways in which QBism could be applied to the construction of new tools and strategies for existing problems in quantum information and computation. In the second half of the talk, we will encounter the first of these, an agent-based modeling proposal where multiple, suitably interacting, QBist decision-makers might collectively work out the solution to a task of interest in the right circumstances. I will describe some initial explorations of modeling agent belief dynamics in two contexts: first, an expectation sampling interaction with an eye to agential agreement, and, second, a setting where agents are players of quantum games. In the future, we imagine it is possible that a sufficiently mature development of the agent-based program we have begun could suggest new approaches to quantum algorithm design.

Zoom Link: https://pitp.zoom.us/j/95668668835?pwd=MUJtRGMxbEFzSEdVVmZ3TkR3dVVVZz09

The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the often assumed no-restriction hypothesis, the set of accessible measurements within a given theory can be limited for different reasons, and this raises a question of what restrictions on measurements are operationally relevant. We argue that all operational restrictions must be closed under simulation, where the simulation scheme involves mixing and classical post-processing of measurements. We distinguish three classes of such operational restrictions: restrictions on measurements originating from restrictions on effects; restrictions on measurements that do not restrict the set of effects in any way; and all other restrictions. As a setting to detect nonclassicality in restricted theories we consider generalizations of random access codes, an intriguing class of communication tasks that reveal an operational and quantitative difference between classical and quantum information processing. We formulate a natural generalization of them, called random access tests, which can be used to examine collective properties of collections of measurements. We show that the violation of a classical bound in a random access test is a signature of either measurement incompatibility or super information storability, and that we can use them to detect differences in different restrictions.