Quantum Physics

We are used to thinking of there being different types of fault-tolerant gates allowing reliable computation on states in a noisy quantum computer: Some are transversal, some involve measurement and magic states, some involve topological manipulations, etc.  In this talk, we will demonstrate that transversal gates can be seen as a topological effect, and we will propose an over-arching framework for thinking about fault tolerance in terms of fiber bundles over the Grassmanian, the manifold of subspaces of Hilbert space.  The violin will harmonize with the chalkboard to put the talk to music.

Zoom Link: https://pitp.zoom.us/j/97600230984?pwd=NDJ4VjdvUS9palA4YzFnZHBwcnJkUT09

While Quantum Field Theory is the most accurate theory we have for predicting the microscopic world, there are still open problems regarding its mathematical description. In particular, the usual quantum mechanical description of measurements, unitary kicks, and other local operations has the potential to produce pathological causality violations. Not all local operations lead to such violations, but any that do cannot be physically realisable. It is an open question whether a given local operation in the theory respects causality, and hence whether a given local operation is physical. In this talk I will work toward a general condition that distinguishes causal and acausal local operations.

Zoom Link: https://pitp.zoom.us/j/98089863001?pwd=K2RWL2lNWFd4VDZYd013eUN3alNmQT09

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

We study the entanglement dynamics of quantum many-body systems at long times. For upper bounds, we prove the following: (I) For any geometrically local Hamiltonian on a lattice, starting from a random product state the entanglement entropy is bounded away from the maximum entropy at all times with high probability. (II) In a spin-glass model with random all-to-all interactions, starting from any product state the average entanglement entropy is bounded away from the maximum entropy at all times. We also extend these results to any unitary evolution with charge conservation and to the Sachdev-Ye-Kitaev model. For lower bounds, we say that a Hamiltonian is an ``extensive entropy generator'' if starting from a random product state the entanglement entropy obeys a volume law at long times with overwhelming probability. We prove that (i) any Hamiltonian whose spectrum has non-degenerate gaps is an extensive entropy generator; (ii) in the space of (geometrically) local Hamiltonians, the non-degenerate gap condition is satisfied almost everywhere. These results imply ``unbounded growth of entanglement’’ in many-body localized systems.
References: arXiv:2102.07584 & 2104.02053

Zoom Link: https://pitp.zoom.us/j/96027097746?pwd=R2V2ZktJZUV1VkliN3pzM0IzbGR0UT09

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

In this talk I will assess various proposals for the source of the intuition that there is something problematic about contextuality, and argue that contextuality is best thought of in terms of fine-tuning. I will suggest that as with other fine-tuning problems in quantum mechanics, this behaviour can be understood as a manifestation of teleological features of physics. I will also introduce several formal mathematical frameworks that have been used to analyse contextuality and discuss how their results should be interpreted. 

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

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.