Scientific Series

Finding ground states of quantum many-body systems is one of the most important---and one of the most notoriously difficult---problems in physics, both in scientific research and in practical applications.  Indeed, we know from a complexity-theoretic perspective that all methods  (quantum or classical) must necessarily fail to find the ground state efficiently in general. The ground state energy problem is already NP-hard even for classical, frustration-free, local Hamiltonians with constant spectral gap. For general quantum Hamiltonians, the problem becomes QMA-hard.

Nonetheless, as ground state problems are of such importance, and classical algorithms are often successful despite the theoretical exponential worst-case complexity, a number of quantum algorithms for the ground state problem have been proposed and studied. From quantum phase estimation-based methods, to adiabatic state preparation, to dissipative state engineering, to the variation quantum eigensolver (VQE), to quantum/probabilistic imaginary-time evolution (QITE/PITE).

Dissipative state engineering was first introduced in 2009 by Verstraete, Cirac and Wolf and by Kraus et al. However, it only works for the restricted class of frustration-free Hamiltonians.

In this talk, I will show how to construct a dissipative state preparation dynamics that provably produces the correct ground state for arbitrary Hamiltonians, including frustrated ones. This leads to a new quantum algorithm for preparing ground states: the Dissipative Quantum Eigensolver (DQE). DQE has a number of interesting advantages over previous ground state preparation algorithms:

• The entire algorithm consists simply of iterating the same set of   simple local measurements repeatedly.
• The expected overlap with the ground state increases monotonically with the length of time this process is allowed to run.
• It converges to the ground state subspace unconditionally, without any assumptions on or prior information about the Hamiltonian (such as spectral gap or ground state energy bound).
• The algorithm does not require any variational optimisation over parameters.
• It is often able to find the ground state in low circuit depth in practice.
• It has a simple implementation on certain types of quantum hardware, in particular photonic quantum computers.
• It is immune to errors in the initial state.
• It is inherently fault-resilient, without incurring any fault-tolerance overhead. I.e.\ not only is it resilient to errors on the quantum state, but also to faulty implementations of the algorithm itself; the overlap of the output with the ground state subspace degrades smoothly with the error rate, independent of the total run-time.

I give a mathematically rigorous analysis of the DQE algorithm and proofs of all the above properties, using non-commutative generalisations of methods from classical probability theory.

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Zoom link https://pitp.zoom.us/j/96022753460?pwd=SWlUVkVta1RyY3dsWUJWckRqOHdNdz09

We study the Petz map, which is a universal recovery channel of a tripartite quantum state upon erasing one party, in quantum many-body systems. The fidelity of the recovered state with the original state quantifies how much information shared by the two parties is not mediated by one of the party, and has a universal lower bound in terms of the conditional mutual information (CMI). I will study this quantity in two different contexts. First, in a CFT ground state, we show that the fidelity is universal, which means it only depends on the central charge and the cross ratio. We compute this universal function numerically and show that it is consistently better than the naive CMI bound. Secondly, we show that for two broad classes of the states, the CMI lower bound is saturated. These include stabilizer states (in any dimensions) and the ground state of 2+1D topological order.

Zoom link: https://pitp.zoom.us/j/92623435839?pwd=N1JIdkUwWHFkZGpqb1p1V3NKYy91QT09

Activation of Bell nonlocality refers to the phenomenon where some entangled mixed states that admit a local hidden variable model in the standard Bell scenario nevertheless reveal their nonlocal nature in more exotic measurement scenarios. It has recently been shown that by broadcasting the subsystems of a bipartite quantum state, one can activate Bell nonlocality and significantly improve noise tolerance bounds for device-independent and semi-device-independent entanglement certification, with a single copy of the state and local measurements. In this talk I will review the state of the art on activation of nonlocality and existence of local hidden variable models, introduce the broadcasting technique and outline several interesting results and research directions.

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Zoom link  https://pitp.zoom.us/j/91214624839?pwd=dXNUOERLMldScjczemlaSUhFbFNWQT09

With the main purpose of identifying the existence of gravitational radiation at infinity (scri), a novel approach to the asymptotic structure of spacetime is presented, focusing mainly in cases with non-negative cosmological constant. The basic idea is to consider the strength of tidal forces experienced by scri. To that end I will introduce the asymptotic (radiant) super-momentum, a causal vector defined at scri with remarkable properties that, in particular, provides an innovative characterization of gravitational radiation valid for the general case with Λ ≥ 0 (and which has been proven to be equivalent when Λ = 0 to the standard one based on the News tensor). This analysis is also shown to be supported by the initial- (or final-) value Cauchy-type problem defined at scri. The implications are discussed in some detail. The geometric structure of scri, and of its cuts, is clarified. The question of whether or not a News tensor can be defined in the presence of a positive cosmological constant is addressed. Several definitions of asymptotic symmetries are presented. Conserved charges that may detect gravitational radiation are exhibited. Balance laws that might be useful as diagnostic tools to test the accuracy of model waveforms discussed. An interpretation of the Geroch `rho' tensor is found. The whole thing will be complemented with a series of illustrative examples based on exact solutions. In particular we will see that exact solutions with black holes will be radiative if, and only if, they are accelerated.

Zoom link: https://pitp.zoom.us/j/95879544523?pwd=MFl5UEtUZ0hUcU1hNk1SZ2R4MThxUT09

Merging neutron stars have long been speculated to produce Gamma-Ray Bursts (GRBs). While this has been the standard assumption for short GRBs for decades, this was only officially confirmed with the still relatively recent detection of gravitational wave counterpart GRB 170817A. In this presentation, I will discuss how we model short GRBs and their afterglows produced by the relativistic jets launched during the merger. A recent development of interest includes the apparent confirmation of some 'long' GRBs to also follow from mergers rather than collapsing massive stars, which has implication for the prospects of future multi-messenger detections. Joint modelling of GRB / afterglow data and GW signals makes it possible to further constrain the shared model parameters between the two, most notably the orientation of the system.

Zoom link: https://pitp.zoom.us/j/95551884959?pwd=bUVGVzhXK3pLb3MxMGV4ejZzUmRYdz09

A number of no-go theorems suggest that theories upholding both unitarity and relativity must deny that events are absolute. I'll show how quantum causal influences allow us to articulate an attractive conception of relational events. This will lead us towards a precise, observer-independent reformulation of quantum theory, in which relational events emerge from causation.

Zoom link: https://pitp.zoom.us/j/98649944363?pwd=Y25NOUROelY2ZmFpVWhTZFErV2MwUT09

While General Relativity has withstood tests on solar system scales, progress in observational cosmology now enables tests on the largest scales. I will present results from our tests of gravity using Dark Energy Survey Year 3 weak lensing and clustering data in addition to a variety of complementary data. One outcome of this analysis was the necessity to further explore lensing consistency so I will present preliminary results of such tests using the latest Cosmic Microwave Background (CMB) lensing data. These analyses are setting the scene for future tests of fundamental physics with CMB and galaxy surveys: I will show expected results and challenges from the Rubin Observatory. I will finally argue for the use of machine learning for theory exploration, to better organize our efforts within the future experimental landscape. As PI is a leading center in outreach, I will end my talk by sharing my experience with science content creation on various social media platforms.

Zoom link: https://pitp.zoom.us/j/96929387143?pwd=WW1CZElpMkN2U1RQUjB3VERxRVQ5dz09

In 2020 our Oxford-based Quantinuum team performed Quantum Natural Language Processing (QNLP) on IBM quantum hardware [1, 2].  Key to having been able to achieve what is conceived as a heavily data-driven task, is the observation that quantum theory and natural language are governed by much of the same compositional structure -- a.k.a. tensor structure.  

Hence our language model is in a sense quantum-native, and we provide an analogy with simulation of quantum systems in terms of algorithmic speed-up [forthcoming].  Meanwhile we have made all our software available open-source, and with support [github.com/CQCL/lambeq].    

The compositional match between natural language and quantum extends to other domains than language, and argue that a new generation of AI can emerge when fully pushing this analogy, while exploiting the completeness of categorical quantum mechanics / ZX-calculus [3, 4, 5] for novel reasoning purposes that go hand-in-hand with modern machine learning.

[1]     B. Coecke, G. De Felice, K. Meichanetzidis and A. Toumi (2020) Foundations for Near-Term Quantum Natural Language Processing.  https://arxiv.org/abs/2012.03755

[2]     R. Lorenz, A. Pearson, K. Meichanetzidis, D. Kartsaklis and B. Coecke (2020) QNLP in Practice: Running Compositional Models of Meaning on a Quantum Computer.  https://arxiv.org/abs/2102.12846

[3]     B. Coecke and A. Kissinger (2017) Picturing Quantum Processes. A first course on quantum theory and diagrammatic reasoning.  Cambridge University Press.

[4]     B. Coecke, D. Horsman, A. Kissinger and Q. Wang (2021) Kindergarten quantum mechanics graduates (...or how I learned to stop gluing LEGO together and love the ZX-calculus).  https://arxiv.org/abs/2102.10984

[5]     B. Coecke and S. Gogioso (2022) Quantum in Pictures.  Quantinuum, 2023.

Zoom Link: https://pitp.zoom.us/j/92333285960?pwd=MlpJSklmMlVlUlRTTWhsNjc2T2Y4QT09

The notorious exponential complexity of quantum problems can be avoided for systems with limited correlations. For example, states of one-dimensional systems with bounded entanglement are approximable by matrix product states. We consider fermionic systems, where correlations can be defined as deviations from Gaussian states. Heuristically, one expects a link between compact non-Gaussian ansatzes and bounded fermionic correlations. This connection, however, has not been rigorously demonstrated. Our work resolves this conceptual gap.

We focus on pure states with a fixed number of fermions. Generalizing the so-called Plücker relations, we introduce k-particle correlation measures ω_k. The vanishing of ω_k at a constant k defines a class H_k of states with limited correlations. These sets H_k are nested, ranging from Gaussian for k=1 to the full n-fermion Hilbert space H for k=n+1. States in H_{k=O(1)} can be represented using a non-Gaussian ansatz of polynomial size. Classes H_k have physical meaning, containing all truncated perturbation series around Gaussian states. We also identify non-perturbative examples of states in H_{k=O(1)}, by a numerical study of excited states in the 1D Hubbard model. Finally, we discuss the information-theoretic implications of our results for the widely used coupled-cluster ansatz.

Zoom Link: TBD

I will introduce the stability problem for spacetimes from the initial value formulation perspective in general relativity. After introducing some notions on how to quantitatively characterize (in)stability, I will present a result for a class of spacetimes called gravitational solitons which exhibit slower decay compared to black holes. This is joint work with Hari Kunduri (McMaster University).

Zoom Link: TBD

Event Horizon Telescope (EHT) has produced images of the black hole in the galaxy M87 and in the center of our galaxy, and I will briefly review what we have learned from the images.  In the near future we expect that repeated visits to M87, or high fidelity images of the galactic center, will produce movies of the turbulent plasma in these sources.  The statistical properties of the movies can be predicted using state-of-the-art numerical simulations.  I will explore what information can be extracted from the movies, especially information about source inclination and black hole spin.

Zoom link TBA