Quantum Physics

Recent work has defined what it means for one quantum system to simulate the full physics of another, and demonstrated that—within a very demanding definition of simulation —there exist families of local Hamiltonians that are universal, in the sense that they can simulate all other quantum Hamiltonians. This rigorous mathematical framework of Hamiltonian simulation not only gave a theoretical foundation for describing analogue Hamiltonian simulation. It also unified many previous Hamiltonian complexity results, and implied new ones. It has even found applications in constructing the first rigorous holographic dualities between local Hamiltonians, providing richer toy models of AdS/CFT duality in quantum gravity.

All previous constructions of universal Hamiltonians have relied heavily on using perturbation gadgets, and constructing complicated ‘chains’ of simulations to prove that simple models are indeed universal. In recent work we developed a new method for proving universality. Unlike perturbation- gadget approaches, this directly leverages the ability to encode computation into the ground states of QMA-hard Hamiltonians. With this technique we are able to derive necessary and sufficient complexity-theoretic conditions characterising universal Hamiltonians. We also use our new simulation method to provide a simple construction of two new universal models. Both of these are translationally invariant systems in 1D, and we show that one of these constructions is efficient in terms of the number of spins in the universal construction (but not in terms of the norm of the simulating Hamiltonian). This is the first translationally invariant universal model which is efficient in terms of system size overhead.

Based on joint work with Stephen Piddock, Johannes Bausch and Toby Cubitt (arXiv:2003.13753, arXiv:2101.12319)

A brief introduction to entanglement of multipartite pure quantum states will be given. As the Bell states are known to be maximally entangled among all two-qubit quantum states, a natural question arises: What is the most entangled state for the quantum system consisting of N sub-systems with d levels each? The answer depends on the entanglement measure selected, but already for four-qubit system, there is no state which displays maximal entanglement with respect to all three possible splittings of the systems into two pairs of qubits.

To construct strongly entangled multipartite quantum states one can use various mathematical techniques involving combinatorial designs, topological methods related to knot theory or the Majorana (stellar) representation of permutation symmetric quantum states.
 

We present two classical algorithms for the simulation of universal quantum circuits on n qubits constructed from c instances of Clifford gates and t arbitrary-angle Z-rotation gates such as T gates. Our algorithms complement each other by performing best in different parameter regimes. The Estimate algorithm produces an additive precision estimate of the Born rule probability of a chosen measurement outcome with the only source of run-time inefficiency being a linear dependence on the stabilizer extent (which scales like ≈1.17^t for T gates). Our algorithm is state-of-the-art for this task:

as an example, in approximately 25 hours (on a standard desktop computer), we estimated the Born rule probability to within an additive error of 0.03, for a 50 qubit, 60 non-Clifford gate quantum circuit with more than 2000 Clifford gates. The Compute algorithm calculates the probability of a chosen measurement outcome to machine precision with run-time O(2^t−r(t−r)t) where r is an efficiently computable, circuit-specific quantity. With high probability, r is very close to min{t,n−w} for random circuits with many Clifford gates, where w is the number of measured qubits. Compute can be effective in surprisingly challenging parameter regimes, e.g., we can randomly sample Clifford+T circuits with n=55, w=5, c=105 and t=80 T-gates, and then compute the Born rule probability with a run-time consistently less than 104 seconds using a single core of a standard desktop computer. We provide a C+Python implementation of our algorithms.

It has been shown that, despite being local, a perturbation applied to a single site of the one-dimensional XXZ model is enough to bring this interacting integrable spin-1/2 system to the chaotic regime. In this talk, we show that this is not unique to the XXZ model, but happens also to the spin-1/2 Ising model in a transverse field and to the spin-1 Lai-Sutherland chain. The larger the system is, the smaller the amplitude of the local perturbation for the onset of chaos. We focus on two indicators of chaos, the correlation hole, which is a dynamical tool, and the distribution of off-diagonal elements of local observables, which is used in the eigenstate thermalization hypothesis. Both methods avoid spectrum unfolding and can detect chaos even when the eigenvalues are not separated by symmetry sectors.

The prepare-and-measure scenario is ubiquitous in physics. However, beyond the paradigmatic example of dense coding, there is little known about the correlations p(b|x,y) that can be generated between a sender with input x and a receiver with input y and outcome b. Contrasting dense coding, we show that the most powerful protocols based on qubit communication require high-dimensional entanglement. This motivates us to systematically characterise the sets of correlations achievable with classical and quantum communication, respectively, assisted by a potentially unbounded amount of entanglement. We obtain two different SDP hierarchies for both the classical and quantum case: one based on NPA and one based on informationally-restricted correlations. In the talk, I will discuss the advantages and drawbacks of each, and show that they can be used obtain tight or nearly-tight bounds on in several concrete case studies. As examples of applications, these new tools are used to construct device-independent dimension witnesses robust to unbounded shared entanglement and several resource inequalities for quantum communications.

Discriminating between quantum computing architectures that can provide quantum advantage from those that cannot is of crucial importance. From the fundamental point of view, establishing such a boundary is akin to pinpointing the resources for quantum advantage; from the technological point of view, it is essential for the design of non-trivial quantum computing architectures. Wigner negativity is known to be a necessary resource for computational advantage in several quantum-computing architectures, including those based on continuous variables (CVs). However, it is not a sufficient resource, and it is an open question under which conditions CV circuits displaying Wigner negativity offer the potential for quantum advantage. In this work, we identify vast families of circuits that display large Wigner negativity, and yet are classically efficiently simulatable, although they are not recognized as such by previously available theorems. These families of circuits employ bosonic codes based on either translational or rotational symmetries (e.g., Gottesman-Kitaev-Preskill or cat codes), and can include both Gaussian and non-Gaussian gates and measurements. Crucially, within these encodings, the computational basis states are described by intrinsically negative Wigner functions, even though they are stabilizer states if considered as codewords belonging to a finite-dimensional Hilbert space. We derive our results by establishing a link between the simulatability of high-dimensional discrete-variable quantum circuits and bosonic codes.

Agency accounts of causation are often criticised as being unacceptably subjective: if there were no human agents there would be no causal relations, or, at the very least, if humans had been different then so too would causal relations. Here we describe a model of a causal agent that is not human, allowing us to explore the latter claim.   

Our causal agent is special kind of open, dissipative physical system, maintained far from equilibrium by a low entropy source of energy, with accurate sensors and actuators. It has a memory to record sensor measurements and actuator operations, and a learning system that can access the sensor and actuator records to learn and represent the causal relations. We claim that causal relations are relations between the internal sensor and actuator records and the causal concept inherent in these correlations is then inscribed in the physical dynamics of the internal learning machine. We use this model to examine the relationships between three familiar asymmetries aligned with causal asymmetry: time's arrow, the thermodynamic arrow and the arrow of deliberation and action. We consider both classical and quantum agent models and illustrate some differences between the two. 
 

To analyze the performance of adaptive measurement protocols for the detection and quantification of state resources, we introduce the framework of quantum preparation games. A preparation game is a task whereby a player sequentially sends a number of quantum states to a referee, who probes each of them and announces the measurement result. The measurement setting at each round, as well as the final score of the game, are decided by the referee based on the past history of settings and measurement outcomes. We show how to compute the maximum average score that a player can achieve under very general constraints on their preparation devices and provide practical methods to carry out optimizations over n-round preparation games. We apply our general results to devise new adaptive protocols for entanglement detection and quantification. Given a set of experimentally available local measurement settings, we provide an algorithm to derive, via convex optimization, optimal n-shot protocols for entanglement detection using these settings. We also present families of adaptive protocols for multiple-target entanglement detection with arbitrarily many rounds. Surprisingly, we find that there exist instances of entanglement detection problems with just one target entangled state where the optimal adaptive protocol supersedes all non-adaptive alternatives.

The predictions of quantum theory resist generalised noncontextual explanations. In addition to the foundational relevance of this fact, the particular extent to which quantum theory violates noncontextuality limits available quantum advantage in communication and information processing. In the first part of this work, we formally define contextuality scenarios via prepare-and-measure experiments, along with the polytope of general contextual behaviours containing the set of quantum contextual behaviours. This framework allows us to recover several properties of set of quantum behaviours in these scenarios . Most surprisingly, we discover contextuality scenarios and associated noncontextuality inequalities that require for their violation the individual quantum preparation and measurement procedures to be mixed states and unsharp measurements. With the framework in place, we formulate novel semidefinite programming relaxations for bounding these sets of quantum contextual behaviours. Most significantly, to circumvent the inadequacy of pure states and projective measurements in contextuality scenarios, we present a novel unitary operator based semidefinite relaxation technique. We demonstrate the efficacy of these relaxations by obtaining tight upper bounds on the quantum violation of several noncontextuality inequalities and identifying novel maximally contextual quantum strategies. To further illustrate the versatility of these relaxations we demonstrate the monogamy of preparation contextuality in a tripartite setting, and present a secure semi-device independent quantum key distribution scheme powered by quantum advantage in parity oblivious random access codes.

In the last two decades the field of nonequilibrium quantum many-body physics
has seen a rapid development driven, in particular, by the remarkable progress
in quantum simulators, which today provide access to dynamics in quantum
matter with an unprecedented control. However, the efficient numerical
simulation of nonequilibrium real-time evolution in isolated quantum matter
still remains a key challenge for current computational methods especially
beyond one spatial dimension. In this talk I will present a versatile and
efficient machine learning inspired approach. I will first introduce the
general idea of encoding quantum many-body wave functions into artificial
neural networks. I will then identify and resolve key challenges for the
simulation of real-time evolution, which previously imposed significant
limitations on the accurate description of large systems and long-time
dynamics. As a concrete example, I will consider the dynamics of the
paradigmatic two-dimensional transverse field Ising model, where we observe
collapse and revival oscillations of ferromagnetic order and demonstrate that
the reached time scales are comparable to or exceed the capabilities of state-
of-the-art tensor network methods.

With ongoing efforts to observe quantum effects in larger and more complex systems, both for the purposes of quantum computing and fundamental tests of quantum gravity, it becomes important to study the consequences of extending quantum theory to the macroscopic domain. Frauchiger and Renner have shown that quantum theory, when applied to model the memories of reasoning agents, can lead to a conflict with certain principles of logical deduction. Is this incompatibility a peculiar feature of quantum theory, or can modelling reasoning agents using other physical theories also lead to such contradictions? What features of physical theories are responsible for such paradoxes? 

Multi-agent paradoxes have been previously analysed only in quantum theory. To address the above questions, a framework for analysing multi-agent paradoxes in general physical theories is required. Here, we develop such a framework that can in particular be applied to generalized probabilistic theories (GPTs). We apply the framework to model how observers’ memories may evolve in box world, a post-quantum GPT and using this, derive a stronger paradox that does not rely on post-selection. Our results reveal that reversible, unitary evolution of agents’ memories is not necessary for deriving multi-agent logical paradoxes, and suggest that certain forms of contextuality might be. 

https://iopscience.iop.org/article/10.1088/1367-2630/ab4fc4

Many physical states of interest, such as ground states of gapped quantum many-body systems, are expected to obey an area law of entanglement entropy. I will report on a series of recent results that suggest a deep connection between area law and two seemingly unrelated subjects: topological quantum field theory and quantum marginal problem. Recently, we deduced --- only using area law and quantum information-theoretic tools --- the existence of new topological charges and invariants associated with the domain walls between topologically ordered systems in two spatial dimensions. Moreover, the same set of tools were also used in finding a solution to the quantum marginal problem. This is the problem in which one asks whether a set of reduced density matrices on bounded subsystems are compatible with some globally well-defined many-body quantum state. Since this problem was first posed in 1959, a solution that goes beyond the mean-field ansatz has remained elusive until now. These results suggest that area law is not just a qualitative statement about entanglement; it is an important equation that lets us "solve" quantum many-body systems that appear in nature.

Based on arXiv:2008.11793 and arXiv:2010.07424