Quantum Physics

In recent years, random quantum circuits have played a central role in the theory of quantum computation. Much of this prominence is due to recent random quantum circuit sampling experiments which have constituted the first claims of "quantum supremacy".   While random quantum circuits enjoy certain advantages that make them ideal for implementation by near-term quantum experiments, it is unclear a priori why they should be difficult to simulate classically. While we know several examples of quantum algorithms which attain exponential speedups over classical computation, they all seem to rely on highly structured circuits (such as quantum Fourier transforms) which are far from typical. Why then should we expect a generic quantum circuit to realize a large computational advantage?

In this talk we will explain the complexity theoretic basis for the classical hardness of random circuit sampling.

This talk will be based on joint work with Adam Bouland, Chinmay Nirkhe, and Umesh Vazirani (https://arxiv.org/abs/1803.04402), as well as Adam Bouland, Yunchao Liu and Zeph Landau (https://arxiv.org/abs/2102.01738).

Zoom Link: https://pitp.zoom.us/j/92408058752?pwd=b1JoeTVISlpjaXk3ZjBoSi9pYjNUZz09

Classical probabilistic models of quantum systems are not only relevant for understanding the non-classical features of quantum mechanics, but they are also useful for determining the possible advantage of using quantum resources for information processing tasks.  A common feature of these models is the presence of inaccessible information, as captured by the concept of preparation contextuality:  There are ensembles of quantum states described by the same density operator, and hence operationally indistinguishable, and yet in any probabilistic (ontological) model, they should be described by distinct probability distributions.  In this talk, I discuss a method for quantifying this inaccessible information and present a family of lower bounds on this quantity in terms of experimentally measurable quantities. These bounds, which can also be interpreted as a new class of robust non-contextuality inequalities, are obtained based on a family of guessing games.  As an application of this result, I derive a noise threshold for the presence of contextually in a noisy system, in terms of the average gate fidelity of the noise channel.

We evaluate the usefulness of holographic stabilizer codes for practical purposes by studying their allowed sets of fault-tolerantly implementable gates. We treat them as subsystem codes and show that the set of transversally implementable logical operations is contained in the Clifford group for sufficiently localized logical subsystems. As well as proving this concretely for several specific codes, we argue that this restriction naturally arises in any stabilizer subsystem code that comes close to capturing certain properties of holography. We extend these results to approximate encodings, locality-preserving gates, certain codes whose logical algebras have non-trivial centers, and discuss cases where restrictions can be made to other levels of the Clifford hierarchy. A few auxiliary results may also be of interest, including a general definition of entanglement wedge map for any subsystem code, and a thorough classification of different correctability properties for regions in a subsystem code.

With gate error rates in multiple technologies now below the threshold required for fault-tolerant quantum computation, the major remaining obstacle to useful quantum computation is scaling, a challenge greatly amplified by the huge overhead imposed by quantum error correction itself. I’ll discuss a new fault-tolerant quantum computing scheme that can nonetheless be assembled from a small number of experimental components, potentially dramatically reducing the engineering challenges associated with building a large-scale fault-tolerant quantum computer. The architecture couples a single controllable qubit to a pair of delay lines which terminate in a detector. Below a threshold value for the error rate associated with the controllable qubit, the logical error rate decays exponentially with the square root of the delay line coherence time. The required gates can be implemented using existing technologies in quantum photonic and phononic systems. With continued incremental improvements in only a few components, we expect these systems to be promising candidates for demonstrating fault-tolerant quantum computation with comparatively modest experimental effort.

Experimental metaphysics is the study of how empirical results can reveal indisputable facts about the fundamental nature of the world, independent of any theory. It is a field born from Bell’s 1964 theorem, and the experiments it inspired, proving the world cannot be both local and deterministic. However, there is an implicit assumption in Bell’s theorem, that the observed result of any measurement is absolute (it has some value which is not ‘relative to its observer’). This assumption may be called into question when the observer becomes a quantum system (the “Wigner’s Friend” scenario), which has recently been the subject of renewed interest. Here, building on work by Brukner, we derive a theorem, in experimental metaphysics, for this scenario [1]. It is similar to Bell’s 1964 theorem but dispenses with the assumption of determinism. The remaining assumptions, which we collectively call "local friendliness", yield a strictly larger polytope of bipartite correlations than those in Bell's theorem (local determinism), but quantum mechanics still allows correlations outside the local friendliness polytope.  We illustrate this in an experiment in which the friend system is a single photonic qubit [1]. I argue that a truly convincing experiment could be realised if that system were a sufficiently advanced artificial intelligence software running on a very large quantum computer, so that it could be regarded genuinely as a friend. I will briefly discuss the implications of this far-future scenario for various interpretations and modifications of quantum theory.

[1] Kok-Wei Bong, Aníbal Utreras-Alarcón, Farzad Ghafari, Yeong-Cherng Liang, Nora Tischler, Eric G. Cavalcanti, Geoff J. Pryde and Howard M. Wiseman, “A strong no-go theorem on the Wigner’s friend paradox", Nature Physics (2020).

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.