Quantum Information

Monitored many-body systems fall broadly into two dynamical phases, ``entangling'' or ``disentangling'', separated by a transition as a function of the rate at which measurements are made on the system. Producing an analytical theory of this measurement-induced transition is an outstanding challenge. Recent work made progress in the context of tree tensor networks, which can be related to all-to-all quantum circuit dynamics with forced (postselected) measurement outcomes. So far, however, there are no exact solutions for dynamics of spin-1/2 degrees of freedom (qubits) with ``real'' measurements, whose outcome probabilities are sampled according to the Born rule. Here we define dynamical processes for qubits, with real measurements, that have a tree-like spacetime interaction graph, either collapsing or expanding the system as a function of time. The former case yields an exactly solvable measurement transition. We explore these processes analytically and numerically, exploiting the recursive structure of the tree. We compare the case of ``real'' measurements with the case of ``forced'' measurements. Both cases show a transition at a nontrivial value of the measurement strength, with the real measurement case exhibiting a smaller entangling phase. Both exhibit exponential scaling of the entanglement near the transition, but they differ in the value of a critical exponent. An intriguing difference between the two cases is that the real measurement case lies at the boundary between two distinct types of critical scaling. On the basis of our results we propose a protocol for realizing a measurement phase transition experimentally via an expansion process.

Quantum theory has a temporal composition, which is expressed under many different operational frameworks. Here, points in time are imbued with a Hilbert space structure, and quantum states are passed between times through a series of experimental interventions. A multi-time quantum process, therefore, carries the same complex properties as a many-body quantum state. This invites the question: to what extent can temporal correlations be as interesting as spatial ones, and how can we access them? One particular avenue through which this structure manifests is in open quantum systems. System-environment dynamics can precipitate non-Markovian processes by which correlations persist between different times. Recently, the advent of high-fidelity quantum devices has made it possible to probe coherent quantum systems. In this talk, I will discuss my recent work in which we show how this serves as a novel test bed to capture many-time physics. We build frameworks to extract generic spatiotemporal properties of quantum stochastic processes, show how process complexity may be manipulated, and elevate user-control into the theory to make it self-consistent. Remarkably, many of these complex features are already present in naturally occurring noise, and hence the results have direct application to the development of fault-tolerant quantum devices. I will also briefly discuss some of my future research goals: the existence of exotic temporal phenomena and how emergent spatiotemporal features can be captured through renormalisation group approaches; the learnability of spacetime quantum correlations and avenues here to quantum advantage; and the taming of correlated noise in quantum devices through bespoke error suppression and error correction. 

Quantum neural networks have been widely studied in recent years, given their potential practical utility and recent results regarding their ability to efficiently express certain classical data. However, analytic results to date rely on assumptions and arguments from complexity theory. Due to this, there is little intuition as to the source of the expressive power of quantum neural networks or for which classes of classical data any advantage can be reasonably expected to hold. In this talk, I will discuss my recent results (arXiv:2209.14353) studying the relative expressive power between a broad class of neural network sequence models and a class of recurrent models based on Gaussian operations with non-Gaussian measurements. We explicitly show that quantum contextuality is the source of an unconditional memory separation in the expressivity of the two model classes. Additionally, we use this intuition to study the relative performance of our introduced model on a standard translation data set exhibiting linguistic contextuality and show that the quantum model outperforms state-of-the-art classical models even in practice. I will also briefly discuss connections to my previous work studying the trainability of variational quantum algorithms (arXiv:2109.06957, arXiv:2205.05786).

Constraint satisfaction problems are known to always be "easy" or "hard", in the sense of being either solvable in P or being NP-complete, with no intermediate difficulty levels. The quantum analog of constraint problems, frustration-free Hamiltonians, are known to exhibit at least two more levels of complexity: QMA (for arbitrary local Hamiltonians) and MA (for stoquastic Hamiltonians). Wondering if other complexity classes can occur, we answer in the affirmative: there are interactions which can be freely arranged on qubits in any arrangement, such that the resulting frustration problem is BQP-complete, and captures exactly the difficulty of quantum computation. Simple modifications of this construction show that quantum constraint problems can be complete for QCMA and BPP as well. Based on https://arxiv.org/abs/2101.08381

Optical astronomical imaging looks for better imaging quality in extreme cases of weak and subdiffraction limits. I focus on the quantum enhancement of astronomical interferometric imaging, including its fundamental limit and practical issues. For the fundamental aspects, I ignore any resource limit and noise and consider the ideal imaging problems. I show that the resolution limit can be enhanced with more carefully chosen measurement strategies and the general imaging quality can be enhanced by postprocessing the stellar photons with a quantum computer. For the practical aspects, I try to overcome the transmission loss suffered by interferometric imaging using quantum network, consider the possibility to implement a local scheme with better performance, and discuss the feasibility of decomposing thermal states into temporally localized pulses.

Scrambling of quantum information is an important feature at the root of randomization and benchmarking protocols, the onset of quantum chaos, and black-hole physics.

Unscrambling this information is possible given perfect knowledge of the scrambler [ArXiv: 1710.03363].

We show that one can retrieve the scrambled information without any previous knowledge of the scrambler, by a learning algorithm that allows the building of an efficient decoder. Surprisingly, complex quantum scramblers admit Clifford decoders: the salient properties of a scrambling unitary can be efficiently described even if exponentially complex, as long as it is not fully chaotic. This is possible because all the redundant complexity can be described as an entropy, and for non-chaotic black holes can be efficiently pushed away, just like in a refrigerator. This entropy is not due to thermal fluctuations but to the non-stabilizer behavior of the scrambler.

We give a new definition of self-testing for correlations in terms of states on C*-algebras. We show that this definition is equivalent to the standard definition for any class of finite-dimensional quantum models which is closed under submodels and direct sums, provided that the correlation is extremal and has a full-rank model in the class. This last condition automatically holds for the class of POVM quantum models, but does not necessarily hold for the class of projective models by a result of Mancinska and Kaniewski. For extremal binary correlations and for extremal synchronous correlations, we show that any self-test for projective models is a self-test for POVM models. The question of whether there is a self-test for projective models which is not a self-test for POVM models remains open. An advantage of our new definition is that it extends naturally to commuting operator models. We show that an extremal correlation is a self-test for finite-dimensional quantum models if and only if it is a self-test for finite-dimensional commuting operator models, and also observe that many known finite-dimensional self-tests are in fact self-tests for infinite-dimensional commuting operator models.

Zoom link: https://pitp.zoom.us/j/95783943431?pwd=SDFyQVVZR1d4WlVNSDZ4OENzSmJQUT09

We present broadly applicable nonperturbative results on the behavior of eigenvalues and eigenvectors under the addition of self-adjoint operators and under the multiplication of unitary operators, in finite-dimensional Hilbert spaces. To this end, we decompose these operations into elementary 1-parameter processes in which the eigenvalues move similarly to the spheres in Newton's cradle. As special cases, we recover level repulsion and Cauchy interlacing. We discuss two examples of applications. Applied to adiabatic quantum computing, we obtain new tools to relate algorithmic complexity to computational slowdown through gap narrowing. Applied to information theory, we obtain a generalization of Shannon sampling theory, the theory that establishes the equivalence of continuous and discrete representations of information. The new generalization of Shannon sampling applies to signals of varying information density and finite length.

Zoom link: https://pitp.zoom.us/j/94120657832?pwd=SmpsWFhhVCtyeXM3a0pVQU9lMGFLdz09

We revisit the problem of how interactions emerge in quantum gravity. Namely, we show that bulk scattering of multiple particles in the AdS space requires multipartite entanglement on the boundary. This statement can be proven by two totally different methods, 1) general relativity and 2) quantum cryptographic argument. Furthermore, we argue that interactions among particles in the scattering event emerge from the mechanism of entanglement-assisted quantum error-correcting codes (EAQECCs) which utilize pre-existing multipartite entanglement in CFT. We also propose a concrete protocol to implement a certain class of multi-partite unitary interactions by using transversal logical operators of quantum codes. This talk is based on a (very) recent work with Alex May and Jonathan Sorce.

Zoom Link: https://pitp.zoom.us/j/91349028320?pwd=TGF2Q2ZNdTZtZGxkQ0NiMURLdW5Zdz09

The phase diagram of a material is of central importance in describing the properties and behaviour of a condensed matter system. Indeed, the study of quantum phase transitions has formed a central part of 20th and 21st Century physics. We examine the complexity and computability of determining the phase diagram of a general Hamiltonian. We show that in the worst case it is uncomputable and in more restricted cases, where the Hamiltonian is “better behaved”, it remains computationally intractable even for a quantum computer. Finally, we take a look at the relations between the Renormalization Group and uncomputable Hamiltonians.

Zoom Link: https://pitp.zoom.us/j/96048987715?pwd=WGtwWk1SUnFsanNIVTZVYjNmbTh3Zz09

As a recent combination of two strong global leaders in quantum computing, Honeywell Quantum Solutions and Cambridge Quantum, Quantinuum integrates quantum hardware and software, including solutions for drug discovery, materials science, finance, and other applications. Quantinuum aims to be a center of gravity for quantum computing, supporting collaboration across the ecosystem. For this we have also developed “TKET”, an open-source architecture-agnostic quantum software stack and ‘best in class’ compiler. This enables our partners, collaborators and clients to effortlessly work across multiple platforms and tackle some of the most intriguing and important problems in quantum computing. 

Bio: Dr. Mark Jackson is the Senior Quantum Evangelist at Quantinuum. He received his B.S. in Physics and Mathematics from Duke University and Ph.D. in Theoretical Physics from Columbia University. He then spent 10 years researching superstring theory and cosmology, co-authoring almost 40 technical articles. To promote the public understanding of science, he founded the science crowdfunding platform Fiat Physica and non-profit Science Partnership Fund. He is Adjunct Faculty at Singularity University and a Director of Astronomers Without Borders.

Zoom link: https://pitp.zoom.us/j/98433088425?pwd=UzgwcGpUYnBKNzJmMnQ1ZVNOdGVXZz09

Tensor network provides a geometric representation of quantum many-body wave functions. Inspired by holography, we discuss a geometric realization of (one-shot) entanglement distillation for tensor networks including the multi-scale entanglement renormalization ansatz and matrix product states. We evaluate the trace distances between the ‘distilled' states and EPR states step by step and see a trend of distillation. If time permits, I will mention a possible field theoretic generalization of this geometric distillation.

Zoom link: https://pitp.zoom.us/j/98545776462?pwd=b1Z3ZENNRWVITlNOZG1GdzJaMmN1Zz09