CQI Seminar

Digital quantum simulations of gauge theories are an active field of research within the community of lattice simulations of gauge theories. I will focus on digital quantum simulations of the Schwinger Model with theta-term. This is a U(1) gauge theory which exhibits confinement, and by probing the system from the outside with two charged objects it is possible to observe an analogous process to string breaking. Placing the gauge theory on a lattice yield a discretized version that can be simulated on (quantum) computers. I will present two techniques, one for estimating the eigenenergies of the lattice theory and another auxiliary algorithm for suppressing high-energy excitations. This two newly introduced algorithms combine to give very precise estimations for ground state energy both for the Schwinger Model and for the string breaking picture.

Protecting secrets is a key challenge in our contemporary information-based era. In common situations, however, revealing secrets appears unavoidable, for instance, when identifying oneself in a bank to retrieve money. In turn, this may have highly undesirable consequences in the unlikely, yet not unrealistic, case where the bank’s security gets compromised. This naturally raises the question of whether disclosing secrets is fundamentally necessary for identifying oneself, or more generally for proving a statement to be correct. Developments in computer science provide an elegant solution via the concept of zero-knowledge proofs: a prover can convince a verifier of the validity of a certain statement without facilitating the elaboration of a proof at all. In this work, we report the experimental realisation of such a zero-knowledge protocol involving two separated verifier-prover pairs. Security is enforced via the physical principle of special relativity, and no computational assumption (such as the existence of one-way functions) is required.Our implementation exclusively relies on off-the-shelf equipment and works at both short (60m) and long distances (>400m) in about one second. This demonstrates the practical potential of multi-prover zero-knowledge protocols, promising for identification tasks.

The process matrix framework was developed to allow for scenarios with indefinite or quantum causal order, a phenomenon that is expected to be relevant for quantum gravity. A popular approach towards a quantum theory of gravity is the Page-Wootters formalism, which describes time-evolution of systems via correlations between a clock system and other quantum systems encoded in history states. We combined the process matrix framework with a generalization of the Page-Wootters formalism with multiple clocks. Each of these clocks can be thought of as corresponding to an agent and conditioning on a certain clock gives the respective agent's perspective inside an a priori general quantum process. We implemented scenarios where different definite causal orders are coherently controlled and explain why certain non-causal processes might not be compatible with this framework.

Imagine a world where refrigerator magnets, compasses, and magnetic storage devices don't exist. Surprisingly, this is precisely the universe implied by classical physics: as Bohr and van-Leeuwen demonstrated, a classical system's magnetisation invariably vanishes to zero in thermodynamic equilibrium. Hence, quantum models, such as the Heisenberg spin-chain model, were invented to explain the phenomenon of magnetism. In this talk, I shall explore those models' history and intricacies. And I shall clarify why those quantum models require decoherence to explain the structure of magnetic materials.

The first part of the talk will be about the design of signatures via the use of non-abelian cryptographic group actions, in particular the ones coming from coding theory assumptions. This family of schemes came to interest during the new NIST call for standardisation of signature designs, thanks to the trust of the community on their (quantum) resistance and the very malleable underlying structure. The core idea is to consider a zero knowledge proof for the knowledge of a secret group element $g$ such that x' = g * x with x,x' public, then render it to a signature (non-interactive protocol) via the classical Fiat-Shamir transform. Several schemes have been proposed with different instantiations of these assumptions: for example, LESS and MEDS use code equivalence (on different metrics). The mathematical structure of the group action can be exploited to optimize the schemes and to define a threshold version of the signature for any group action, moreover for the ones induced by linear code equivalence it is possible to exploit Abelian subgroups of the general linear group to achieve better parameters. The second part of the talk will be about the possible uses of the RLWE problem to achieve a secure post quantum federated learning (a machine learning technique that allows a set of users to train a shared model via local evaluated updated). To this end, we can use verifiable multi key homomorphic encryption to encrypt and aggregate the updates, that can then be validated via the use of zero knowledge proof for the range of the parameters.

Twin-Field Quantum Key Distribution (TF-QKD) enables two distant parties to establish a shared secret key, by interfering weak coherent pulses (WCPs) in an intermediate measuring station. This allows TF-QKD to reach greater distances than traditional QKD schemes and makes it the only scheme capable of beating the repeaterless bound on the bipartite private capacity. Here, we generalize TF-QKD to the multipartite scenario. Specifically, we propose a practical conference key agreement (CKA) protocol that only uses WCPs and linear optics and prove its security with a multiparty decoy-state method. Our protocol allows an arbitrary number of parties to establish a secret conference key by single-photon interference, enabling it to overcome recent bounds on the rate at which conference keys can be established in quantum networks without a repeater.

Most eligible Hamiltonians are not needed to completely describe quantum dynamics; a bounded subset of the Hermitian matrices is sufficient to generate the unitary group. I advocate removing the rest. The identification of global phases for state vectors induces a further reduction of the necessary Hamiltonians. Some strange geometry arises as a result.

Quantum correlations in general and quantum entanglement in particular embody both our continued struggle towards a foundational understanding of quantum theory as well as the latter's advantage over classical physics in various information processing tasks. Consequently, the problems of classifying (i) quantum states from more general (non-signalling) correlations, and (ii) entangled states within the set of all quantum states, are at the heart of the subject of quantum information theory. In this talk I will present two recent results ([1] and [2]) that shed new light on these problems, by exploiting a surprising connection with time in quantum theory: First, I will sketch a solution to problem (i) for the bipartite case, which identifies a key physical principle obeyed by quantum theory: quantum states preserve time orientations—roughly, the unitary evolution in local subsystems. Second, I will show that time orientations are intimately connected with quantum entanglement: a bipartite quantum state is separable if and only if it preserves arbitrary time orientations. As a variant of Peres's well-known entanglement criterion, this provides a solution to problem (ii).

String-diagrams allow us to manipulate tensor networks (and thus arbitrary linear maps) using drawings. Quantum circuits are drawn 'because' they are string diagrams. To foster the full power of diagrammatic simplifications in quantum circuits, some specific tensors and rules governing them are introduced: the ZX calculus. I shall introduce it, exemplify it with the teleportation circuit, and use it to prove the Gottesman-Knill theorem.

Quantum Signal Processing (QSP) is a powerful technique for designing quantum algorithms in which one can apply a polynomial transformation to the eigenvalues of a unitary. In this talk, I show that QSP can be used to tackle a new problem, which I called phase extraction, and that this can be used to provide quantum speed-up for proportional sampling, a problem of interest in machine-learning applications and quantum state preparation.

Quantum circuit diagrams are a diagrammatic language for describing algorithms in quantum computers and protocols in quantum cryptography, developed in part by Penrose and Feynman to bear resemblance to classical circuit diagrams. Quantum circuits are assembled piece by piece from a toolbox of standard pieces, like how a Lego castle is built from Lego bricks. In this pedagogical talk I will walk you through my effort to make sense of and standardize one piece in this toolbox: the vertical line.

Two-photon absorption (TPA) refers to the simultaneous absorption of two quanta of light by a quantum system. Since its first observation and description it has become a crucial tool in spectroscopy and microscopy; it allows for enhanced resolutions beyond what is capable with single-photon processes and further enables the interrogation of photosensitive samples. With recent years' progress in the availability of quantum sources of light, as well as their detection, TPA has seen renewed interest from a quantum metrological perspective. Within this framework, the goal is to find and describe potential quantum advantages in these tasks. This talk will begin by outlining the general problem of TPA as well as the mathematical tools underlying quantum metrology. We will also outline our recent results in search of optimal single-mode quantum states for TPA.

In this talk I will sketch some ideas of how to transfer techniques from quantum foundations and information, to Relativity Theory. More specifically, I want to discuss how one can use device-independent techniques, like the one used for Bell's theorem, to draw a distinction between special relativistic physics and non-special relativistic physics, e.g., general relativity.