Workshop on Quantum Computing

Oct 19, 2022, 9:00 AM → Oct 21, 2022, 6:00 PM Asia/Nicosia

Livadhiotis City Hotel

Karl Jansen (DESY Zeuthen)

Wednesday, 19 October

1 Welcome

Speaker: Karl Jansen (DESY Zeuthen)

Session 1

Convener: Karl Jansen (DESY Zeuthen)

2 New directions in particle tracking with quantum algorithms

In this talk I will discuss a few future opportunities to study particle tracking with quantum algorithms.
These go from using quantum algorithms for the clustering of energy deposits within tracking detectors (potentially using quantum machine learning), to using lookup tables combined with a Grover search to realise an ATLAS FTK-like system, and to exploring new collider scenarios, like a high energy muon collider.

Speaker: Federico Meloni (DESY)

NewDirectionsQuantumTracking.pdf

10:45 AM Coffee

3 QUBO-tuning for particle track reconstruction: optimisation strategies and parameter settings

Quadratic Unconstraint Binary Optimization (QUBO) offers an exceptional approach to tackle particle track reconstruction - to encode the data into a single equation and solve it as a whole.
To minimise the QUBO cost function, a quantum device can be employed. However, a quantum device of the required size to solve common track reconstruction tasks does not exist.
Therefore, an efficient and effective optimization strategy has to be chosen, in which the QUBO is eventually split into smaller parts and solved successively.

The basic geometry of the positron tracking system of LUXE (Laser Und XFEL Experiment) provides a proper playground to probe the QUBO formulation for particle track reconstruction. In this work, events from a custom Monte Carlo event generator, PTARMIGAN (Ponderomotive trajectories and radiation emission) are propagated through a dipole magnet and the detector system, using a simplified simulation.

The effect of different QUBO splitting techniques on the final track reconstruction efficiency is explored. Additionally, the impact of various settings for the linear and quadratic terms of the QUBO, as well as the impact of the initial solution guess is investigated.

Speaker: David Spataro (DESY)

QUBO-tuning for particle track reconstruction.pdf

4 Towards a complete track reconstruction framework in LUXE

LUXE (Laser Und XFEL Experiment) is a proposed experiment at DESY and European XFEL in Hamburg Germany aiming to study non-perturbative quantum electrodynamics (QED) in electron-laser and photon-laser collisions. One of the key measurements is the number of positrons produced via non-linear Breit-Wheeler process. The positrons are measured with a Silicon pixel tracking detector. The reconstruction of positron tracks in LUXE is challenging and various methods have been studied including the use of quantum computing. The talk will introduce the classical Combinatorial Kalman Filter method and compare its performance with the other methods. In addition, I will present how to go beyond the simplified study and the challenges ahead. The complementarity with the other positron detector as well as the work integrating the different tracking methods into a common digitisation and reconstruction framework for LUXE will also be discussed.

Speaker: Yee Chinn Yap

20221019-YeeY-Cyprus.pdf

12:45 PM Lunch

Session 2

Convener: Stefan Kühn

5 Determining the Mass Renormalization of the Schwinger Model with Wilson Fermions using Tensor Networks

Studies of the Schwinger model in the Hamiltonian formulation have hitherto used the Kogut-Susskind staggered approach. However, Wilson fermions offer an alternative approach and are often used in Monte Carlo simulations. Tensor networks allow the exploration of the Schwinger model even with a topological θ-term, where Monte Carlo methods would suffer from the sign problem. Here, we study the one-flavour Schwinger model with Wilson fermions and a topological θ-term using Matrix Product States (MPS) methods in the Hamiltonian formulation. The mass parameter in this model receives an additive renormalization shift from the Wilson term. In order to perform a continuum extrapolation, the knowledge of this shift is important. We present a method suitable for tensor networks that determines the mass renormalization using observables such as the electric field density, which vanish when the renormalized mass is zero. Using this shift, the continuum extrapolation is performed for various observables.

Speaker: Takis Angelides (DESY)

Cyprus Workshop Presentation.pdf

Cyprus Workshop Presentation.pptm

5:15 PM Coffee

6 Strategies for the Determination of the Running Coupling of (2+1)-dimensional Quantum Electrodynamics (QED) with Quantum Computing

We propose to utilize NISQ-era quantum devices to compute short distance quantities in (2 + 1)-
dimensional QED and to combine them with large volume Monte Carlo simulations and perturbation
theory. Since the theory is asymptotically free, it would serve as a training ground for future studies of Quantum Chromodynamics in (3 + 1)-dimensions on quantum computers. From the definition of the QED Hamiltonian on the lattice, we compute observables, e.g. the energy, with a Variational Quantum approach suitable also for excited energy levels. We explore methods for the encoding of the system efficiently on a quantum circuit and for the minimization procedure. In the latter case, we examine techniques to combine operators and circuits, and test the performances of the optimizers available (in Qiskit). In particular, we perform a calculation of the mass gap in the small and intermediate regime, demonstrating, in the latter case, that it can be resolved reliably. The so-obtained mass gap can be employed to match corresponding results from Monte Carlo simulations, which can be used eventually to find the lattice spacing and hence set the physical scale.

Speaker: Arianna Crippa (Deutsches Elektronen-Synchrotron (DESY))

AC_qed2p1.odp

AC_qed2p1.pdf

7 A qubit-ADAPT VQE Implementation for Diatomic Molecules using Explicitly Correlated Basis Functions

Variational hybrid classical-quantum algorithms such as the Variational Quantum Eigensolver represent a major research field in the era of Noisy-Intermediate Scale Quantum (NISQ) devices [1]. The use of such algorithms promises advances in many sciences such as solid-state and high-energy physics as well as in quantum chemistry, where a proper understanding of electron-correlation is decisive for an accurate description of molecular structure. In order to catch the essence of electron correlation from an exponentially growing Hilbert space, elaborate polynomially-scaling numerical methods such as Coupled-Cluster or Configuration Interaction have been developed and successfully applied over the past decades. In the simplest possible cases of few-electron diatomic molecules, however, explicitly correlated basis functions such as the so-called Kołos-Wolniewicz [2] basis are particularly attractive as they provide highly accurate energies while requiring only a small amount of basis functions and therefore, with regard to implementation on a NISQ device, a small number of qubits. While a lot of efforts have been spent in recent years on implementing variational algorithms employing a formulation based on second quantisation, treatments in first quantisation, however, still seem to be rather scarce. Whichever quantisation is ultimately chosen, a variational algorithm requires an ansatz allowing for the optimisation of variational parameters. The ADAPT approach [3] iteratively extends its ansatz at each step by choosing an operator from a pool that maximises the energy gradient with respect to its associated variational parameter. Its hardware-efficient variant of qubit-ADAPT naturally goes along with the use of first quantisation as all symmetry properties can be imprinted in the basis functions rather than in the corresponding Fock operators, thus bypassing the need for fermion-qubit mappings and its rather complicated operator pool. Another potential strength of the approach lies in the capability of mitigating the so-called Barren-plateau problem by providing a payoff between expressibility and trainability. In this talk, the method will be introduced and preliminary results on the electronic structure of the hydrogen molecule using the qubit-ADAPT ansatz and Kolos basis functions will be presented and discussed.

References

[1] S. McArdle et al.: Rev. Mod. Phys. 92, 015003 (2020)
[2] W. Kołos and L. Wolniewicz, J. Chem. Phys. 41, 3663 (1964)
[3] H.L. Tang et al.: PRX Quantum 2, 020310 (2021)

Speaker: Hakon Volkmann (Humboldt-Universität zu Berlin)

talk.pdf

Thursday, 20 October

Session 3

Convener: Alejandro Saenz (Humboldt-Universität zu Berlin)

8 Quantum Angle Generator for Image Generation

The Quantum Angle Generator (QAG) is a new generative model for quantum computers and described in this paper. The QAG model consists of a parameterized quantum circuit trained with an objective function. It utilizes angle encoding for the conversion between the generated quantum data and classical data. Therefore, it requires one qubit per feature or pixel, while the output resolution is adjusted by the number of shots performing the image generation. This approach allows the generation of highly precise images on recent quantum computers.
In this paper the model is optimised for a High Energy Physics (HEP) use case generating simplified one-dimensional energy distributions measured by a specific particle detector, a calorimeter. With a reasonable number of shots, a high level of accuracy is achieved by the QAG model.
The advantages of the QAG model are lined out - such as simple and stable training, a reasonable amount of qubits, circuit calls, circuit size and computation time compared to other quantum generative models, e.g. quantum GANs (qGANs) and Quantum Circuit Born Machines.

Speaker: Florian Rehm (CERN / RWTH Aachen University)

Cyprus_QAG_QGAN_Florian_Rehm_v2.pdf

10:45 AM Coffee

9 Parallel Implementation of Quantum Circuits

Often running quantum circuits on real hardware is time consuming due to queueing. For problems where the circuit size is small, and in order to maximise the output of a single execution, different instances of the circuit can be run simultaneously.
As an example, a small Quantum Circuit Born Machine is trained using the parameter shift rule, which requires the circuit to be run twice with a slightly different parameterisation.

Speaker: Alexis-Harilaos Verney-Provatas (DESY)

Cyprus_Workshop.pdf

10 Studying the variational quantum eigensolver algorithm for particle track reconstruction in an ATLAS-like detector

Particle track reconstruction poses a key computing challenge for future collider experiments. Quantum computing carries the potential for exponential speedups and the rapid progress in quantum hardware might make it possible to address the problem of particle tracking in the near future.
The solution of the tracking problem can be encoded in the ground state of a quadratic unconstrained binary optimization. In our study, sets of three hits in the detector are grouped into triplets.
True triplets are part of trajectories of particles, while false triplets are random combinations of three hits.
By approximating the ground state, the variational quantum eigensolver algorithm aims at identifying true triplets. Different circuits and optimizers are tested for small instances of the tracking problem with up to 23 triplets. Precision and recall are determined in a noiseless simulation and the effects of readout errors are studied.
It is planned to repeat the experiments on real hardware and to combine the solutions of small instances to address the full-scale tracking problem.

Speaker: Tim Schwägerl (Desy, Humboldt-University of Berlin)

particle_tracking_larnaca-1.pdf

12:45 PM Lunch

Session 4

Convener: Federico Meloni (DESY)

11 Exploring the phase structure of the multi-flavor Schwinger model with quantum computing

We propose a variational quantum eigensolver suitable for exploring the phase structure of the multi-flavor Schwinger model in the presence of a chemical potential. The parametric ansatz we design incorporates the symmetries of the model and can be implemented on both measurement-based and circuit-based quantum hardware. We numerically demonstrate that our ansatz is able to capture the phase structure of the model and allows for faithfully approximating the ground state. Our results show that our approach is suitable for current intermediate-scale quantum hardware and can be readily implemented on existing quantum devices.

Speaker: Stefan Kühn

S_Kuehn-Schwinger_1WayQC.pdf

5:15 PM Coffee

12 Classical Splitting of Parametrized Quantum Circuits

Barren plateaus appear to be a major obstacle to using variational quantum algorithms to simulate large-scale quantum systems or replace traditional machine learning algorithms. They can be caused by multiple factors such as expressivity, entanglement, locality of observables, or even hardware noise. We propose classical splitting of ansätze or parametrized quantum circuits to avoid barren plateaus. Classical splitting is realized by splitting an N qubit ansatz to multiple ansätze that consists of O(logN) qubits. We show that such an ansatz can be used to avoid barren plateaus. We support our results with numerical experiments and perform binary classification on classical and quantum datasets. Then, we propose an extension of the ansatz that is compatible with variational quantum simulations. Finally, we discuss a speed-up for gradient-based optimization and hardware implementation, robustness against noise and parallelization, making classical splitting an ideal tool for noisy intermediate scale quantum (NISQ) applications.

Speaker: Cenk Tüysüz (DESY)

cyprus22_tuysuz.pdf

13 Numerical calculations for the static force for the (2+1) dimensional lattice QED

We work on the Kogut-Susskind Hamiltonian formulation for the (2+1)d QED with open boundary conditions for a ladder lattice with up to 5 plaquettes. We add a pairs of external static charges at variable distances in an attempt to investigate confinement and we study the static force for variable values of coupling and the kinetic strength. We also identify the states of maximal translational symmetry which in an infinite lattice would correspond to zero momentum states.

Speaker: Georgios Polykratis (The Cyprus Institute)

G_Polykratis.pdf

8:00 PM Dinner

Friday, 21 October

Session 5

Convener: Constantia Alexandrou (University of Cyprus and The Cyprus Institute)

14 Boltzmann machines for medical data

Classical and quantum Boltzmann machines for analyzing medical data.

Speaker: Maria Demidik (DESY)

Larnaca_21102022.pdf

Larnaca_21102022.pptx

10:45 AM Coffee

15 Cristalline phases in the finite winding number sectors of a quantum link ladder

In this talk I will present the ground state properties of the U(1) gauge invariant quantum link ladder with spin $1/2$ gauge fields. The model is inserted in a an external electric field which cause the winding electric fluxes to condense in the ground state.
I will show how the electric flux tubes arrange themselves in the bulk giving rise to crystalline patterns, whose period can be controlled by tuning the external field. I will show different observables that describes the properties of the ground states in different winding number sectors.

Speaker: Paolo Stornati (ICFO)

16 Optimizing flight gate assignment problem using the variational quantum eigensolver

The optimal flight gate assignment is a difficult optimization problem in the air transportation system, which aims to minimize the total transit time of the passengers by optimizing the gate assignment of each flight. Considering the objective function and constraints, this problem can be constructed as a Quadratic Unconstraint Binary Optimization problem (QUBO) using the one-hot encoding and be solved by quantum computing.

In this work, we do simulations of the variational quantum eigensolver (VQE) to optimize the flight gate assignment problem. Firstly, we use the Conditional Value-at-Risk (CVaR) method to modify the expectation to be optimized by a classical optimizer. The CVaR approach leads to a higher success rate in getting the optimal solution. Secondly, we use binary encoding to construct the Hamiltonian, which can satisfy one of the constraints naturally and will be optimized more efficiently than the QUBO approach. Lastly, we compare the performance of the quantum circuits with and without entanglements, and see an advantage of the entanglement circuit in our simulation results.

Speaker: Yahui Chai

FGA_VQE.pdf

12:45 PM Lunch

Session 6

17 Dimensional Expressivity Analysis for Parametric Quantum Circuits

In this talk, we will be looking at quantum circuits comprising parametric gates and analyze their expressivity in terms of the space of states that can be generated by a given circuit.

A standard tool in quantum computing are Variational Quantum Simulations (VQS) which form a class of hybrid quantum-classical algorithms for solving optimization problems. For example, the objective may be to find the ground state of a Hamiltonian by minimizing the energy. As such, VQS use parametric quantum circuit designs to generate a family of quantum states (e.g., states obeying physical symmetries) and efficiently evaluate a cost function for the given set of variational parameters (e.g., energy of the current quantum state) on a quantum device. The optimization is then performed using a classical feedback loop based on the measurement outcomes of the quantum device. In the case of energy minimization, the optimal parameter set therefore encodes the ground state corresponding to the given Hamiltonian provided that the parametric quantum circuit is able to encode the ground state. Hence, the design of parametric quantum circuits is subject to two competing drivers. On one hand, the set of states, that can be generated by the parametric quantum circuit, has to be large enough to contain the ground state. On the other hand, the circuit should contain as few parametric quantum gates as possible to minimize noise from the quantum device. In other words, when designing a parametric quantum circuit we want to ensure that there are no redundant parameters.

Thus, I will introduce the dimensional expressivity analysis as a means of analyzing a given parametric design in order to remove redundant parameters as well as any unwanted symmetries. Furthermore, I will discuss the hardware implementation of the dimensional expressivity analysis.

Speaker: Tobias Hartung (Northeastern University - London)

hartung.pdf

18 Quantum Error Correction for quantum tracking: Overview and Limits

Quantum Error Correction (QEC) is an important field of research toward the realisation of large-scale fault-tolerant quantum computers. Finding and correcting errors is crucial in recovering information in all quantum computations, given potentially corrupted data due to the noisy nature of the quantum hardware used. QEC efforts mainly focus on protecting information by implementing error-correcting codes, a practice referred to as decoding. In this talk, I will give an overview of the most common theoretical and experimental decoding methods. Moreover, the applicability of these methods for quantum particle track reconstruction, including the recently published qiskit framework for QEC, will be discussed.

Speaker: Annabel Kropf (DESY)

IntroQEDCyprus.pdf