Designing optimal strategies for controlling complex quantum systems

AI_CDT_DecisionMaking

Details

Introduction

Complex processes, such as chemical reactions or financial markets, are challenging to predict due to vast data requirements, temporal correlations, and sensitivity to initial conditions [1]. Weather forecasting exemplifies these challenges, involving large parameter spaces, memory effects, and high sensitivity to small perturbations. Accurate modelling of such systems is critical for both computational optimisation and socio-economic decision-making.

Machine learning (ML) and artificial intelligence (AI) have revolutionised our ability to model, predict, and optimise classical systems, as recognised by the 2024 Nobel Prize in Physics for advancing predictive science [2]. The question now arises: can similar breakthroughs extend to complex quantum processes?

Quantum Complexity and ML.

Quantum systems present distinct challenges beyond classical complexity: They are easily disturbed by interactions, leading to inherently random observations. This fragility complicates the development of scalable quantum technologies, despite their potential for exponential computational advantages [e.g., 3-5]. Environmental noise introduces additional complexity, necessitating sophisticated error-mitigation techniques like dynamical decoupling (DD) [6], which uses control pulses to preserve quantum coherence.

Optimising DD schemes is a formidable task due to process complexity. A recently developed framework captures memory effects in quantum processes, permitting deduction of all observable behaviours from experimental interactions [7]. This project aims to leverage these developments and apply ML to optimise DD protocols for arbitrary quantum processes.

Beyond State-of-the-Art.

Standard quantum control methods involve two steps: (i) process tomography to model the system [8], and (ii) control parameter optimisation based on the model [9]. However, quantum systems require exponentially more data than classical ones—modelling a qubit across N times requires O(2^(4N)) parameters, making the standard approach impractical at scale.

Our goal is to bypass this bottleneck by directly optimising control sequences without first constructing a detailed model. We propose a model-free, “on-the-fly” optimisation method that focuses only on necessary aspects of the system. Adapting ML techniques such as differential programming, we will develop algorithms to learn optimal DD sequences for unknown quantum processes. This approach is efficient, scalable, and experimentally feasible, aligning with constraints in current quantum computing setups.

The central research question is: How can we design optimal quantum control sequences with minimal system information and limited control resources? Answering this promises to significantly advance quantum error mitigation and control optimisation.

Research Plan.

This interdisciplinary project combines quantum information theory and ML. The student will be supervised by Dr. Philip Taranto (Quantum ML & AI, Dept. of Physics) and Dr. Mauricio A. Álvarez & Dr. Wei Pan (ML, Dept. of Computer Science) at the University of Manchester. Weekly meetings will provide balanced support from both quantum and ML perspectives.

The project will be structured into three tasks (T), with 6-month milestones (M) ensuring progress:

T1: Investigate state-of-the-art DD techniques.

M1.1: Conduct literature review of optimal control and DD.

M1.2: Implement a basic “learn & act” DD protocol.

T2: Develop a model-free, ML-driven optimisation for control protocols.

M2.1: Implement an ML-based DD optimisation strategy.

M2.2: Evaluate performance and compare with standard methods.

T3: Extend findings to other quantum control problems.

M3.1: Apply methods to quantum noise mitigation.

M3.2: Extend to quantum error correction schemes.

This project is expected to result in two high-impact publications, advancing ML approaches to quantum control and error mitigation.

Student Desirable Background:

Students with a strong background in physics — in particular quantum theory — are desirable, as this is the main application domain of this project. Skills in applied mathematics/statistics (e.g., ML, AI, probabilistic models) as well as computer programming (e.g., Python, Mathematica) are also desired, as these will be the main technical tools used throughout this project.

Before you apply

We strongly recommend that you contact the supervisor(s) for this project before you apply. Please include details of your current level of study, academic background and any relevant experience and include a paragraph about your motivation to study this PhD project.

How to apply:

Please apply through the below link for the PhD Artificial Intelligence CDT:

https://pgapplication.manchester.ac.uk/psc/apply/EMPLOYEE/SA/s/WEBLIB_ONL_ADM.CIBAA_LOGIN_BT.FieldFormula.IScript_Direct_Login?Key=UMANC1251000021489F

Dr Philip Taranto is the main supervisor for this project.

Dr Taranto will join the Department of Physics and Astronomy in January 2025.

To view his profile please visit: https://tarantophilip.github.io

[tarantophilip.github.io]

Your application will not be processed without all of the required documents submitted at the time of application, and we cannot accept responsibility for late or missed deadlines. Incomplete applications will not be considered.

After you have applied you will be asked to upload the following supporting documents:

• Final Transcript and certificates of all awarded university level qualifications
• Interim Transcript of any university level qualifications in progress
• CV
• Supporting statement: A one or two page statement outlining your motivation to pursue postgraduate research and why you want to undertake postgraduate research at Manchester, any relevant research or work experience, the key findings of your previous research experience, and techniques and skills you’ve developed. (This is mandatory for all applicants and the application will be put on hold without it).
• Contact details for two referees (please make sure that the contact email you provide is an official university/work email address as we may need to verify the reference)
• English Language Certificate (if applicable)

Equality, diversity and inclusion is fundamental to the success of The University of Manchester, and is at the heart of all of our activities. We know that diversity strengthens our research community, leading to enhanced research creativity, productivity and quality, and societal and economic impact. (Equality, diversity and inclusion | The University of Manchester)

We actively encourage applicants from diverse career paths and backgrounds and from all sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation and transgender status.

We also support applications from those returning from a career break or other roles. We are dedicated to supporting work-life balance and offer flexible working arrangements to accommodate individual needs. Our selection process is free from bias, and we are committed to ensuring fair and equal opportunities for all applicants.

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