Periodic Reporting for period 1 - FoQaCiA (Foundations of quantum computational advantage)
Reporting period: 2022-10-01 to 2024-03-31
Quantum computation is a technology with enormous promise. Many quantum algorithms have been developed to provide speed-ups for problems in quantum simulation, optimization, and linear algebra. The FoQaCiA project takes the view that the future success of quantum computing critically depends on advances at the most fundamental level. The basic techniques employed by the known quantum algorithms are few and far between. Largely, it still remains to be discovered how to harness the quantum systematically for computation. FoQaCiA aims to reach beyond existing paradigms such as quantum Fourier transform, amplitude amplification, Trotterized evolution, and variational quantum eigensolvers, to identify and validate novel quantum algorithmic building blocks.
There are four main FoQaCiA goals, each reflected in a scientific work package: (i) investigating the role of contextuality and other forms of nonclassicality as resources enabling quantum computational advantage; (ii) developing techniques for classically simulating quantum computation and analysing their complexity; (iii) applying number-theoretic techniques to shed light on quantum phenomena and to develop methods for exact synthesis of quantum circuits; (iv) reducing the overhead of fault-tolerant quantum computation. The project focuses on these areas due to their established importance for quantum computation, and for their rich phenomenology we can pick through to isolate and study the quantum structures of interest.
The FoQaCiA project starts from the very foundations of quantum theory, and asks how quantum programming techniques can arise from them. Besides the basic science uncovered by the fundamental insights that we aim to develop, the technology they embody will be reflected in new methods, algorithms and software. Thus, we aim to reach technology readiness levels from basic principles (TRL level 1), to proofs of concept (TRL level 3).
There are four main FoQaCiA goals, each reflected in a scientific work package: (i) investigating the role of contextuality and other forms of nonclassicality as resources enabling quantum computational advantage; (ii) developing techniques for classically simulating quantum computation and analysing their complexity; (iii) applying number-theoretic techniques to shed light on quantum phenomena and to develop methods for exact synthesis of quantum circuits; (iv) reducing the overhead of fault-tolerant quantum computation. The project focuses on these areas due to their established importance for quantum computation, and for their rich phenomenology we can pick through to isolate and study the quantum structures of interest.
The FoQaCiA project starts from the very foundations of quantum theory, and asks how quantum programming techniques can arise from them. Besides the basic science uncovered by the fundamental insights that we aim to develop, the technology they embody will be reflected in new methods, algorithms and software. Thus, we aim to reach technology readiness levels from basic principles (TRL level 1), to proofs of concept (TRL level 3).
During the first reporting period, the FoQaCiA consortium published a total of 43 papers and preprints featuring work on all four scientific work packages. The primary focus is on theory, but there were also some experimental tests of the ideas developed by the project, using integrated photonic chips and ion traps. On a more applied side, the FoQaCiA project released 7 open software packages with code to reproduce some published results and to enable further work on these topics by the wider community.
WP1 investigates the interplay between nonclassicality criteria and causality in pinpointing the source of quantum advantage in different tasks. On this topic, the project published numerous studies. We have proved fundamental results on nonlocality and contextuality, developed unified theoretical frameworks for causality and contextuality and took the first steps in applying them to analyse quantum advantage in various computational setpus. We also implemented new experimental tests of coherence, dimension, and contextuality, and we published a paper on a practical measurement-based scheme for hybrid quantum/classical computation using d-level systems instead of qubits.
WP2 focuses on new techniques for classical simulation of quantum computation. We have explored emerging features of classical simulation using extensions of the stabilizer formalism, in particular the so-called Λ polytopes, which can represent positively a wider range of states and dynamics than usual stabilizer subtheory. We also published two open source software packages embodying newly derived stabilizer techniques for simulation of qubits and qudits, one other piece of software for optimising sum-over-Clifford decompositions to improve stabiliser-rank or stabiliser-extent simulations, and two further software packages developing related ideas for cryptographic applications.
WP3 studies some discrete structures arising in quantum circuits and error correction, in particular quantum measurements known as symmetric informationally-complete (SIC) POVMs, and techniques for obtaining exact circuit synthesis for operations on d-level quantum systems (qudits). In this first reporting period, we have developed and released code to work with general Clifford and Heisenberg groups of unitaries, and tackled the problem of qutrit circuit synthesis, with ongoing work on qudit circuit synthesis for d>3, and improving some already obtained results on SIC-POVMs for certain dimensions.
In WP4 we work with optimization of techniques useful for fault-tolerance of future, larger-scale quantum computers, which often rely on a technique known as magic state injection and distillation. We have characterized certain qutrit gates which admit a magic state injection circuit of half the usual size, and are currently developing work capable of delivering the same advantage for qudits. We have done some preliminary work devising topological rules for manipulating entangled resource states for quantum computation in the form of 3D graph states, which in the future will enable us to explore this computationally. We are also unveiling connections between the foundational notion of contextuality and both 3D cluster states and the resource theory magic states.
WP1 investigates the interplay between nonclassicality criteria and causality in pinpointing the source of quantum advantage in different tasks. On this topic, the project published numerous studies. We have proved fundamental results on nonlocality and contextuality, developed unified theoretical frameworks for causality and contextuality and took the first steps in applying them to analyse quantum advantage in various computational setpus. We also implemented new experimental tests of coherence, dimension, and contextuality, and we published a paper on a practical measurement-based scheme for hybrid quantum/classical computation using d-level systems instead of qubits.
WP2 focuses on new techniques for classical simulation of quantum computation. We have explored emerging features of classical simulation using extensions of the stabilizer formalism, in particular the so-called Λ polytopes, which can represent positively a wider range of states and dynamics than usual stabilizer subtheory. We also published two open source software packages embodying newly derived stabilizer techniques for simulation of qubits and qudits, one other piece of software for optimising sum-over-Clifford decompositions to improve stabiliser-rank or stabiliser-extent simulations, and two further software packages developing related ideas for cryptographic applications.
WP3 studies some discrete structures arising in quantum circuits and error correction, in particular quantum measurements known as symmetric informationally-complete (SIC) POVMs, and techniques for obtaining exact circuit synthesis for operations on d-level quantum systems (qudits). In this first reporting period, we have developed and released code to work with general Clifford and Heisenberg groups of unitaries, and tackled the problem of qutrit circuit synthesis, with ongoing work on qudit circuit synthesis for d>3, and improving some already obtained results on SIC-POVMs for certain dimensions.
In WP4 we work with optimization of techniques useful for fault-tolerance of future, larger-scale quantum computers, which often rely on a technique known as magic state injection and distillation. We have characterized certain qutrit gates which admit a magic state injection circuit of half the usual size, and are currently developing work capable of delivering the same advantage for qudits. We have done some preliminary work devising topological rules for manipulating entangled resource states for quantum computation in the form of 3D graph states, which in the future will enable us to explore this computationally. We are also unveiling connections between the foundational notion of contextuality and both 3D cluster states and the resource theory magic states.
To amplify their impact, all scientific results of our project have been made publicly available as preprints on the arXiv repository. We have so far posted 7 open software packages that enable reproduction of our results, facilitating further work to be done by the wider community using the techniques developed by the project. Going forward, we will remain attentive to the potential for innovation and exploitation through IP protection in the form of patents. A first FoQaCiA conference was organized at the Perimeter Institute for Theoretical Physics in May 2024, with the videos of all 34 talks made freely available online. FoQaCiA researchers have presented their work in over 20 outreach events, and disseminated the project’s results through poster presentations and 61 talks at conferences, workshop, and research seminars.