Continuous-time quantum computing and simulation: perspectives and challenges

In the first half Dr Ben Lanyon will present a trapped-ion quantum simulator. His approach is based on a 1D string of trapped atomic calcium ions, between which his group can turn on tunable-range interactions using lasers. He achieved full individual qubit (ion) control and entangled states for up to 20 qubits (N Friis et al., Phys. Rev. X., 2018). Dr Lanyon presents the system capabilities, challenges and recent results on extending the system to 50 qubits. In the second half Dr Lanyon will present his recent results on interfacing these registers of trapped ions with travelling photons. In particular, using cavity-QED techniques the group achieve on demand entanglement between the ion-qubit state and a travelling photon with probability of over 50%. Secondly, he observes that the entanglement remains after the photon travels over 50km of optical fibre (V. Krutyanskiy et al., npj Quantum Information, 2019). This opens up the possibility of entangling these registers of ions, hundreds of kilometres apart and more.

Quantum dots, quantum emitters in a semiconductor matrix, are most often proposed as a bright and efficient source of single photons for many quantum technologies. And, as Professor Ruth Oulton has demonstrated previously, a near-perfect single photon source goes hand-in-hand with potentially deterministic interactions with input photons. However, it is the spin degree of freedom in their ground state which gives them the greatest scope for quantum simulations. Photons input into a QD device can be entangled with the long coherence time spin system, and protocols to produce entangle chains of photons (1D cluster states) have already been demonstrated. Professor Oulton will discuss how one may entangle very long coherence time photons with the spin. Reflecting the long photon from a quantum dot spin precessing in a magnetic field results in a phase modulation of the photon wave function in time, with periodic entanglement resulting. Professor Oulton will discuss the potential of spin-photon entangled states as building blocks for analogue and digital quantum simulations.

Quantum annealing makes less stringent demands on qubit coherence than gate-based approaches, thereby enabling proof-of-principle demonstrations of annealers with around 2000 superconducting flux qubits.  Furthermore by capacitively shunting the flux qubit and reducing the circulating current one can achieve both high coherence and low leakage, making the flux qubit an excellent approximation to a two-level quantum system. Nevertheless most measurements on experimental annealers are plagued by noise, and the role of coherence in quantum annealing is not currently understood. Professor Paul Warburton will describe his group’s experimental and analytical work on both understanding coherence in flux qubit annealers and how to optimise their use for real-world applications in the presence of noise. They have used the Schrieffer-Wolf transformation to extract the Pauli coefficients from quantum circuit models and developed this technique to investigate non-stoquastic Hamiltonians arising from simultaneous inductive and capacitive qubit interactions. They have analysed the extent to which Landau-Zener-Stückelberg oscillations can be used as a coherence metric in the context of quantum annealing. The group has also developed a new method for embedding real-world problems with high qubit connectivity onto hardware graphs of limited degree and show experimentally that this method outperforms rival embedding techniques for annealers in the presence of noise. The research is based upon work supported by EPSRC (grant reference EP/R020159/1) and the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via the US Army Research Office contract W911NF-17-C-0050. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the ODNI, IARPA, or the US Government. 

Energy landscape shaping is a way to alter the natural evolution of a quantum system to achieve certain objectives utilising the continuous evolution of the system instead of applying discrete quantum gates and dynamic control. Using spin networks as an abstract model system Dr Sophie Shermer will discuss how to design energy landscapes to control information flow between nodes in various networks. Energy landscape design will be formulated as an optimal control problem and in terms of linear feedback control systems. Various solutions to the optimal control problems arising will be examined in terms of robustness. Robustness of the evolution with regard to uncertainty in system parameters, initial conditions and environmental effects such as decoherence is crucial, and the development of better tools inspired by classical engineering is essential for robust quantum technology. Dr Shermer will discuss classical engineering approaches to robustness and the challenges in applying them to quantum systems, as well as some promising results suggesting that classical limits on robustness need not apply to the latter. Possible implementations of energy landscape control using cold atoms trapped in optical lattices as experimental testbeds for pseudo-spin networks will also be considered.

Professor Dieter Jaksch will discuss how nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. This is achieved by utilising multiple copies of variational quantum states to treat nonlinearities efficiently and by introducing tensor networks as a programming paradigm. He will demonstrate the key concepts of the algorithm using the nonlinear Schrödinger equation as a canonical example. He will present numerical results showing that the variational quantum ansatz can be exponentially more efficient than matrix product states and present experimental proof-of-principle results obtained on an IBM Q device.

With quantum computing technologies nearing the era of commercialisation and quantum advantage, machine learning (ML) has been proposed as one of the promising killer applications. Despite significant effort, there has been a disconnect between most quantum ML proposals, the needs of ML practitioners, and the capabilities of near-term quantum devices towards a conclusive demonstration of a meaningful quantum advantage in the near future. In this talk, Dr Alejandro Perdomo-Ortiz provides concrete examples of intractable ML tasks that could be enhanced with near-term devices. He argues that to reach this target, the focus should be on areas where ML researchers are struggling, such as generative models in unsupervised and semi-supervised learning, instead of the popular and more tractable supervised learning tasks. Alejandro focuses on hybrid quantum-classical approaches and illustrates some of the key challenges he foresees for near-term implementations. He will present as well recent experimental implementations of these quantum ML models in both, superconducting-qubit and ion-trap quantum computers.

There are many parallels between digital and analogue quantum simulation. For example until very recently, the best digital simulation algorithms used quantum random walks. Using this and other examples, Dr Steve Brierley will explore the similarities and differences between digital and analogue simulation with a view to what each community might learn from the other.