Research - Quantum Computing.

Deep Reinforcement Learning for Efficient Measurement of Quantum Devices.

S. B. Orbell, V. Nguyen, D.T. Lennon, H. Moon, F. Vigneau, L.C. Camenzind, L. Yu, D.M. Zumbühl, G.A.D. Briggs, M.A. Osborne, D. Sejdinovic, N. Ares

https://arxiv.org/abs/2009.14825

Deep reinforcement learning is an emerging machine learning approach which can teach a computer to learn from their actions and rewards similar to the way humans learn from experience. It offers many advantages in automating decision processes to navigate large parameter spaces. This paper proposes a novel approach to the efficient measurement of quantum devices based on deep reinforcement learning. We focus on double quantum dot devices, demonstrating the fully automatic identification of specific transport features called bias triangles. Measurements targeting these features are difficult to automate, since bias triangles are found in otherwise featureless regions of the parameter space. Our algorithm identifies bias triangles in a mean time of less than 30 minutes, and sometimes as little as 1 minute. This approach, based on dueling deep Q-networks, can be adapted to a broad range of devices and target transport features. This is a crucial demonstration of the utility of deep reinforcement learning for decision making in the measurement and operation of quantum devices.

Research - Quantum Computing.

Optimising the quantum clock speed.

S. B. Orbell

The Rabi frequency (f_Rabi) is defined as the frequency of oscillation of the quantum state around the Bloch sphere when the electrical driving frequency is equal to the Larmor frequency. The Rabi frequency (f_Rabi) therefore gives an approximate measure of the number of gate operations that can be performed on a qubit per unit time. The (T₂) relaxation time quantifies the (dephasing) rate at which the information about the systems quantum state decays. The product of the decay time (T₂) and the Rabi frequency (f_Rabi) is therefore often used as a quality factor for a qubit as it approximately quantifies the number of coherent gate operations that can be performed before the information encoded in the qubit is lost via relaxation.

Research - Optimal quantum control.

Optimal quantum control via automatic differentiation.

S. B. Orbell

Quantum gates serve as logical unitary operations on the computational subspace of a quantum system. The fidelity of a quantum gate defines the closeness of the input-output state mapping to that of the ideal unitary operation. It is an essential metric in benchmarking and evaluating quantum devices, as achieving high-fidelity operations is imperative for the practical realization of a fault tolerant platform for running quantum algorithms. Given a quantum system in a well-defined initial state, and a Hamiltonian describing the dynamics of the evolution of the system under the time-dependent Schrödinger equation \begin{align} i\hbar \frac{\partial}{\partial t} \Psi(t) &= \hat{H} \Psi(t) \\ \hat{H} &= \hat{H}_0 + \hat{H}_C [u(t)] \end{align} with a drift term \(H_0\) and a control term \(H_C\) defined by a time dependent control vector \(u(t)\). The problem of optimal quantum control is to find a function \(u(t)\) which evolves the system to a desired target state, or implements a target transformation. For a transition to a target state \(\ket{\psi_{target}}\), the solution can be found by minimising the fidelity \begin{align} L(u(t)) = 1 - | \braket{\psi_{\mathrm{control}} |\psi_{\mathrm{target}}}|^2 \end{align} where \(\Psi(t=T) = \ket{\psi_{\mathrm{control}}} = U(u(t))\ket{\psi_{\mathrm{initial}}}\), averaged over a set of initial states, \(\Psi(t=0)=\ket{\psi_{\mathrm{initial}}}\), which define a Haar measure for the system. We use the following Hamiltonian for two-coupled Loss DiVincenzo hole spin qubits at a Si/SiGe double quantum dot. \begin{align} H_{eff} = &H_0 + [S, V] \\ H_{eff} = &\left( \begin{array}{ccccc} \epsilon & 0 & 0 & 0 & 0 \\ 0 &\beta \Sigma & 0 & 0 & 0 \\ 0 & 0 & \beta \Delta & 0 & 0 \\ 0 & 0 & 0 & -\beta \Delta & 0 \\ 0 & 0 & 0 & 0 & -\beta \Sigma \\ \end{array} \right) + \frac{1}{\epsilon} \left( \begin{array}{ccccc} 2 \left(t_c^2+t_{\text{SO}}^2\right) & 0 & 0 & 0 & 0 \\ 0 & -t_{\text{SO}}^2 & -t_c t_{\text{SO}} & t_c t_{\text{SO}} & t_{\text{SO}}^2 \\ 0 & -t_c t_{\text{SO}} & -t_c^2 & t_c^2 & t_c t_{\text{SO}} \\ 0 & t_c t_{\text{SO}} & t_c^2 & -t_c^2 & -t_c t_{\text{SO}} \\ 0 & t_{\text{SO}}^2 & t_c t_{\text{SO}} & -t_c t_{\text{SO}} & -t_{\text{SO}}^2 \\ \end{array} \right) \end{align} In most cases of interest, an analytical solution to this control problem does not exist, hence optimal control solutions must be found numerically. We can optimize the fidelity of quantum operations with respect to the control pulse using a gradient-based optimization technique, namely the ADAM optimizer. The fidelity is computed using time evolution in the Schrödinger picture. This allows for an efficient, iterative refinement of the control pulses, driving the system toward optimal gate operations. The advantage of this method, with respect to previous gradient based optimal control techniques, such as GRAPE, is that we can add any modifications to our simulation, and still trivially acquire gradients. These modifications can include affects from a realistic quantum device measurement setup, such as filtering affects, non-linear transmissions, experimental noise sources.

Research - Si\SiGe Singlet-Triplet qubit.

Measurements and simulations of a Singlet-Triplet hole spin qubit in Si\SiGe heterostructure.

S. B. Orbell

We consider a tunnel coupled double quantum dot in the presence of an external magnetic field and the spin-orbit interaction (SOI). For the small magnetic fields considered in this work, \( B < 20 \, \text{mT} \), we may neglect orbital effects arising from the canonical momentum and model the system by the Hamiltonian \begin{equation} H_{\text{tot}} = H_{\text{orb}} + H_{Z} + H_{\text{SO}} \, \end{equation} where \( H_{Z} \) is the Zeeman Hamiltonian and \( H_{\text{SO}} \) describes the SOI.

Research - Machine Learning.

Hardware accelerated denoising diffusion probabilistic models.

S. B. Orbell

https://medium.com/graphcore/a-new-sota-for-generative-modelling-denoising-diffusion-probabilistic-models-8e21eec6792e

Generative models create latent representations, which distil information from big data in order to generate realistic and novel data points. In the long term, these models could be vital in developing accurate world models, as well as learning categorical and continuous features of a dataset in an unsupervised way. Currently, generative models are demonstrating their value in a variety of downstream tasks such as inpainting, super-resolution, and generating continuous exploration spaces for reinforcement learning. Generative Adversarial Networks (GANs) have represented the state of the art (SotA) for some time, however recently OpenAI has published results that make a strong case for a new era of Denoising Diffusion Probabilistic models dominating generative SotA applications. I have employed Graphcore's IPU processor to gain a computational advantage over the standard implementation of these models, using NVIDIA GPU's.

Other Projects.

Byskit - a bayesian network compiler and library for quantum circuits in Qiskit.

S. B. Orbell, J. Hickie, B. Severin.

https://github.com/mlvqc/Byskit

Development began during the 2020 IBMQ hackathon

Byskit plants an initial step towards taking full advantage of the amplitude amplification when running discrete Bayesian networks on a quantum computer. It provides the ability to easily translate a simple classical discrete Bayesian network to its corresponding quantum circuit.

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