Bayesian Optimization & Quantum Computing

(source)Bayesian Optimization & Quantum ComputingHow Bayesian Optimization can help Quantum Computing become a realityCharles BrecqueBlockedUnblockFollowFollowingJan 8Quantum computers have the potential to be exponentially faster than traditional computers which will revolutionise the way we currently solve a number of applications.

You can find out how in this detailed article but we are still years away from general purpose Quantum Computers.

However, for certain applications Bayesian Optimization can help stabilise quantum circuits and this article will summarise how OPTaaS did so in this paper which has been submitted to Science.

The team behind the paper was composed of researchers from the University of Maryland, UCL, Cambridge Quantum Computing, Mind Foundry, Central Connecticut State University and IonQ.

The TaskThe researchers behind the paper were applying a hybrid quantum learning scheme on a trapped ion quantum computer to accomplish a generative modelling task.

Generative models aim to learn representations of data in order to make subsequent tasks easier.

Hybrid quantum algorithms use both classical and quantum resources to solve potentially difficult problems.

The Bars-and-Stripes (BAS) data-set was used in the study as it can be easily visualised in terms of images containing horizontal bars and vertical stripes where each pixel represents a qubit.

The experiment was performed on four qubits within a seven-qubit fully programmable trapped ion quantum computer.

The quantum circuits are structured as layers of parameterised gates which will be calibrated by the optimization algorithms.

The following Figure taken from the paper illustrates the set up.

Training the Quantum CircuitThe researchers used two optimization methods in the paper for the training algorithm:Particle Swarm Optimization (PSO): a stochastic scheme that works by creating many “particles” randomly distributed across that explore the landscape collaborativelyBayesian Optimization with OPTaaS: a global optimizayion paradigm that can handle the expensive sampling of many-parameter functions by building and updating a surrogate model of the underlying objective function.

You can find a more detailed article on Bayesian Optimization bellow:The intuitions behind Bayesian Optimization with Gaussian ProcessesIn certain applications the objective function is expensive or difficult to evaluate.

In these situations, a general…towardsdatascience.

comThe optimization process consists in simulating the training procedure for a classical simulator in place of the quantum processor for a given set of parameters.

Once the optimal parameters have been identified, the training procedure is then run on the ion quantum computer in Figure 1.

The Cost functions used to quantify the difference between the BAS distribution and the experimental measurements of the circuit are variants of the original Kullback-Leibler Divergence and are detailed in the paper.

Results and OutlookThe training results for PSO and OPTaaS are provided in the following figures:Quantum circuit training results with PSOQuantum circuit training results with OPTaaSThe simulations are in orange and the ion quantum computer results are in blue.

Column (a) corresponds to a circuit with two layers of gates and all-to-all connectivity.

Columns (b) and (c ) correspond to a circuit with two and four layers and start connectivity, respectively.

(a), (b) and (c ) have 14, 11 and 26 tuneable parameters respectively.

We observe that the circuit is able to converge well to produce the BAS distribution only for the first circuit with PSO whereas with OPTaaS all circuits are able converge.

According to the researchers, the success of OPTaaS on the 26 parameter circuit represents the most powerful hybrid quantum application to date.

If you would like to understand the work in more detail, please read the paper and you can also sign up for an OPTaaS trial from my profile.

Team and ResourcesMind Foundry is an Oxford University spin-out founded by Professors Stephen Roberts and Michael Osborne who have 35 person years in data analytics.

The Mind Foundry team is composed of over 30 world class Machine Learning researchers and elite software engineers, many former post-docs from the University of Oxford.

Moreover, Mind Foundry has a privileged access to over 30 Oxford University Machine Learning PhDs through its spin-out status.

Mind Foundry is a portfolio company of the University of Oxford and its investors include Oxford Sciences Innovation, the Oxford Technology and Innovations Fund, the University of Oxford Innovation Fund and Parkwalk Advisors.


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