The work is supported by the Engineering and Physical Sciences Research Council of the UK (EPSRC) Grant number EP/W032643/1.

1. Setting up Dwave Ocean Environment
<ol>
	<li>Download and install the ocean tools from the link: https://docs.ocean.dwavesys.com/en/stable/overview/install.html
	<ol>
		<li>At the terminal, type python -m venv ocean.</li>
		<li>At the terminal, type . ocean/bin/activate, as shown in Figure 1.</li>
		<li>At the terminal, type git clone https://github.com/dwavesystems/dwave-ocean-sdk.git 
		Next, type&#160;cd dwave-ocean-sdk, as shown in Figure 2. 
		Then, type python setup.py install</li>
	</ol>
	</li>
</ol>
<img alt="Figure 1" class="xfigimg" src="/files/ftp_upload/64930/64930fig01.jpg" /> 
Figure 1: Ocean virtual environment activation. Ocean package, as D-wave API integrated, provides a cloudy user experience over the user&#39;s own computer to the D-wave machine premise. <a href="https://www.jove.com/files/ftp_upload/64930/64930fig01large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 2" class="xfigimg" src="/files/ftp_upload/64930/64930fig02.jpg" /> 
Figure 2: Ocean SDK installation. Ocean package provides necessary tool kits for developers, including a handy Cplex installation. <a href="https://www.jove.com/files/ftp_upload/64930/64930fig02large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
2. Installation of Cplex Python API interface
<ol>
	<li>Download and install Cplex: https://pypi.org/project/cplex/
	<ol>
		<li>At the terminal, type pip install cplex.</li>
	</ol>
	</li>
</ol>
3. Experiment configuration parameters
<ol>
	<li>Set up the experiment configuration parameters mentioned in Table 1 using Python programming notation in the script, as shown in Supplementary Figure 1. Once the script is run and executed, the underlying language will process to store the variables in RAM. A screenshot of the Python codes where the parameters are assigned values respectively is attached (Supplementary Figure 1).</li>
</ol>
<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>d0</td>
			<td>87.7085 m</td>
		</tr>
		<tr>
			<td>E</td>
			<td>50 * 1 x 10-09 joules</td>
		</tr>
		<tr>
			<td>epson_fs</td>
			<td>1 * 10-12* 10 joules</td>
		</tr>
		<tr>
			<td>epson_mp</td>
			<td>0.0013 * 1 * 10-12 joules</td>
		</tr>
		<tr>
			<td>packet size</td>
			<td>4000 bits</td>
		</tr>
	</tbody>
</table>
Table 1: Energy model parameter and packet size settings.
Supplementary Figure 1: Script1. Script to set up the experiment parameters. <a href="https://www.jove.com/files/ftp_upload/64930/Supplementary Figure 1.pdf" target="_blank">Please click here to download this File.</a>
4. Python scripts
<ol>
	<li>Prepare the Python scripts to generate 198 sensor node 2D positions that are equally scattered into six sectors that divide the circular area with a radius of 50 m. 
	NOTE: The circular graph is segmented into 6 sectors. In each sector, the position of each node is treated with two corresponding variables. One is the angle, and the other is the radius. Assign values to both angle and radius using a uniform random distribution generator. The detailed procedure is shown in Supplementary Figure 2 and Supplementary Figure 3.</li>
	<li>Within each sector, ensure that the 33 sensor nodes are scattered randomly by a normal distribution. Save the 2D positions into text files by each sector under the name spelling rule as &#39;posdata&#39;+sector_no+&#39;.txt&#39; (Figure 3 and Figure 4).
	<ol>
		<li>Segment the circular area with a radius of 50 m into six sectors. The starting angular values for these six sectors make the vector A= [60,120,180,240,300,360].
		<ol>
			<li>Suppose the sector index is i, set the pole length for jth sensor node as l_{i,j}=50*random.random()</li>
			<li>Suppose the sector index is i, set the angular value for jth sensor node as ang_{i,j}=(60*random.random() + A_i - 60) * 2 * pi / 360</li>
			<li>Set the Cartesian coordinates of the jth sensor node in ith sector as 
			x_{i,j}=l_{i,j}*cos(ang_{i,j}) 
			y_{i,j}=l_{i,j}*sin(ang_{i,j})</li>
		</ol>
		</li>
	</ol>
	</li>
</ol>
Supplementary Figure 2: Script2. Script to configure the two dimension position locations for each node by sector. <a href="https://www.jove.com/files/ftp_upload/64930/Supplementary Figure 2.pdf" target="_blank">Please click here to download this File.</a>
Supplementary Figure 3: Script3. Script to configure each node position values within 1 sector. <a href="https://www.jove.com/files/ftp_upload/64930/Supplementary Figure 3.pdf" target="_blank">Please click here to download this File.</a>
<img alt="Figure 3" class="xfigimg" src="/files/ftp_upload/64930/64930fig03.jpg" /> 
Figure 3: Node positions generated and stored separated into 6 files each corresponding to one sector. Two-dimension position locations are saved in 6 posdata+&#39;idx&#39; files. Each presents a sector. <a href="https://www.jove.com/files/ftp_upload/64930/64930fig03large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 4" class="xfigimg" src="/files/ftp_upload/64930/64930fig04.jpg" /> 
Figure 4: Node positions stored in sector 0. The positions are in two dimensions and generated using a uniform random generator. The first column is the horizontal locations, and the second column is the vertical locations. <a href="https://www.jove.com/files/ftp_upload/64930/64930fig04large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
5. Preparing the initial energy levels
<ol>
	<li>Prepare the initial energy levels for all 198 sensor nodes. Assign half of them with initial energy at 0.5 J and the other half with initial energy at 1 J. Create an array to store each node&#39;s energy level, and use a loop to assign cells sequenced in even numbers the value 1 and those sequenced in odd numbers the value of 0.5. Supplementary Figure 4 shows the Python codes, and the result is shown in Figure 5.</li>
</ol>
Supplementary Figure 4: Script4. Script to assign half of the node&#39;s energy of 1 joule and the other 0.5 joules. <a href="https://www.jove.com/files/ftp_upload/64930/Supplementary Figure 4.png" target="_blank">Please click here to download this File.</a>
<img alt="Figure 5" class="xfigimg" src="/files/ftp_upload/64930/64930fig05.jpg" /> 
Figure 5: Energy_buffer initial assignment. Half of the nodes are assigned with energy 1 joule, while the other halves are assigned with 0.5 joules. <a href="https://www.jove.com/files/ftp_upload/64930/64930fig05large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
6. Preparing Advanced_Leach algorithm script (Figure 6 and Figure 7)
<ol>
	<li>Prepare a functional script where the cluster head is selected and the cluster is formed. 
	NOTE: The cluster is selected using a loop on the condition that the number of cluster heads selected is less than the overall number of nodes divided by 6. The condition is to ensure that within each cluster, the source node amount is equal to or less than 6. Within the loop, each node is assigned a random number between [0,1]. Those smaller than a given criteria number become the cluster head, while others become the source nodes. The detailed procedure is shown in Supplementary Figure 5. Then given a fixed pool of cluster heads, the rest of the source nodes select their cluster heads within the shortest distance, given that the cluster head has not hosted more than 6 source nodes yet. The detailed procedure is shown in Supplementary Figure 6.
	<ol>
		<li>Set T_n=P/(1-P*(count%(1/P))), where P = 0.2 (the proportional rate of the number of cluster heads to the overall network size) and the count is the amount of transmission round up to date.</li>
		<li>For each sensor node, attain a random number between[0,1] threshold_rm = random.random()
		<ol>
			<li>If threshold_rm is less than T_n, select this sensor node as the cluster head.</li>
		</ol>
		</li>
		<li>For each of the non-cluster_head nodes, select the closest cluster head sensor node to it as its cluster head. Given a fixed pool of cluster heads, the rest of the source nodes select their cluster heads within the shortest distance, given that the cluster head has not hosted more than 6 source nodes yet. The detailed procedure is shown in Supplementary Figure 6.</li>
	</ol>
	</li>
	<li>Prepare the command lines to calculate the energy depletion process across the whole network for this round. For each run of the algorithm that completes one batch of deliveries of the packets from source nodes to the sink, the energy storage array as prepared will be updated to have reduced cell by cell in values. The energy consumption along the path will be the summation of energy consumption per node-to-node route, which is calculated according to an energy model1. The detailed procedure is shown in Supplementary Figure 7.</li>
	<li>Calculate the required transmission round metrics. 
	NOTE: Per each run of the algorithm to complete one batch of packet delivery, the energy array is updated, the run amount and the number of drained-out nodes are counted. If the value is larger or equal to 1, then FND (first node die) is equal to current run amount. If the value is larger or equal to half of the node amount, then HND(half node die) is equal to current run amount. If the value is equal to the overall node amount, then AND(all node die) is equal to current run amount. The detailed procedure is shown in Supplementary Figure 8.</li>
</ol>
<img alt="Figure 6" class="xfigimg" src="/files/ftp_upload/64930/64930fig06.jpg" /> 
Figure 6: Cluster head array. The sequence numbers of the nodes that have been selected to be the cluster heads. <a href="https://www.jove.com/files/ftp_upload/64930/64930fig06large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 7" class="xfigimg" src="/files/ftp_upload/64930/64930fig07.jpg" /> 
Figure 7: Cluster head index array. As there are six sectors, each with 33 sensor nodes, in the cluster head index array, the number indicates the sequence number of the cluster head the corresponding sensor node belongs to. The position index of the array corresponds to the sequence number of each sensor node. For the sensor node that is selected as the cluster head, the number assigned to its slot in the array is the sequence number of itself. <a href="https://www.jove.com/files/ftp_upload/64930/64930fig07large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
Supplementary Figure 5: Script5. Script to select the cluster head. <a href="https://www.jove.com/files/ftp_upload/64930/Supplementary Figure 5.png" target="_blank">Please click here to download this File.</a>
Supplementary Figure 6: Script6. Script to assign source nodes to clusters. <a href="https://www.jove.com/files/ftp_upload/64930/Supplementary Figure 6.png" target="_blank">Please click here to download this File.</a>
Supplementary Figure 7: Script7. Script to update the energy buffer for all source nodes via reduction of the amount of energy consumed through transmission. <a href="https://www.jove.com/files/ftp_upload/64930/Supplementary Figure 7.png" target="_blank">Please click here to download this File.</a>
Supplementary Figure 8: Script8. Script to calculate the amount of rounds up to which the first node dies, and half of the nodes die. <a href="https://www.jove.com/files/ftp_upload/64930/Supplementary Figure 8.png" target="_blank">Please click here to download this File.</a>
7. Preparing hybrid quantum algorithm script
<ol>
	<li>Prepare a functioning script where the cluster head is selected and the cluster head is formed.
	<ol>
		<li>As the maximum cluster size is 6 in this experiment1, ensure that the amount of cluster heads is no less than current_valid_node_amount/6, the selection procedure will be run in a loop until this criterion is met. 
		NOTE: If current_valid_node_amount is no larger than 6, then these valid nodes form one and only cluster themselves.</li>
		<li>For each of the non-cluster_head_valid nodes, calculate the distance of it to each of the selected cluster heads, and assign to it the cluster head whose cluster size has not exceeded 6 where the distance value is the smallest. 
		NOTE: In Figure 8, all the non-cluster_head_valid nodes&#39; distances to the selected cluster head 24 are calculated, and all the selected cluster head is displayed in Figure 9. Figure 10 displays all the nodes are assigned to their corresponding cluster head, and Figure 11 shows grouping each cluster&#39;s member nodes in a vector array.</li>
	</ol>
	</li>
	<li>Prepare the sub-function script, where the routing optimization problem per cluster is formed and submitted to the D-wave API (Figure 12). The routing paths are computed cluster by cluster.</li>
	<li>Using Python script, calculate the energy depletion process across the whole network to quantitatively evaluate the algorithm by network lifetime in terms of the number of transmission rounds. 
	NOTE: For each run of the algorithm that completes one batch of deliveries of the packets from source nodes to the sink, the energy storage array as prepared will be updated to have reduced cell by cell in values. The energy consumption along the path will be the summation of energy consumption per node-to-node route, calculated according to an energy model1. The detailed procedure is shown in Supplementary Figure 7.</li>
	<li>Using Python script, record the moment when the first node is drained out and when half the nodes are drained out. The detailed procedure is shown in Supplementary Figure 8.</li>
</ol>
<img alt="Figure 8" class="xfigimg" src="/files/ftp_upload/64930/64930fig08.jpg" /> 
Figure 8: toClusterHeadDistance Array for non-cluster_head node with index 24. The first column is the distance and the second column is the cluster head index number <a href="https://www.jove.com/files/ftp_upload/64930/64930fig08large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 9" class="xfigimg" src="/files/ftp_upload/64930/64930fig09.jpg" /> 
Figure 9: CHID_buff array. Sequence numbers of the sensor nodes that are selected as the cluster heads. <a href="https://www.jove.com/files/ftp_upload/64930/64930fig09large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 10" class="xfigimg" src="/files/ftp_upload/64930/64930fig10.jpg" /> 
Figure 10 CHIdx_buff array. Assigned cluster head sensor nodes&#39; sequence number to each corresponding sensor node. <a href="https://www.jove.com/files/ftp_upload/64930/64930fig10large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 11" class="xfigimg" src="/files/ftp_upload/64930/64930fig11.jpg" /> 
Figure 11: CH_BUFF array. Cluster group per cluster head sensor nodes corresponding to the array CHID_buff. Each cluster group consists of 0 or more than 0 sensor nodes. Each cluster group array displays the sequence numbers of sensor nodes that are in it. <a href="https://www.jove.com/files/ftp_upload/64930/64930fig11large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 12" class="xfigimg" src="/files/ftp_upload/64930/64930fig12.jpg" /> 
Figure 12: Routing path computation per sector. For each sector, the routing paths for all source nodes are computed. <a href="https://www.jove.com/files/ftp_upload/64930/64930fig12large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>

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The current state-of-the-art commercial quantum processor can be used in computational problems of any network topology1. Quantum processor application is not constrained by the number of physical qbits any of the quantum processors has been able to implement. 
In sensor network lifetime prolongation design, the results show an advancement in method to achieve even longer network life by using a quantum processor. The results imply that quantum advantage is ready to be exploited commercially in both public and private sectors.
For managerial implications, Quantum Advantage is able to be the next milestone to pave a promising way for near-future Hi-Tech sustainable prosperity. Current Hi-Tech, in terms of Learning-strategy and/or Artificial Intelligence (AI), requires in any method the power drive to process/hold the data. From a high-level perspective of Green Globe, it does not stand out as a good candidate16. ML/AI though it makes computation more economically efficient, does not provide a root cause analytical solution because efficient computing is traded off by high-power computational facilities. Therefore, they are fundamentally bounded by the high-performance computer (HPC). Quantum computing which revolutionizes the computing paradigm, has proved effective in computing faster than legacy computers across multiple practical trial applications17,18. Quantum-assisted ML, as far as the author is concerned, is PML (probabilistic machine learning). ML algorithm (script/high-low level programming language) runs on a computing device that can be either a classical computer or quantum computing. Given the same ML algorithm of executable command lines n, let f_cc(n) indicate the consumption in computation for classical computers and f_qc(n) indicate the consumption in computation for quantum computers. f_cc(n) is a weighted summation of computational consumption of classical computer executable alpha_i for the n command lines. f_qc(n) is an equally weighted summation of computational consumption of quantum computer executable alpha_j for the equally same n command lines. The weights stay unchanged as the upper-level ML command lines are equally the same. Simply put, this work and previous work1 have shown that alpha_j is always less than alpha_i so f_qc(n) is always less than f_cc(n).
Regarding academic Implications, previously established processors/computing facilities are conventionally used to help researchers think/generate/develop their ideas and plans. Quantum computing indicates researchers' methodological approach awaits an epic evolution. It could be disruptive but optimistically. From now on, researchers not used to theoretical algorithm design/analysis need to work hand in hand to devise/generate quantum algorithms to solve their research topic. Most quantum algorithms for practical research are not handily available. In one sentence, researchers' computing devices changed. Virtual environment setup and QPU API completely rely on a satisfactory internet connection.
Limitations of the study include (i) Link capacity has not been considered1. The packet loss rate is ignored. Future works will consider the underlying sensor networking protocol to appropriately formulate the problem considering both energy consumption and loss control (either with a re-transmission scheme or not). (ii) Network topology is assumed to be known beforehand. Node positions are fixed. (iii) Time required to run the hybrid quantum algorithm per round is longer than the Advanced Leach algorithm but with higher accuracy. (iv) The algorithm could not work offline.

Energy conservation in sensor networks has been a very critical issue in design1. Classical methods normally tackle the problem using an ad hoc approach2,3,4,5,6. That said, these methods emulate the sensor nodes as individually managed intelligent assets that could also cooperate to serve both the interests of the individual and the community. Due to the volatile environment where sensors work, in some works, random algorithms are introduced in order to capture the environmental uncertainties, while in others, bio-intelligence is borrowed to devise heuristic algorithms that could achieve common sense acceptable results7. To illustrate further, for those random algorithms, for one hand, environmental uncertainties might not be as random as the random sequence generated by a classical CPU, for the other hand, even if the environmental uncertainties are absolutely random, they could not be captured by the random process simulator generated by classical CPU; for those bio-intelligence algorithms, first of all, no rigorous mathematical analysis has been derived to make a conceptual proof work, secondly, the convergence to truth or the error tolerance boundary can only be configured given an informed ground truth - though a significant amount of works in literature have demonstrated to some extent these heuristic algorithms work, for one thing, these algorithms are analyzed (not simulated) against well-defined use case scenarios, they stops at certain criteria that are still worth pondering in further research, for another, as said before, a majority of the algorithms have not been validated against software simulation that can be more readily deployed in the microprocessors that make a sensor into its being8.
We do not consider machine learning (ML) here because it needs to employ data analytics which requires a relatively large volume of computational power that is not portable in sensor devices9.
To address the above-mentioned concerns, we provide a hybrid quantum algorithm. The algorithm is hybrid in that the cluster head selection mechanism is implemented using a classical random algorithm during the routing computations conducted using a quantum processor once the network topology is set up. The method is justified as follows: (1) As discussed in the first paragraph regarding the environmental uncertainties, we do not want to endeavor further to apply a quantum sequence generator to capture the environmental dynamic because it might be historically traceable. The environmental dynamic that can be historically traceable has been justified by various machine learning research works in network science. For the current stage, we stay with the classical approach. (2) The exact method that relies on abstract mathematical analysis guarantees to arrive at ground truth. Quantum experimental physics has so far been sophisticatedly supported by physical mathematics. Moreover, algorithm applications like the Shor algorithm10 have existed to prove this rounded theory.
An adequate amount of literature survey is provided below for comparison. The HEESR protocol proposed11 has demonstrable merits in results, but the authors have specified the simulation configuration parameters well, for example, the exact random distribution function of the node position, the proper justification of the cluster head percentage p (0.2%), and the scaling parameter for distribution of energy level (1-2 joules) among nodes a_i. It prohibited the author from proceeding further to duplicate the experiments and conduct the comparison. The Power routing mechanism12 employs the curve fitting method to approximate converged continuous functions from discrete data sets obtained from unspecified sample space for determinants that impact the decision process of the optimal network routing. The curve fitting method13 requires prior information on the network topology. Real circumstances might not have prior information readily available. Even when prior information exists, network topology might not be regular enough to be able to be mapped onto fitting curves that are able to facilitate derivable computation. Following the same logic, DORAF protocol14 has not justified how and why to borrow the Boltzmann function and Logistic Function to approximate the network determinants. Ismail et al.15 have provided a sound reference for future research endeavors into energy-efficient routing protocol design in the underwater network.

<table><tbody><tr><td>Dell Laptop</td><td>Dell</td><td>N/A</td><td></td></tr><tr><td>Ubuntu 18.04.6 LTS</td><td>Canonical Ltd</td><td>18.04.6 LTS</td><td></td></tr><tr><td>Python3.8</td><td>Python Software Foundation</td><td>3.8.0</td><td></td></tr><tr><td>Dwave QPU</td><td>Dwave</td><td>https://docs.ocean.dwavesys.com/en/stable/overview/install.html</td><td></td></tr></tbody></table>

large scale energy efficient sensor network routing using a quantum processor unit

The sensor network energy conservation method, which is a usage hybrid of a classical computer and quantum processor, has proved to perform better than the heuristic algorithm using a classical computer. In this manuscript, the technical context for the significance of the method is presented and justified. Then the experimental steps are demonstrated in an operational sequence with illustrations if ever needed. The method has been validated by positive results across a randomly generated sample set of network topologies. The successful experimental results of this method have provided a better approach for sensor network lifetime maximization problems and demonstrated that the current state of art quantum processor has been able to solve large practical engineering problems with merits that override current methods in the literature. In other words, quantum advantage can be exploited to best efforts. It has gone beyond the stage of proof of concept to proof of feasibility.

Results from one run sample are shown in Table 2, Table 3, and Table 4. The detailed datasets for the three batches of data are available in the Supplementary Data 1 folder.
<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td colspan="3">Dataset 1</td>
		</tr>
		<tr>
			<td>198 nodes in a circular area with a radius of 50m</td>
			<td>Hybrid Quantum Algorithm</td>
			<td>Advanced_Leach Algorithm</td>
		</tr>
		<tr>
			<td>FND</td>
			<td>1442</td>
			<td>727</td>
		</tr>
		<tr>
			<td>HND</td>
			<td>2499</td>
			<td>1921</td>
		</tr>
	</tbody>
</table>
Table 2: Batch 1 of results from the experiment.
<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td colspan="3">Dataset 2</td>
		</tr>
		<tr>
			<td>198 nodes in a circular area with a radius of 50m</td>
			<td>Hybrid Quantum Algorithm</td>
			<td>Advanced_Leach Algorithm</td>
		</tr>
		<tr>
			<td>FND</td>
			<td>757</td>
			<td>1463</td>
		</tr>
		<tr>
			<td>HND</td>
			<td>1925</td>
			<td>2500</td>
		</tr>
	</tbody>
</table>
Table 3: Batch 2 of results from the experiment.
<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td colspan="3">Dataset 3</td>
		</tr>
		<tr>
			<td>198 nodes in a circular area with a radius of 50m</td>
			<td>Hybrid Quantum Algorithm</td>
			<td>Advanced_Leach Algorithm</td>
		</tr>
		<tr>
			<td>FND</td>
			<td>790</td>
			<td>1461</td>
		</tr>
		<tr>
			<td>HND</td>
			<td>1888</td>
			<td>2500</td>
		</tr>
	</tbody>
</table>
Table 4: Batch 3 of results from the experiment.
Three metrics are selected with definitions4 as below: 
FND - first node die. The number of transmissions round up to which the first sensor node energy is drained out; 
HND - half node die. The number of transmissions rounds up to which half amount of the sensor nodes&#39; energy is drained out; 
LND - last node die. The number of transmissions rounds up to which the whole sensor network is dead.
From the results, we can see that the hybrid quantum algorithm has more efficiency than the advanced_leach algorithm.
Further results of the time complexity of the proposed method and the compliance plot are shown in Figure 13 and Figure 14, respectively.
<img alt="Figure 13" class="xfigimg" src="/files/ftp_upload/64930/64930fig13.jpg" /> 
Figure 13: Time complexity of the Hybrid Quantum algorithm. Time in the unit of second spent in running one cycle of HQA across various network sizes. <a href="https://www.jove.com/files/ftp_upload/64930/64930fig13large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 14" class="xfigimg" src="/files/ftp_upload/64930/64930fig14.jpg" /> 
Figure 14: Results of the Hybrid Quantum algorithm that complies with the Advanced Leach algorithm. FND and HND or HQA and ALA share a similar plot shape pattern. <a href="https://www.jove.com/files/ftp_upload/64930/64930fig14large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
Supplementary Data 1: Dataset of the three batches of experiments performed in this study. <a href="https://www.jove.com/files/ftp_upload/64930/Supplementary Data 1.zip" target="_blank">Please click here to download this File.</a>

Watch this Scientific Journal Video about Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit at JoVE.com

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

This study provides a method to use a quantum processor unit to compute the routes for various traffic dynamics that work to outperform classical methods in literature to maximize network lifetime.

The sensor network energy conservation method, which is a usage hybrid of a classical computer and quantum processor, has proved to perform better than ...

large-scale-energy-efficient-sensor-network-routing-using-quantum

Nanyang Technological University

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JoVE Journal

Engineering

487 Views.  Imperial College London. This study provides a method to use a quantum processor unit to compute the routes for various traffic dynamics that work to outperform classical methods in literature to maximize network lifetime.

Video: Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Quasi-light Storage for Optical Data Packets

Today's telecommunication is based on optical packets which transmit the information in optical fiber networks around the world. Currently, the processing of the signals is done in the electrical domain. Direct storage in the optical domain would avoid the transfer of the packets to the electrical and back to the optical domain in every network node and, therefore, increase the speed and possibly reduce the energy consumption of telecommunications. However, light consists of photons which propagate with the speed of light in vacuum. Thus, the storage of light is a big challenge. There exist some methods to slow down the speed of the light, or to store it in excitations of a medium. However, these methods cannot be used for the storage of optical data packets used in telecommunications networks. Here we show how the time-frequency-coherence, which holds for every signal and therefore for optical packets as well, can be exploited to build an optical memory. We will review the background and show in detail and through examples, how a frequency comb can be used for the copying of an optical packet which enters the memory. One of these time domain copies is then extracted from the memory by a time domain switch. We will show this method for intensity as well as for phase modulated signals.

The article describes a procedure to store optical data packets with an arbitrary modulation, wavelength, and data rate. These packets are the basis of modern telecommunications.

Today's telecommunication is based on optical packets which transmit the information in optical fiber networks around the world. Currently, the processing ...

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Engineering non-classical states of the electromagnetic field is a central quest for quantum optics1,2. Beyond their fundamental significance, such states are indeed the resources for implementing various protocols, ranging from enhanced metrology to quantum communication and computing. A variety of devices can be used to generate non-classical states, such as single emitters, light-matter interfaces or non-linear systems3. We focus here on the use of a continuous-wave optical parametric oscillator3,4. This system is based on a non-linear &#967;2 crystal inserted inside an optical cavity and it is now well-known as a very efficient source of non-classical light, such as single-mode or two-mode squeezed vacuum depending on the crystal phase matching. 
Squeezed vacuum is a Gaussian state as its quadrature distributions follow a Gaussian statistics. However, it has been shown that number of protocols require non-Gaussian states5. Generating directly such states is a difficult task and would require strong &#967;3 non-linearities. Another procedure, probabilistic but heralded, consists in using a measurement-induced non-linearity via a conditional preparation technique operated on Gaussian states. Here, we detail this generation protocol for two non-Gaussian states, the single-photon state and a superposition of coherent states, using two differently phase-matched parametric oscillators as primary resources. This technique enables achievement of a high fidelity with the targeted state and generation of the state in a well-controlled spatiotemporal mode.

We describe the reliable generation of non-Gaussian states of traveling optical fields, including single-photon states and coherent state superpositions, using a conditional preparation method operated on the non-classical light emitted by optical parametric oscillators. Type-I and type-II phase-matched oscillators are considered and common procedures, such as the required frequency filtering or the high-efficiency quantum state characterization by homodyning, are detailed.

Engineering non-classical states of the electromagnetic field is a central quest for quantum optics1,2. Beyond their fundamental significance, such states ...

Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping

As mass-produced silicon transistors have reached the nano-scale, their behavior and performances are increasingly affected, and often deteriorated, by quantum mechanical effects such as tunneling through single dopants, scattering via interface defects, and discrete trap charge states. However, progress in silicon technology has shown that these phenomena can be harnessed and exploited for a new class of quantum-based electronics. Among others, multi-layer-gated silicon metal-oxide-semiconductor (MOS) technology can be used to control single charge or spin confined in electrostatically-defined quantum dots (QD). These QD-based devices are an excellent platform for quantum computing applications and, recently, it has been demonstrated that they can also be used as single-electron pumps, which are accurate sources of quantized current for metrological purposes. Here, we discuss in detail the fabrication protocol for silicon MOS QDs which is relevant to both quantum computing and quantum metrology applications. Moreover, we describe characterization methods to test the integrity of the devices after fabrication. Finally, we give a brief description of the measurement set-up used for charge pumping experiments and show representative results of electric current quantization.

The fabrication process and experimental characterization techniques relevant to single-electron pumps based on silicon metal-oxide-semiconductor quantum dots are discussed.

As mass-produced silicon transistors have reached the nano-scale, their behavior and performances are increasingly affected, and often deteriorated, by ...

Fiber Optic Distributed Sensors for High-resolution Temperature Field Mapping

The reliability of computational fluid dynamics (CFD) codes is checked by comparing simulations with experimental data. A typical data set consists chiefly of velocity and temperature readings, both ideally having high spatial and temporal resolution to facilitate rigorous code validation. While high resolution velocity data is readily obtained through optical measurement techniques such as particle image velocimetry, it has proven difficult to obtain temperature data with similar resolution. Traditional sensors such as thermocouples cannot fill this role, but the recent development of distributed sensing based on Rayleigh scattering and swept-wave interferometry offers resolution suitable for CFD code validation work. Thousands of temperature measurements can be generated along a single thin optical fiber at hundreds of Hertz. Sensors function over large temperature ranges and within opaque fluids where optical techniques are unsuitable. But this type of sensor is sensitive to strain and humidity as well as temperature and so accuracy is affected by handling, vibration, and shifts in relative humidity. Such behavior is quite unlike traditional sensors and so unconventional installation and operating procedures are necessary to ensure accurate measurements. This paper demonstrates implementation of a Rayleigh scattering-type distributed temperature sensor in a thermal mixing experiment involving two air jets at 25 and 45 &#176;C. We present criteria to guide selection of optical fiber for the sensor and describe installation setup for a jet mixing experiment. We illustrate sensor baselining, which links readings to an absolute temperature standard, and discuss practical issues such as errors due to flow-induced vibration. This material can aid those interested in temperature measurements having high data density and bandwidth for fluid dynamics experiments and similar applications. We highlight pitfalls specific to these sensors for consideration in experiment design and operation.

We demonstrate use of a fiber optic distributed sensor for mapping the temperature field of mixing air jets. The Rayleigh scattering-based sensor generates thousands of data points along a single fiber to provide exceptional spatial resolution that is unattainable with traditional sensors such as thermocouples.

The reliability of computational fluid dynamics (CFD) codes is checked by comparing simulations with experimental data. A typical data set consists ...

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Silicon photonic chips have the potential to realize complex integrated quantum information processing circuits, including photon sources, qubit manipulation, and integrated single-photon detectors. Here, we present the key aspects of preparing and testing a silicon photonic quantum chip with an integrated photon source and two-photon interferometer. The most important aspect of an integrated quantum circuit is minimizing loss so that all of the generated photons are detected with the highest possible fidelity. Here, we describe how to perform low-loss edge coupling by using an ultra-high numerical aperture fiber to closely match the mode of the silicon waveguides. By using an optimized fusion splicing recipe, the UHNA fiber is seamlessly interfaced with a standard single-mode fiber. This low-loss coupling allows the measurement of high-fidelity photon production in an integrated silicon ring resonator and the subsequent two-photon interference of the produced photons in a closely integrated Mach-Zehnder interferometer. This paper describes the essential procedures for the preparation and characterization of high-performance and scalable silicon quantum photonic circuits.

Silicon photonic chips have the potential to realize complex integrated quantum systems. Presented here is a method for preparing and testing a silicon photonic chip for quantum measurements.

Silicon photonic chips have the potential to realize complex integrated quantum information processing circuits, including photon sources, qubit ...

Resonance Fluorescence of an InGaAs Quantum Dot in a Planar Cavity Using Orthogonal Excitation and Detection

The ability to perform simultaneous resonant excitation and fluorescence detection is important for quantum optical measurements of quantum dots (QDs). Resonant excitation without fluorescence detection &#8211; for example, a differential transmission measurement &#8211; can determine some properties of the emitting system, but does not allow applications or measurements based on the emitted photons. For example, the measurement of photon correlations, observation of the Mollow triplet, and realization of single photon sources all require collection of the fluorescence. Incoherent excitation with fluorescence detection &#8211; for example, above band-gap excitation &#8211; can be used to create single photon sources, but the disturbance of the environment due to the excitation reduces the indistinguishability of the photons. Single photon sources based on QDs will have to be resonantly excited to have high photon indistinguishability, and simultaneous collection of the photons will be necessary to make use of them. We demonstrate a method to resonantly excite a single QD embedded in a planar cavity by coupling the excitation beam into this cavity from the cleaved face of the sample while collecting the fluorescence along the sample&#39;s surface normal direction. By carefully matching the excitation beam to the waveguide mode of the cavity, the excitation light can couple into the cavity and interact with the QD. The scattered photons can couple to the Fabry-Perot mode of the cavity and escape in the surface normal direction. This method allows complete freedom in the detection polarization, but the excitation polarization is restricted by the propagation direction of the excitation beam. The fluorescence from the wetting layer provides a guide to align the collection path with respect to the excitation beam. The orthogonality of the excitation and detection modes enables resonant excitation of a single QD with negligible laser scattering background.

Resonant excitation of a single self-assembled quantum dot can be achieved using an excitation mode orthogonal to the fluorescence collection mode. We demonstrate a method using the waveguide and Fabry-Perot modes of a planar microcavity surrounding the quantum dots. The method allows complete freedom in the detection polarization.

The ability to perform simultaneous resonant excitation and fluorescence detection is important for quantum optical measurements of quantum dots (QDs). ...

Generation and Coherent Control of Pulsed Quantum Frequency Combs

We present a method for the generation and coherent manipulation of pulsed quantum frequency combs. Until now, methods of preparing high-dimensional states on-chip in a practical way have remained elusive due to the increasing complexity of the quantum circuitry needed to prepare and process such states. Here, we outline how high-dimensional, frequency-bin entangled, two-photon states can be generated at a stable, high generation rate by using a nested-cavity, actively mode-locked excitation of a nonlinear micro-cavity. This technique is used to produce pulsed quantum frequency combs. Moreover, we present how the quantum states can be coherently manipulated using standard telecommunications components such as programmable filters and electro-optic modulators. In particular, we show in detail how to accomplish state characterization measurements such as density matrix reconstruction, coincidence detection, and single photon spectrum determination. The presented methods form an accessible, reconfigurable, and scalable foundation for complex high-dimensional state preparation and manipulation protocols in the frequency domain.

A protocol is presented for the practical generation and coherent manipulation of high-dimensional frequency-bin entangled photon states using integrated micro-cavities and standard telecommunications components, respectively.

We present a method for the generation and coherent manipulation of pulsed quantum frequency combs. Until now, methods of preparing high-dimensional ...

A Modular Microfluidic Technology for Systematic Studies of Colloidal Semiconductor Nanocrystals

Colloidal semiconductor nanocrystals, known as quantum dots (QDs), are a rapidly growing class of materials in commercial electronics, such as light emitting diodes (LEDs) and photovoltaics (PVs). Among this material group, inorganic/organic perovskites have demonstrated significant improvement and potential towards high-efficiency, low-cost PV fabrication due to their high charge carrier mobilities and lifetimes. Despite the opportunities for perovskite QDs in large-scale PV and LED applications, the lack of fundamental and comprehensive understanding of their growth pathways has inhibited their adaptation within continuous nanomanufacturing strategies. Traditional flask-based screening approaches are generally expensive, labor-intensive, and imprecise for effectively characterizing the broad parameter space and synthesis variety relevant to colloidal QD reactions. In this work, a fully autonomous microfluidic platform is developed to systematically study the large parameter space associated with the colloidal synthesis of nanocrystals in a continuous flow format. Through the application of a novel translating three-port flow cell and modular reactor extension units, the system may rapidly collect fluorescence and absorption spectra across reactor lengths ranging 3 - 196 cm. The adjustable reactor length not only decouples the residence time from the velocity-dependent mass transfer, it also substantially improves the sampling rates and chemical consumption due to the characterization of 40 unique spectra within a single equilibrated system. Sample rates may reach up to 30,000 unique spectra per day, and the conditions cover 4 orders of magnitude in residence times ranging 100 ms - 17 min. Further applications of this system would substantially improve the rate and precision of the material discovery and screening in future studies. Detailed within this report are the system materials and assembly protocols with a general description of the automated sampling software and offline data processing.

Detailed herein are the operation and assembly protocols of a modular microfluidic screening platform for the systematic characterization of colloidal semiconductor nanocrystal syntheses. Through fully adjustable system arrangements, highly efficient spectra collection may be carried out across 4 orders of magnitude reaction time scales within a mass transfer-controlled sampling space.

Colloidal semiconductor nanocrystals, known as quantum dots (QDs), are a rapidly growing class of materials in commercial electronics, such as light ...

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

To form a coherent quantum transport in hybrid superconductor-semiconductor (S-Sm) junctions, the formation of a homogeneous and barrier-free interface between two different materials is necessary. The S-Sm junction with high interface transparency will then facilitate the observation of the induced hard superconducting gap, which is the key requirement to access the topological phases (TPs) and observation of exotic quasiparticles such as Majorana zero modes (MZM) in hybrid systems. A material platform that can support observation of TPs and allows the realization of complex and branched geometries is therefore highly demanding in quantum processing and computing science and technology. Here, we introduce a two-dimensional material system and study the proximity induced superconductivity in semiconducting two-dimensional electron gas (2DEG) that is the basis of a hybrid quantum integrated circuit (QIC). The 2DEG is a 30 nm thick In0.75Ga0.25As quantum well that is buried between two In0.75Al0.25As barriers in a heterostructure. Niobium (Nb) films are used as the superconducting electrodes to form Nb- In0.75Ga0.25As -Nb Josephson junctions (JJs) that are symmetric, planar and ballistic. Two different approaches were used to form the JJs and QICs. The long junctions were fabricated photolithographically, but e-beam lithography was used for short junctions&#8217; fabrication. The coherent quantum transport measurements as a function of temperature in the presence/absence of magnetic field B are discussed. In both device fabrication approaches, the proximity induced superconducting properties were observed in the In0.75Ga0.25As 2DEG. It was found that e-beam lithographically patterned JJs of shorter lengths result in observation of induced superconducting gap at much higher temperature ranges. The results that are reproducible and clean suggesting that the hybrid 2D JJs and QICs based on In0.75Ga0.25As quantum wells could be a promising material platform to realize the real complex and scalable electronic and photonic quantum circuitry and devices.

Quantum integrated circuits (QICs) consisting of array of planar and ballistic Josephson junctions (JJs) based on In0.75Ga0.25As two-dimensional electron gas (2DEG) is demonstrated. Two different methods for fabrication of the two-dimensional (2D) JJs and QICs are discussed followed by the demonstration of quantum transport measurements in sub-Kelvin temperatures.

To form a coherent quantum transport in hybrid superconductor-semiconductor (S-Sm) junctions, the formation of a homogeneous and barrier-free interface ...

A Silicon-tipped Fiber-optic Sensing Platform with High Resolution and Fast Response

In this article, we introduce an innovative and practically promising fiber-optic sensing platform (FOSP) that we proposed and demonstrated recently. This FOSP relies on a silicon Fabry-Perot interferometer (FPI) attached to the fiber end, referred to as Si-FOSP in this work. The Si-FOSP generates an interferogram determined by the optical path length (OPL) of the silicon cavity. Measurand alters the OPL and thus shifts the interferogram. Due to the unique optical and thermal properties of the silicon material, this Si-FOSP exhibits an advantageous performance in terms of sensitivity and speed. Furthermore, the mature silicon fabrication industry endows the Si-FOSP with excellent reproducibility and low cost toward practical applications. Depending on the specific applications, either a low-finesse or high-finesse version will be utilized, and two different data demodulation methods will be adopted accordingly. Detailed protocols for fabricating both versions of the Si-FOSP will be provided. Three representative applications and their according results will be shown. The first one is a prototype underwater thermometer for profiling the ocean thermoclines, the second one is a flow meter to measure flow speed in the ocean, and the last one is a bolometer used for monitoring exhaust radiation from magnetically confined high-temperature plasma.

This work reports an innovative silicon-tipped fiber-optic sensing platform (Si-FOSP) for high-resolution and fast-response measurement of a variety of physical parameters, such as temperature, flow, and radiation. Applications of this Si-FOSP span from oceanographic research, mechanical industry, to fusion energy research.

In this article, we introduce an innovative and practically promising fiber-optic sensing platform (FOSP) that we proposed and demonstrated recently. This ...