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Quantum : Recent Advances and Outlook Wesley O’Quinn and Shiwen Mao

Abstract Note that a computer is not made of smaller transistors, but rather quantum bits (or is currently at the nexus ) that harness the quantum effects that cause of physics and engineering. Although current gen- chaos in a classical system. Due to the effects of eration quantum processors are small and noisy, superposition, each added is equivalent to advancements are happening at an astounding doubling the power of the computer. This stands rate. In addition, machine learning has played a in stark contrast to needing double the number of crucial role in many recent advances. The combina- transistors in order to double the processing power tion of these two fields, Learn- of a conventional computer. ing, is a small but extremely promising new field On the other hand, machine learning has with the possibility of unlimited abilities. This work played a crucial role in many recent advances (e.g., seeks to provide an introduction to this emerging wireless communication and networking systems). field, along with a discussion of recent advances as In particular, harnesses the power well as problems that are yet to be solved. of extremely massive amounts of data. To properly utilize this information, more computing power is Introduction constantly necessary. Quantum computing rep- Quantum computing is currently at the nexus of resents the potential to properly utilize this data. physics and engineering. This type of computing The combination of these two fields, Quantum was primarily proposed by the physics community Machine Learning, is a promising new field with and, until recently, remained a vaguely theoretical the possibility of extravagant abilities [1]. concept. In spite of this, many well-known meth- Before jumping into the topic at hand, it is ods such as Shor’s factoring, Grover’s Search, and helpful to provide a brief background of quan- Linear Systems algorithms were formulated and tum computing. For the purposes of this article, promised paradigm shifting ability if practically we will define quantum computing as any process realized. Although current generation quantum that utilizes the effects of quantum for processors are small and noisy, advancements improved computing capability. Most large com- are happening at an astounding rate, due largely puting corporations such as IBM, , and in part to government and private sector funding. , as well as smaller start-ups such as D Recently, the National Quantum Initiative Act was Wave, Rigetti, and IonQ, have made great strides passed. This bill provided up to 1.2 billion dollars in developing the quantum hardware. To make in research grant money to accelerate quantum development even easier, many of the companies related development. Private sector funding has mentioned provide access to their facility through also accelerated to provide startup capital and the cloud free of charge. Although the type of fund a variety of research. hardware used varies significantly between dif- One of the primary motivations for the devel- ferent companies, the basic characteristics of the opment of quantum computers is the upcoming systems can be broken down into two separate plateau of traditional computers. The exponential types: Universal Quantum Computing and Quan- growth of transistors on a computer chip, as pre- tum Annealing. dicted by Moore’s law, will soon come to a close. This is not due to any economic reason, but sim- Universal Quantum Computing ply due to the laws of physics. Current generation A universal quantum computer uses three main transistors are roughly ten nanometers. It has been properties to provide a fundamentally different shown that transistors under seven nanometers type of computation. These three qualities are begin to experience the effects of quantum tunnel- superposition, entanglement, and phase. Superpo- ling. This phenomenon is created when barriers in sition basically means that a qubit can represent the transistor become arbitrarily small, that is, when many more states than a traditional bit. For exam- the size of a gate reaches a certain thickness an ple, when a qubit is in superposition, it can be any can “jump” over the barrier, creating cur- number of states until made to collapse to either rent where it should not be. This non-classical effect a one or a zero. This can be visualized in Fig. 1. renders the transistors almost useless. Although Entanglement takes into account what Einstein chip manufacturers may be able to overcome this called “spooky action at a distance.” It basically effect to some extent, the size of the transistor will means that gates can be connected via this prop- basically reach its limit soon. erty. Finally, phase cancellation or interference Digital Object Identifier: 10.1109/MWC.001.1900341 The authors are with Auburn University.

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MAO_LAYOUT.indd 126 6/9/20 3:50 PM ACCEPTED FROM OPEN CALL is at the core of many quantum algorithms. This Once the basic hard- makes use of the fact that these qubits have not ware has been intro- only magnitude, but also phase. duced, it is helpful to This type of computation has high potentials in take a step back and machine learning. There is also reason to believe analyze how these sys- that with more research and development, other benefi ts may come to light. Currently, one of the tems can be used from key limitations is hardware development. Every a machine learning per- processor in the field has major struggles with spective. As , which in essence destroys any infor- computing is funda- mation encoded in the qubits. This being the case, mentally diff erent than it is diffi cult to execute complex algorithms on such FIGURE 1. Superposition illustrated [2]. processors. traditional computing, so too can quantum toring. This is proposed as a method for breaking machine learning be Quantum annealing is a more limited type of com- RSA (Rivest-Shamir-Adleman) encryption. In addi- used in radically diff er- putation mechanism, but has seen Moore’s law tion, Grover’s algorithm uses phase amplifi cation ent fashions. type advancements over the past two years. This to fi nd items in an unsorted database. This could type of system fi nds a minimum of a certain type be used in a variety of applications from graph of function. The idea is to map problems onto this theory to machine learning. Finally, the quantum function and then use the quantum processor to linear systems algorithm is particularly well suited solve the respective problem. To visualize this, for machine learning. the system can be thought of as a landscape of Even so, quantum computing faces massive hills and valleys. The solution is tied to the mini- engineering and programming issues. On the hard- mum point. Just as water will end up in the lowest ware side, noise plays a major role. Current gener- valleys, so too will the solution be marked by the ation quantum processors are limited almost solely annealer. It has been shown that the D Wave 2x to toy problems since very few operations can take system could outperform both simulated anneal- place before noise degrades all the computations ing and quantum monte carlo by up to a factor to a meaningless level. To limit this, processors of 108 on certain optimization problems. More must run at almost absolute zero temperature, recent works have proved the practical applicabil- greatly increasing the cost and creating many engi- ity of the system [3]. neering problems. In addition, it is not clear how to fully harness the capabilities of the processor. Since it is so diff erent from classical programming, Once the basic hardware has been introduced, algorithm development is slow and plagued with it is helpful to take a step back and analyze how questions. These and other mainly engineering and these systems can be used from a machine learn- programming issues must be addressed before the ing perspective. As quantum computing is funda- promises of quantum computing can be fully har- mentally diff erent than traditional computing, so vested. too can quantum machine learning be used in radically diff erent fashions. For example, the fact eXIstIng plAtForms that quantum annealers inherently fi nd the lowest Since there are a variety of methods to accom- energy states means that optimization problems plish quantum computation, the hardware utilized can be encoded into these systems. The quan- varies greatly between companies. A qualitative tum HHL algorithm — a method of solving linear comparison of the exiting platforms is given in systems of equations — which uses fundamen- Table 1. It is also helpful to note the information tal quantum effects, can be leveraged in many made available through [4], which is one of the machine learning contexts. Grover’s search algo- few pieces of literature that provides extensive rithm takes advantage of the quantum property benchmarking data on a variety of platforms. of to mark solutions in an unsorted database. One of the implications of Ibm Q this is that clustering can potentially take place in IBM Q, the quantum branch of IBM, is potential- a much faster manner. To summarize, quantum ly the most well-known platform. Great care has computing provides tools for machine learning been taken to tailor this system to the general developers that were not previously available. This public, which is available in an almost seamless allows for potentially faster processing of data as manner through the cloud. It is not hard for a fi rst well as the ability to generate new forms of algo- time user to begin using the circuit composer, rithms. With this in mind, it is important that one which allows one to design quantum circuits. Fig- understands both current systems available as well ure 2 provides a snapshot of Grover’s algorithm as recent advances. implemented in the circuit composer. Currently, a 14-qubit model is available to the motIvAtIons And chAllenges general public, while their 20-qubit model can be As mentioned in the introduction, a major moti- used only by IBM Q clients. The hardware utilizes a vation for quantum computers is the impending qubit. A microwave resonator is used to end of Moore’s Law. But even more than that, address and couple the qubits. The idea behind this quantum computing promises benefi ts that would system is to create electrically controlled solid-state not be realizable with classical hardware. For quantum computers. Development can take place example, Shor’s factoring algorithm is one of such through , which is an open-source quantum fi rst benefi ts. This particular algorithm will provide programming framework. The advantages of IBM almost an exponential speedup with regard to fac- Q is that a variety of materials are available intro-

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MAO_LAYOUT.indd 127 6/9/20 3:50 PM TABLE 1. Comparison of existing platforms.

ducing both the fi eld of quantum computers and The ability to run problems on the processor can specifi cally IBM’s version of quantum computers. be obtained quickly. A variety of functions have The systems are available immediately for use any- been made available, and the associated docu- where, and the circuit composer is very intuitive. mentation is superb. In summary, D Wave is an Furthermore, publications are available that utilized excellent platform for more limited applications. this system for research [5]. other plAtForms IonQ Other major players in the field have not been IonQ has produced considerable results over the mentioned, due to the fact that access to their past few years, through the use of tech- hardware via the cloud is not currently available. nology. The qubits are housed in an ultra high Even so, some of these platforms provide mean- vacuum chamber, and then precision lasers are ingful resources. Microsoft has developed a lan- used to connect the qubits and perform opera- guage specifically for programming a quantum tions. The reason this company is unique is due computer, referred to as Q#. They also provide to the low error scalability of their systems. See a quantum development kit, which can integrate [4] for a hard data comparison of Trapped Ion seamlessly with Azure to simulate 40+ qubits. technology with other platforms performed at the Google’s quantum branch operates under its University of Maryland (UMD). Gaining access section. Currently, its quan- to the system entails an application process; only tum processor dubbed “Bristlecone” is extremely certain users can obtain access to the system. advanced, housing 72 qubits. One major con- Moreover, literature on the software used is not tribution this team has made is the open source readily accessible, especially to individuals new to framework . the fi eld, which could make any prospective proj- ect using this system more diffi cult. recent AdvAnces Most advances in this fi eld are very recent. This is rIgettI computIng true for two reasons: fi rst, hardware and its avail- Rigetti’s approach to the field is to develop a full ability through the cloud is an extremely recent stack solution. They plan to do this through a quan- event. Second, most of the research tends to build tum-classical approach. Rather than viewing the upon itself in a very foundational way. With the quantum processor as a standalone unit, Rigetti onset of quantum cloud computer systems, the seems to view it more as a piece of hardware such potential for use is available in a way not seen in as a GPU. They have also recently released the prior decades. Certain computational subroutines Quantum Cloud Services (QCS). The core advan- can be sent to cloud servers where they are pro- tage of this system is the ability to run algorithms cessed. The information is then returned and can remotely through QCS. Both the classical and be utilized for a variety of applications. Frame- quantum hardware are available through servers. works should be developed that will be able to Any project done using this system will be easier take full advantage of the system when it reaches on the software side, but may lack the quantum maturity. If quantum computers hold to a Moore’s hardware that is available through other platforms. law scheme, this situation will occur in the very near future. One of the ways this can be imme- d wAve diately utilized is in the fi eld of machine learning. The D Wave system is highly different from the other systems. As mentioned, this particular com- ArtIFIcIAl QuAntum neurAl networks puter is a type of quantum annealer. A helpful A recent publication in the fi eld which drew signif- way to compare the two systems is to think of icant attention [5] implemented an artifi cial neu- the annealer as an analog system, while the ron on an actual quantum processor. Tacchino gate model is a digital system. This analogy will et al. [5] demonstrated that a model based upon break down if pushed too far, but it is a helpful the classical Rosenblatt “” could be way to think of the process. This system basically implemented on near-term hardware. The beauty finds the lowest energy state. If a problem can of this model is that it can be trained by a hybrid be mapped to the system, it will fi nd a variety of quantum-classical scheme and shows exponential possible optimal solutions. That said, the applica- advantage in storage resources. This work puts tions are still varied and useful. The interface and forward that neural networks in particular meld customer service of D Wave are second to none. almost seamlessly onto quantum hardware. This

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MAO_LAYOUT.indd 128 6/9/20 3:50 PM FIGURE 2. Grover’s algorithm implementation using the circuit composer.

is true due to the fact that intrinsically, has the property of representing and storing large complex valued vectors and matri- ces. Linear operations on such vectors can be performed as well. For simplistic representation, simple McCulloch-Pitts binary neurons were uti- lized. The model was then tested in a two-qubit model on an IBM Q quantum processor. A larger version was then implemented on the IBM quan- FIGURE 3. The QSVM circuit [7]. tum simulator. The results showed that the net- work could indeed be implemented, trained, and produce significant results. This work represents study was conducted by an in-depth look at the a compelling first step into the field of quantum relationship between HMM and HQMM. neural networks. Recently, a collaborative group of researchers at the Georgia Institute of Technology and Carnegie QuAntum support vector mAchInes Mellon University published a paper that accom- In a recent article produced by a collaboration plished three diff erent tasks [10]. First, it was proven of researchers at MIT and Google, a support that HMM could be simulated on a . vector machine was implemented with quantum Next, the HQMM algorithm was reformulated to hardware [6]. In this article, a method is given relax the constraints on quantum circuits. Finally, for implementing a quantum optimized binary a learning algorithm is presented to estimate the classifi er. It is interesting to note that for this sys- parameters of an HQMM from data. This article tem, where classical sampling algorithms would provides many novel ideas that have yet to be imple- require polynomial time, exponential speedup mented. Moreover, this work demonstrates that can be achieved. The improvement was devel- while the proposed HQMMs cannot model data oped through a non-sparse matrix exponentia- any better than a suffi ciently large HMM, it can bet- tion technique, which effi ciently achieved a matrix ter model the same data with fewer hidden states. inversion of the training data inner-product matrix. An interesting characteristic of research related to This algorithm was developed specifically with is that many times, advances Big Data classifi cation in mind and proved that a can be made in classical computing through the quantum support vector machine (QSVM) could work. The reason for this is the paradigm shift that indeed be realized on hardware. In [7], a 4-qubit must occur before progress can be made. The way nuclear magnetic resonance test bench was used. quantum programming is done is fundamentally dif- In this study, the system was trained on standard ferent from classical programming; therefore, ideas character fonts and then used to classify handwrit- produced in the fi eld tend to be novel in concept. ten characters. Although the test data was simplis- For example, the algorithm produced in [10] can be tic, the scheme performed admirably. The circuit utilized in both classical or quantum hardware. utilized in this research can be seen in Fig. 3. QuAntum AnneAlIng leArnIng hIdden QuAntum mArkov models Along with the gate model type, annealing pro- Hidden Markov models (HMMs) are a special cessors have grown extensively. For example, D case of the family. This par- Wave demonstrated the use of a 28-qubit system ticular model is the premier algorithm used for in 2007. In 2015, they announced that the 1000- . It is also utilized in many qubit barrier had been broken. Finally, in 2017, a other fields, including reinforced learning. Due two thousand qubit model was released for com- to its widespread usage, it is important that the mercial purchase. With promises for a lower noise quantum applications of this algorithm be stud- and more connected 5000-qubit model to be ied. This is especially relevant since the format of released by mid 2020, the scalability is massive. HMMs lends itself to smooth transition into the language of open quantum systems [8]. A variety trAFFIc optImIzAtIon of theoretical studies have been based on this Although not directly related to machine learning, concept. Monras et al. [9] introduced the idea of Volkswagen’s paper detailing the use of a quan- Hidden Quantum Markov Models (HQMM). This tum annealer provides meaningful insights into

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MAO_LAYOUT.indd 129 6/9/20 3:50 PM As quantum machine high level computations with this system. In this the algorithms in question on a gate model sys- learning is an emerging paper [3], the team took into account 418 Beijing tem. One option could be based on the super- field, future research taxis with three possible routes. The target was to conducting technology. Although noise is still a opportunities are highly find the optimal route for each taxi. The problem factor, a 16-qubit model is available through the was then mapped to the Quantum Unconstrained cloud through IBM Q. This system would allow a evolving and almost Binary Optimization problem. At its core, the sys- more in-depth look into the problems in question. endless. Interestingly, tem evolves probabilistically to the lowest energy Also, it is interesting to note that all calculations since theory advances level. This being the case, all problems must be utilized have been either synthetically generat- faster than hardware, formulated in such a way that this minimum ener- ed or handwritten. If the system is implemented, the most intriguing gy state is the solution. Interesting results have the next step would be to utilize real world data. been demonstrated in this project. This novel research would represent the possibil- problems tend to be ity for a wide range of wireless communications actually implementing Restricted Boltzmann Machines problems. Basically any process that utilizes HMM the theoretical work on Quantum annealers lend themselves particular- could potentially benefit from HQMM. hardware. ly well to probabilistic machine learning models. Inherently, quantum machines are probabilistic in Graph Theory and Clustering nature. This is important since many problems are “Unsupervised learning (is) attractive in applica- probabilistic. To use the forthright words of Richard tions where data is cheap to obtain, but labels are Feynman, “Nature isn’t classical … If you want to either expensive or not available [14].” With the make a simulation of nature, you’d better make advent of Big Data, a great deal of unlabeled infor- it quantum mechanical.” Restricted Boltzmann mation is readily available for a variety of machine Machines seem to be a good match for these sys- learning problems. But when the information is tems. Reference [11] proposes and implements measured in the order of exabytes, training could such a scheme on actual hardware. In this paper, be computationally expensive. Clustering is one of the results found through quantum annealing the most important tasks in unsupervised learning. (QA) were compared with To compound this, many clustering problems can (SA). Under certain circumstances, the QA process be inherently represented as graph problems. In returned the perspective found by SA. 2004, Durr et al. proposed a solution to the mini- Other times it returned one of the local minima. mum spanning tree problem [15]. This was done This seemed to arise from the lack of connectivity through the utilization of a quantum enhanced in the QA hardware. It will be interesting to see version of Boruvka’s algorithm. This specific algo- future results as new hardware becomes available. rithm was chosen over Kruskal’s, because of its This seems to be one of the first works in machine highly parallel nature. This work specifically shows learning based on QA. that “if the connection matrix of the minimum spanning tree can be given by a quantum ora- Future Perspectives cle, the computational time on a quantum com- As quantum machine learning is an emerging puter can be reduced using Grover’s algorithm field, future research opportunities are highly to O(N1.5).” Since a minimum spanning tree can evolving and almost endless. Interestingly, since be easily turned into clusters by subtracting the theory advances faster than hardware, the most k minus one connections, where k is the number intriguing problems tend to be actually imple- of clusters, this algorithm lends itself naturally to menting the theoretical work on hardware. Before clustering. The true impedance to this application jumping into open problems, it would be helpful (as well as most algorithms based on Grover’s to mention a few papers that provide the back- search) is the construction of the oracle. It is a ground needed to approach these. Specifically, problem that seems to defy logic, and is in itself Nielsen and Chuang’s textbook [12] is a very use- an interesting problem to study. ful reference. In addition, Reference [13] furnishes an excellent introduction to the field of quantum Models Based on Quantum Annealing machine learning. It discusses most of the work Research in the area of quantum annealing seems which had been done to date, as well as open to have been carried out almost solely by large problems and possible implementations. corporations. This is probably due to the prohib- itive cost of such machines. We predict this will Quantum Feedforward Deep Neural Networks change over the course of the next few years as One interesting development moving forward will cloud models are introduced. Quantum anneal- be the work built upon [5]. Very exciting paths of ers are especially enticing due to the demonstrat- work are proposed in the discussion of this paper. ed scalability. Also due to the software utilized, The first is encoding continuously valued vectors they are more simplistic to develop algorithms for rather than the binary model utilized. This would be use. Finally, real world benefits have already been equivalent to gray scale images rather than black proven through traffic routing problems as well as and white. Even more interesting is the possibility of satellite routing [15]. connecting multiple layers of quantum together. The model could be fully implemented Conclusion on quantum hardware and would effectively form a To use the words of Chad Rigetti, “Quantum com- feedforward deep neural network. puting is arguably the most sophisticated technol- ogy that humans have ever developed.” Although Quantum Bayesian Networks many would agree with this statement, the field is As mentioned in the review of [10], many novel still in its infancy, while the promises of quantum theoretical ideas have been proposed that have computing are almost endless. Therefore, research yet to be implemented. Research in this area in this field is of the utmost value. This article con- would be to provide experimental validation of stitutes a literature review of existing platforms

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MAO_LAYOUT.indd 130 6/9/20 3:50 PM and important issues and hopefully will provide [8] L. A. Clark et al., “Hidden Quantum Markov Models and To use the words of Open Quantum Systems with Instantaneous Feedback,” resources for those interested in pursuing a deep- arXiv e-prints, June 2014, p. arXiv:1406.5847; available: Chad Rigetti, “Quantum er understanding and a desire to apply quantum https://arxiv.org/abs/1406.5847. computing is arguably machine learning to their respective fields. [9] A. Monras, A. Beige, and K. Wiesner, “Hidden Quantum Markov Models and Non-Adaptive Read-Out of Many-Body the most sophisticat- States,” arXiv e-prints, Feb. 2010, p. arXiv:1002.2337; avail- ed technology that Acknowledgments able: https://arxiv.org/abs/1002.2337. This work is supported in part by the NSF under [10] S. Srinivasan, G. Gordon, and B. Boots, “Learning Hid- humans have ever Grant ECCS-1923717 and ACI-1659845, and by den Quantum Markov Models,” arXiv e-prints, Oct. developed.” Although the Wireless Engineering Research and Educa- 2017, p. arXiv:1710.09016; available: https://arxiv.org/ abs/1710.09016. many would agree with tion Center (WEREC) at Auburn University. We [11] Y. Koshka et al., “Determination of the Lowest-Energy this statement, the field would like to thank Dr. Peter Mueller with the States for the Model Distribution of Trained Restricted Boltz- is still in its infancy, IBM Zurich Research Laboratory for his sugges- mann Machines Using a 1000 Qubit D-Wave 2x Quantum tions with regard to the IBM Q systems, and the Computer,” Neural Computation, vol. 29, no. 7, July 2017, while the promises of pp. 1815–37. authors of [4] for constructive feedback. We [12] M. A. Nielsen and I. L. Chuang, Quantum Computation and quantum computing would also like to thank Dr. Mark Novotny with , New York, NY: Cambridge University are almost endless. Mississippi State University for his explanation Press, 2000. Therefore, research of his recent work with quantum annealers. We [13] J. Adcock et al., “Advances in Quantum Machine Learn- ing,” arXiv e-prints, Dec. 2015, p. arXiv:1512.02900; avail- in this field is of the are indebted to Mr. Michal Stechly with Zapata able: https://arxiv.org/abs/1512.02900. Computing for his exceptional work in explaining [14] J. Biamonte et al., “Quantum Machine Learning,” Nature, utmost value. concepts related to NISQ processors and related vol. 549, no. 7671, Sept. 2017, pp. 195–202. suggestions. Finally, Dr. Joel Gottlieb at D-Wave [15] . Durr et al., “Quantum Query Complexity of Some Graph Problems,” arXiv e-prints, Jan. 2004, pp. quant–ph/0 401 Systems has been an invaluable resource in both 091; available: https://arxiv.org/abs/quant-ph/0401091. this work and future works. Biographies References Wesley O’Quinn received the B.S. degree in electrical engi- [1] V. Dunjko, J. M. Taylor, and H. J. Briegel, “Quantum-En- neering and B.A. degree in Chinese language from Georgia hanced Machine Learning,” Phys. Rev. Lett., vol. 117, p. Southern University, Statesboro, GA as an honors student, both 130501, Sept. 2016; available: https://link.aps.org/ in 2019. He is with the Southern Nuclear Operating Company doi/10.1103/PhysRevLett.117.130501. as an engineer and is pursuing a Ph.D. in electrical and comput- [2] A. Daley, “ and Quantum Many-Body Sys- er engineering at Auburn University, Auburn, AL. His research tems: Quantum Computing,” Jan. 2012; available: http:// interests include machine learning/deep learning, quantum com- qoqms.phys.strath.ac.uk/research qc.html. puting, signal processing, wireless system design, and energy [3] F. Neukart et al., “Traffic Flow Optimization Using a Quan- harvesting. tum Annealer,” Aug. 2017; available: https://arxiv.org/ abs/1708.01625. Shiwen Mao [S’99, M’04, SM’09, F’19] received a Ph.D. in elec- [4] P. Murali et al., “Full-stack, Real-system Quantum Computer trical and computer engineering from Polytechnic University, Studies: Architectural Comparisons and Design Insights,” Brooklyn, N.Y. in 2004. He is the Samuel Ginn Professor and Proc. ISCA’19, Phoenix, AZ, June 2019, pp. 1–14. Director of the Wireless Engineering Research and Education [5] F. Tacchino et al., “An Artificial Neuron Implemented on an Center at Auburn University, Auburn, AL. His research interests Actual Quantum Processor,” Nature npj Quantum Informa- include wireless networks, multimedia communications, and tion, vol. 5, no. 26, Mar. 2019. smart grid. He is a co-recipient of several best paper awards, [6] P. Rebentrost, M. Mohseni, and S. Lloyd, “Quantum Support several service awards, and a best demo award from the IEEE Vector Machine for Big Data Classification,” Phys. Rev. Lett., Communications Society (ComSoc). He received the IEEE Com- vol. 113, no. 13, Sept. 2014, p. 130503. Soc TC-CSR Distinguished Technical Achievement Award in [7] Z. Li et al., “Experimental Realization of a Quantum Support 2019, the NSF CAREER Award in 2010, and The 2004 IEEE Vector Machine,” Phys. Rev. Lett., vol. 114, no. 14, Apr. Communications Society Leonard G. Abraham Prize in the Field 2015, p. 140504. of Communications Systems. He is a Fellow of the IEEE.

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