Below is a brief summary of my main research areas.

## Variational Quantum Algorithms

We have now reached a point where small-scale quantum computers (approaching 100 qubits) are now becoming available. These quantum computers are not fault-tolerant, and the qubits are noisy. An interesting area of research is focused on what we can do with such Noisy Intermediate-Scale Quantum (NISQ) devices. An interesting class of quantum algorithms that has gained plenty of attention recently is the class of variational hybrid quantum-classical algorithms, a prominent example of which is the Variational Quantum Eigensolver (VQE). My recent work explores a variational hybrid quantum-classical algorithm for the purpose of compiling quantum algorithms.

**Quantum-assisted quantum compiling**[arXiv] [Quantum] [slides]

**SK**, Ryan LaRose, Alexander Poremba, Lukasz Cincio, Andrew T. Sornborger, Patrick J. Coles

Poster presentation at QIP 2019, SQuInT 2019; seminar at IQC.

**Noise Resilience of Variational Quantum Compiling**[arXiv] [New Journal of Physics] [slides]

Kunal Sharma,**SK**, Marco Cerezo, Patrick J. Coles

Contributed talk at QuILT 2019.

Other relevant work: arXiv:1801.00862, arXiv:1304.3061, arXiv:1411.4028

## Quantum networks

Although small-scale quantum computers are now available, they are currently not at the point where they can be useful for meaningful computations tasks (that current classical computers can’t already do). On the other hand, the technology for quantum communication tasks (such as QKD; see below) is mature enough now that quantum communication can be performed over relatively long distances between a handful of nodes.

The next step in quantum communication is to extend small-scale, point-to-point communication to communication between multiple parties in a *quantum network,* with the grand vision being the realization of a *Quantum* *Internet, *an interconnected network of quantum networks much like the internet we currently have. Building large-scale quantum networks remains a challenging experimental task.

My work in this area has been centered around the questions: how do we assess the performance of a quantum network? How good should our devices be in order to attain certain performance requirements? In order to answer these questions, my colleagues and I have been working on developing a general model of a quantum network and using this model, along with reinforcement learning algorithms, to develop quantum communication protocols such as multipartite entanglement distillation protocols and quantum routing protocols.

**Robust quantum network architectures and topologies for entanglement distribution**[arXiv] [Physical Review A]

Siddhartha Das,**SK**, Jonathan P. Dowling

Contributed talk at SQuInT 2018, poster presentation at WQRN 2017, Vienna.

**Practical figures of merit and thresholds for entanglement distribution in quantum networks**[arXiv] [Physical Review Research] [slides]

**SK**, Corey Matyas, Aliza Siddiqui, Jonathan P. Dowling

Contributed talks at quantum network workshops in Arizona and Vienna (video here). Contributed talk at SQuInT 2020 (video here).

**Spooky Action at a Global Distance — Resource-Rate Analysis of a Space-Based Entanglement-Distribution Network for the Quantum Internet**[arXiv]

**SK**, Anthony J. Brady, Renée A. Desporte, Manon P. Bart, Jonathan P. Dowling

News article about the paper: Why the quantum internet should be built in space

General papers: arXiv:0806.4195, Quantum internet: A vision for the road ahead, Why the quantum internet should be built in space

See this How Stuff Works article, in which I talk about the future quantum internet.

## Measures of non-Markovianity of open quantum systems

**Fundamental limits on quantum dynamics based on entropy change**[arXiv] [Journal of Mathematical Physics]

Siddhartha Das,**SK**, George Siopsis, Mark M. Wilde

Contributed talk at CQIQC-VII, Toronto.

## Quantum Shannon Theory/Fundamental Limitations of Quantum Communications

Work in quantum Shannon theory is centered around finding the fundamental limits of quantum information processing tasks. One such task is communication, and the goal is to determine the maximum rate of communication possible over a given quantum channel, a quantity referred to as the *communication capacity* of the quantum channel. There are several different types of communication over a quantum channel, such as classical communication, private communication, and quantum communication. My work in this area has looked at various upper and lower bounds on these communication types.

**Information-theoretic aspects of the generalized amplitude damping channel**[arXiv] [Physical Review A]

**SK**, Kunal Sharma, Mark M. Wilde

Contributed talk at APS March Meeting 2019.

**Second-order coding rates for key distillation in quantum key distribution**[arXiv]

Mark M. Wilde,**SK**, Eneet Kaur, Saikat Guha

**Bounding the forward classical capacity of bipartite quantum channels**[arXiv]

Dawei Ding,**SK**, Yihui Quek, Peter W. Shor, Xin Wang, Mark M. Wilde

## Symmetric extendibility of quantum states

For a given bipartite quantum state ρ^{AB} (describing, say, the quantum systems held by Alice and Bob), does there exist another quantum system B′ such that the joint tripartite state ρ^{ABB′} satisfies Tr_{B′}[ρ^{ABB′}] = Tr_{B}[ρ^{ABB′}] = ρ^{AB}? If such a tripartite state exists, we call ρ^{AB} *symmetrically extendible *and ρ^{ABB′} a *symmetric extension*. What we are essentially asking here is whether there exists a *copy *of Bob’s quantum system that is indistinguishable from Alice’s point of view.

Determining whether a quantum state is symmetrically extendible is not as easy as it might initially seem. In fact, we can currently only do it analytically for two very special types of states, states on two qubits and states on two qudits with several symmetries. Fortunately, using semi-definite programming, we can determine the symmetric extendibility of *any *quantum state.

**Extendibility of bosonic Gaussian states**[arXiv] [Physical Review Letters] [slides]

Ludovico Lami,**SK**, Gerardo Adesso, Mark M. Wilde

Contributed talk at QuILT 2019 and TQC 2020. Poster presentation at Algebraic and Statistical Ways Into Quantum Resource Theories, Banff.

Relevant papers: arXiv:1310.3530v2, arXiv:0906.5255v1, arXiv:0812.3667v1

## Extreme limits of quantum key distribution and bound secrecy

Symmetrically extendible states (see above) turn out to be extremely important for quantum key distribution. In QKD, we are interested in how much information any eavesdropper (call her Eve) might have about the secret key Alice and Bob are trying to create between them. Since they use quantum systems to do this by the very nature of QKD, the states describing these quantum systems can be used to determine how much secret key, if any, they can create.

It turns out that if the state ρ^{AB} describing Alice and Bob’s quantum systems is symmetrically extendible, then since the system B′ is a copy of Bob’s system and is not in Alice or Bob’s possession, we cannot rule out the possibility that it belongs to Eve. This means that Bob and Eve could be indistinguishable from Alice’s point of view, which means that Eve will know just as much as Bob does about the information Alice is communication during the secret key creation process. This means that *no *secret key can be created if we just allow for communication from Alice to Bob.

They might still be able to create a secret key if we allow for *two-way *communication, meaning that we allow Bob to communicate some information as well, which might break the symmetry between himself and Eve. This has been the subject of my Master’s thesis research, in which we considered a particular kind of QKD protocol in the case when Alice and Bob are symmetrically extendible and no protocol has been found to date. We have numerical evidence to suggest that two-way protocols don’t exist. If this turns out to be true, then not only would we have a resolution to this long-standing QKD problem, but we would also have a proof for the existence of *bound secrecy*, which is a kind of correlation that contains secrecy but that secrecy cannot be extracted into a secret key.

**Numerical evidence for bound secrecy from two-way post-processing in quantum key distribution**[arXiv] [Physical Review A]

**SK**, Norbert Lütkenhaus

Poster presentation at QCMC 2016, QCRYPT 2017.

**Symmetric Extendability of Quantum States and the Extreme Limits of Quantum Key Distribution**[Master’s thesis]

Relevant work: Geir Ove Myhr’s PhD Thesis, arXiv:0812.3607v2