**Welcome!**

We are based in the Department of Computer Science at UCL.

We work on various theoretical aspects of quantum and classical information theory, and quantum computation. The activities of the group are also part of the UCL Quantum Science & Technology Institute (UCLQ).

A selection of our publications can be accessed at Recent Publications.

Details of the group seminar can be obtained at Talks.

Please feel free to email the academic staff members to discuss student projects and dissertations.

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## Recent publications

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## Talks

### Upcoming

*To be announced…*

### Previous

**Michael Bremner (UT Sydney)**. 8 August 2017.

*Title:*

Beyond classical computing via low-depth quantum circuit sampling

*Abstract:*

Over the last few years there has been significant attention devoted to devising experimental demonstrations of quantum computational supremacy: namely a quantum computer solving a computational task that goes beyond what a classical machine could achieve. This is, in part, driven by the hope that a clear demonstration of post-classical computation can be performed with a device that is intermediate between the small quantum circuits that can currently be built and a full-scale quantum computer. The theoretical challenge that this poses is twofold: firstly we must identify the physically least expensive quantum computations that are classically unachievable; and we must also determine if this advantage can be maintained in the presence of physical noise. In this talk I will review the IQP and Boson Sampling approaches to quantum computational supremacy, how they can be generalized to other intermediate quantum computing models, and to what extent the experimental resource requirements of these problems can be reduced.

See:

– M. J. Bremner, A. Montanaro, and D. J. Shepherd “Achieving quantum supremacy with sparse and noisy commuting quantum computations”, Quantum 1, 8 (2017). arXiv:1610.01808

– M. J. Bremner, A. Montanaro, and D. J. Shepherd “Average-case complexity versus approximate simulation of commuting quantum computations”, Phys. Rev. Lett. 117, 080501 (2016). arXiv:1504.07999

– S. Boixo, et al, “Characterizing quantum supremacy in near-term devices”, arXiv:1608.00263

– A. Lund, M. J. Bremner, T. C. Ralph “Quantum sampling problems, BosonSampling and quantum supremacy” npj Quantum Information 3, Article number: 15 (2017). arXiv:1702.03061

**Antonios Varvitsiotis (NTU and CQT, Singapore)**. 12 July 2017.

*Title:*

Quantum correlations: Conic formulations, dimension bounds, and matrix factorizations

*Abstract:*

In this talk we focus on the sets of two-party correlations generated from a Bell scenario involving two spatially separated systems with respect to various physical models. In recent worked we showed that the sets of quantum and classical correlations can be expressed as projections of affine sections of the completely positive semidefinite (cpsd) cone and the completely positive cone, respectively. This correspondence allows to set up a dictionary between properties of quantum correlations and features the cpsd cone and additionally, between dimensionality questions concerning quantum correlations and algebraic properties of a new notion of matrix rank. My goal in this talk is to give a brief summary of the most important results obtained in both directions.

**Giuseppe Carleo (ETH Zürich)**. 15 June 2017.

*Title:*

Machine Learning Many-Body Quantum Physics.

*Abstract:*

Machine-learning-based approaches are being increasingly adopted in a wide variety of domains, and very recently their effectiveness has been demonstrated

also for many-body physics [1-4]. In this seminar I will present recent applications to quantum physics.

First, I will discuss how a systematic machine learning of the many-body wave-function can be realized. This goal has been achieved in [1], introducing a variational representation of quantum states based on artificial neural networks. In conjunction with Monte Carlo schemes, this representation can be used to study both ground-state and unitary dynamics, with controlled accuracy. Moreover, I will show how a similar representation can be used to perform efficient Quantum State Tomography on highly-entangled states [5], previously inaccessible to state-of-the art tomographic approaches.

I will then briefly discuss, recent developments in quantum information theory, concerning the high representational power of neural-network quantum states.

[1] Carleo, and Troyer — Science 355, 602 (2017).

[2] Carrasquilla, and Melko — Nat. Physics doi:10.1038/nphys4035 (2017)

[3] Wang — Phys. Rev. B 94, 195105 (2016)

[4] van Nieuwenburg, Liu, and Huber — Nat. Physics doi:10.1038/nphys4037 (2017)

[5] Torlai, Mazzola, Carrasquilla, Troyer, Melko, and Carleo — arXiv:1703.05334 (2017)

**Ansis Rosmanis (CQT Singapore)**. 7 June 2017.

*Title:*

Fidelity of quantum strategies with applications to quantum cryptography.

*Abstract:*

We introduce a definition of the fidelity function for multi-round quantum strategies, which we call the strategy fidelity, which is a generalization of the fidelity function for quantum states. We provide many interesting properties of the strategy fidelity including a Fuchs-van de Graaf relationship with the strategy norm. We also provide a very general monotinicity result for both the strategy fidelity and strategy norm under the actions of strategy-to-strategy linear maps. We illustrate an operational interpretation of the strategy fidelity in the spirit of Uhlmann’s Theorem and discuss its application to the security analysis of quantum protocols for interactive cryptographic tasks such as bit-commitment and oblivious string transfer. Our analysis is very general in the sense that the actions of the protocol need not be fully specified, which is in stark contrast to most other security proofs. Lastly, we provide a semidefinite programming formulation of the strategy fidelity. This is joint work with Gus Gutoski and Jamie Sikora.

**Leonard Wossnig (ETH Zurich). 28 April 2017.**

*Title:*

A quantum linear system algorithm for dense matrices

*Abstract:*

Solving linear systems of equations is a frequently encountered problem in machine learning and optimisation, with applications ranging from Gaussian process regression to the training of neural networks. In the seminal work of Harrow, Hassidim and Lloyd [Physical Review Letters, 103 (15), 150502], a quantum algorithm for linear systems with an exponential increase in efficiency over classical algorithms has been presented. Their algorithm achieves an exponential speedup over classical algorithms when the linear system is sparse and well conditioned.

In this work, we present a quantum algorithm that achieves a quadratic speedup over the HHL algorithm even if the linear system is dense. Therefore we extend the range of linear systems that are efficiently solvable using quantum computation to a larger class of problems.

Our algorithm builds upon a quantum singular value estimation (QSVE) procedure which was introduced by Kerenidis and Prakash [I. Kerenidis and A. Prakash (2016), arXiv:1603.08675]. It extends their results by providing a trick to convert an arbitrary QSVE procedure into a linear system solver. We further prove the correctness of our scheme and the indicated lower bound on the runtime.

**Elizabeth Crosson (CalTech). 11 April 2017**

*Title:*

Ground state isoperimetric inequalities and the energy spectrum of local Hamiltonians

*Abstract:*

By generalizing a standard framework from the analysis of Markov chains to arbitrary (non-stoquastic) Hamiltonians we are naturally led to see that the spectral gap can always be upper bounded by a geometric quantity that depends only on the ground state probability distribution and the range of the terms in the Hamiltonian, but not on any other details of the interaction couplings. This means that for a given probability distribution the inequality can constrain the spectral gap (and other low-lying eigenvalues) of any local Hamiltonian with this distribution as its ground state probability distribution in some basis. These constraints reveal that some probability distributions will take exponential time to be precisely reached by a purely adiabatic evolution, while also showing the necessity of removing bottlenecks in the ground state geometry to improve the performance within the adiabatic paradigm.

**Māris Ozols (Cambridge). 29 March 2017**

*Title:*

How to permute quantum systems continuously

*Abstract:*

Can you write down a Hamiltonian that exchanges two quantum systems continuously? How about three? I will explain how this can be done using basic group theory and representation theory together with Fourier transform. The same tools apply more generally and let you make *any* finite group continuous by embedding it in a certain subgroup of the unitary group! My talk is based on arXiv:1508.00860.