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Dynamic qubit allocation and routing for constrained topologies by CNOT circuit re-synthesis

Recent strides in quantum computing have made it possible to execute quantum algorithms on real quantum hardware. When mapping a quantum circuit to the physical layer, one has to consider the numerous constraints imposed by the underlying hardware architecture. Many quantum computers have constraints regarding which two-qubit operations are locally allowed. For example, in a superconducting quantum computer, connectivity of the physical qubits restricts multi-qubit operations to adjacent qubits [1]. These restrictions are known as connectivity constraints and can be represented by a connected graph (a.k.a. topology), where each vertex represents a distinct physical qubit. When two qubits are adjacent, there is an edge between the corresponding vertices.

Andrey Boris Khesin - Massachusetts Institute of Technology

Publicly verifiable quantum money is a protocol for the preparation of quantum states that can be efficiently verified by any party for authenticity but is computationally infeasible to counterfeit. We develop a cryptographic scheme for publicly verifiable quantum money based on Gaussian superpositions over random lattices. We introduce a verification-of-authenticity procedure based on the lattice discrete Fourier transform, and subsequently prove the unforgeability of our quantum money under the hardness of the short vector problem from lattice-based cryptography.

Felix Motzoi - University of California

In the NISQ era of quantum computing, as system sizes are progressively increasing, there are major concerns about the degradation of performance with increasing complexity. These can largely be reduced to the problems of crosstalk and correlations between system components, of fabrication uncertainties and drift in system parameters, and of multi-parameter optimization across multi-qubit state spaces in a fixed uptime duty cycle. In this presentation, we address inroads towards a more comprehensive, scalable approach for control theoretic solutions to maintaining (given architecture) performance that encompasses: a method to incorporate arbitrary couplings into an effective Hamiltonian frame with superexponential speedup compared to standard perturbative approaches [B. Li, T. Calarco, F. Motzoi, PRX Quantum 3, 030313 (2022)]; a control theoretic approach to tracking uncertainties in quantum circuits giving tight error bounds [M. Dalgaard, C. Weidner, F, Motzoi - Phys. Rev. Lett. 128, 150503 (2022)]; and a machine learning framework for symbolic optimization given particular Hamiltonian and associated uncertainties with a single meta-optimization permitting simultaneous tuneup of all qubits within the architecture belonging to the same class of Hamiltonians [F. Preti, T. Calarco, F. Motzoi, arXiv:2203.13594 (2022)].

Assessing the Trainability of the Variational Quantum State Diagonalization Algorithm at Scale

Developing new quantum algorithms is a famously hard problem. The lack of intuition concerning the quantum realm makes constructing quantum algorithms that solve particular problems of interest difficult. In addition, modern hardware limitations place strong restrictions on the types of algorithms which can be implemented in noisy circuits. These challenges have produced several solutions to the problem of quantum algorithm development in the modern Near-term Intermediate Scale Quantum (NISQ) Era. One of the most prominent of these is the use of classical machine learning to discover novel quantum algorithms by minimizing a cost function associated with the particular application of interest. This quantum-classical hybrid approach, also called Variational Quantum Algorithms (VQAs), has attracted major interest from both academic and industrial researchers due to its flexible framework and expanding list of applications - most notably optimization (QAOA) and chemistry (VQE). What is still unclear is whether these algorithms will deliver on their promise when implemented at a useful scale, in fact there is strong reason to worry whether the classical machine learning model will be able to train in the larger parameter space. This phenomenon is commonly referred to as the Barren Plateaus problem, which occurs when the training gradient vanishes exponentially quickly as the system size increases. Recent results have shown that some cost functions used in training can be proven to result in a barren plateau, while other cost functions can be proven to avoid them. In this presentation, I apply these results to my 2018 paper where my group developed a new Variational Quantum State Diagonalization (VQSD) algorithm and so demonstrate that this algorithm's current cost function will encounter a Barren Plateau at scale. I then introduce a simple modification to this cost function which preserves its function while ensuring trainability at scale. I also discuss the next steps for this project where I am teaching a team of 6 quantum novices across 4 continents the core calculation I use in this work to expand my analysis to the entire literature of VQAs.

Reference: https://uwspace.uwaterloo.ca/handle/10012/18187

Quantum computing promises to dramatically alter how we solve many computational problems by controlling information encoded in quantum bits. With potential applications in optimization, materials science, chemistry, and more, building functional quantum computers is one of the most exciting challenges in research today. To build and use these devices, we need to precisely control quantum bits in the lab, understand the ability and limitations of quantum algorithms, and find new methods to correct for decoherence and other quantum errors.

Research in quantum computing is highly multidisciplinary, with important contributions being made from computer scientists, mathematicians, physicists, chemists, engineers, and more. In this panel, we’ll learn from three researchers at the forefront of the field studying experimental quantum devices, quantum algorithms, and quantum error correction:

• Crystal Senko, Assistant Professor, Institute for Quantum Computing and the Department of Physics

• Shalev Ben-David, Assistant Professor, Institute for Quantum Computing and Cheriton School of Computer Science
• Michael Vasmer, Postdoctoral Researcher, Institute for Quantum Computing and Perimeter Institute for Theoretical Physics

Quantum Perspectives: A Panel Series celebrates 20 years of quantum at IQC. Over the past two decades, IQC’s leading quantum research has powered the development of transformative technologies, from ideas to commercialization, through research in theory, experiment and quantum applications. This year, we’re celebrating IQC’s 20^th anniversary with a panel series exploring all perspectives of quantum, including sensing, materials, communication, simulation and computing.

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Effective JC and anti-JC Interactions via Strong Driving 

The Jaynes-Cummings Model (JCM) approximates the Quantum Rabi Model (QRM) in some regimes and is exactly solvable by only keeping the rotating or `energy-conserving’ terms and dropping the counter-rotating or `non-energy conserving’ terms.

Since the proposal of the JCM, questions on the effect and presence of counter-rotating terms popped up.

Using strong driving, one can induce the effects of the counter-rotating terms on a comparable timescale to the rotating terms. In such a scenario, one can create a Schrödinger cat state in a resonant manner without the need for any type of Kerr nonlinearity.

In this talk, we review the QRM and its descendant, the JCM. Then, we discuss the realization of a Schrödinger cat state, its challenges in practice and how to solve them.

Quantum Chaos in Kicked Top

Quantum-classical correspondence is of fundamental interest as it allows for computing and analysing the quantum properties with respect to their classical counterparts. This helps us study the transition from the quantum to the classical. According to the correspondence principle, quantum mechanics should agree with classical mechanics in appropriate limits. In our first project, we show that currently available NISQ computers can be used for versatile quantum simulations of chaotic systems. We introduce a classical-quantum hybrid approach for exploring the dynamics of the chaotic quantum kicked top (QKT) on a  universal quantum computer. The programmability of this approach allows us to experimentally explore the complete range of QKT chaoticity parameter regimes inaccessible to previous studies. Furthermore, the number of gates in our simulation does not increase with the number of kicks, thus making it possible to study the QKT evolution for arbitrary number of kicks without fidelity loss. Using a publicly accessible NISQ computer (IBMQ), we observe periodicities in the evolution of the 2-qubit QKT, as well as signatures of chaos in the time-averaged 2-qubit entanglement. We also demonstrate a connection between entanglement and delocalization in the 2-qubit QKT, confirming theoretical predictions. However, the connection between classical and quantum mechanics is not straightforward, especially in chaotic systems. The question of why a chaotic system, in certain situations, breaks the correspondence principle remains one of the open questions. Nevertheless, the breaking of Quantum classical correspondence for a large system i.e., the large value of j (but finite), is surprising. It suggests that the system never behaves classically in certain situations, irrespective of the system size. It is also worth exploring this strange behavior from an experimental point of view, as it will decide the parameters of the experimental setup designed for studying Quantum Chaos.

Join us for Quantum Today, where we sit down with researchers from the University of Waterloo’s Institute for Quantum Computing (IQC) to talk about their work, its impact and where their research may lead.

Stacey Jefferey - QuSoft

While the quantum query complexity of k-distinctness is known to be O(n^{3/4−1/4(2k−1)}) for any constant k≥4, the best previous upper bound on the time complexity was ~O(n^{1−1/k}). We give a new upper bound of ~O(n^{3/4−1/4(2k−1)}) on the time complexity, matching the query complexity up to polylogarithmic factors. In order to achieve this upper bound, we give a new technique for designing quantum walk search algorithms, which is an extension of the electric network framework. We also show how to solve the welded trees problem in O(n) queries and O(n^2) time using this new technique, showing that the new quantum walk framework can achieve exponential speedups.

The ability to engineer the electrical, optical and magnetic properties of advanced materials on the nanoscale is of increasing importance to the development of future technologies. One approach to achieving this is through impurity doping, with increased control over the spatial resolution and isotopic purity enabled by the development of dedicated tools. In this talk the 'P-NAME' tool will be described, and the underlying principle surrounding its application for the development of doped systems for quantum technologies including qubits presented. cont.