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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

Jonathan Lavoie, Experimental Physicist, Xanadu Quantum Technologies

A quantum computer attains computational advantage when outperforming the best classical computers running the best-known algorithms on well-defined tasks. No photonic machine offering programmability over all its quantum gates has demonstrated quantum computational advantage: previous machines were largely restricted to static gate sequences. I will discuss a quantum computational advantage using Borealis, the latest of Xanadu’s photonic processors offering dynamic programmability and available on the cloud. This work is a critical milestone on the path to a practical quantum computer, validating key technological features of photonics as a platform for this goal.

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)].

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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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.

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.