Events

Previously, higher-order Hamiltonians (HoH) had been shown to offer an advantage in both metrology and quantum energy storage. In this work, we axiomatize a model of computation that allows us to consider such Hamiltonians for the purposes of computation. From this axiomatic model, we formally prove that an HoH-based algorithm can gain up to a quadratic speed-up (in the size of the input) over classical sequential algorithms—for any possible classical computation. We show how our axiomatic model is grounded in the same physics as that used in HoH-based quantum advantage for metrology and battery charging. Thus we argue that any advance in implementing HoH-based quantum advantage in those scenarios can be co-opted for the purpose of speeding up computation. 

QNC 1201
 

Improved Synthesis of Restricted Clifford+T Circuits

In quantum information theory, the decomposition of unitary operators into gates from some fixed universal set is of great research interest. Since 2013, researchers have discovered a correspondence between certain quantum circuits and matrices over rings of algebraic integers. For example, there is a correspondence between a family of restricted Clifford+T circuits and the group On(Z[1/2]). Therefore, in order to study quantum circuits, we can study the corresponding matrix groups and try to solve the constructive membership problem (CMP): given a set of generators and an element of the group, how to factor this element as a product of generators? Since a good solution to CMP yields a smaller decomposition of an arbitrary group element, it helps us implement quantum circuits using fewer resources. 

Noncommuting charges: Bridging theory to experiment

Noncommuting conserved quantities have recently launched a subfield of quantum thermodynamics. In conventional thermodynamics, a system of interest and an environment exchange quantities—energy, particles, electric charge, etc.—that are globally conserved and are represented by Hermitian operators. These operators were implicitly assumed to commute with each other, until a few years ago. Freeing the operators to fail to commute has enabled many theoretical discoveries—about reference frames, entropy production, resource-theory models, etc. Little work has bridged these results from abstract theory to experimental reality. This work provides a methodology for building this bridge systematically: we present a prescription for constructing Hamiltonians that conserve noncommuting quantities globally while transporting the quantities locally. The Hamiltonians can couple arbitrarily many subsystems together and can be integrable or nonintegrable. Our Hamiltonians may be realized physically with superconducting qudits, with ultracold atoms, and with trapped ions.

Quantum measurements are inherently probabilistic. Further defying our classical intuition, quantum theory often forbids us to precisely determine the outcomes of simultaneous measurements. This phenomenon is captured and quantified through uncertainty relations. Although studied since the inception of quantum theory, this problem of determining the possible expectation values of a collection of quantum measurements remains, in general, unsolved. In this talk, we will go over some basic notions of graph theory that will allow us to derive uncertainty relations valid for any set of dichotomic quantum observables. We will then specify the many cases for which these relations are tight, depending on properties of some graphs, and discuss a conjecture for the untight cases. Finally, we will show some direct applications to several problems in quantum information, namely, in constructing entropic uncertainty relations, separability criteria and entanglement witnesses.

Quantum Machine Learning Prediction Model for Retinal Conditions: Performance Analysis

Quantum machine learning predictive models are emerging and in this study we developed a classifier to infer the ophthalmic disease from OCT images. We used OCT images of the retina in  vision threatening conditions such as choroidal neovascularization (CNV) and diabetic macular edema (DME). PennyLane an open-source software tool based on the concept of quantum differentiable programming was used mainly to train the quantum circuits. The training was tested on an IBM 5 qubits System “ibmq_belem” and 32 qubits simulator “ibmq_qasm_simulator”. The results are promising. 

Jerry Li - Microsoft Research

In this talk, we consider two fundamental tasks in quantum state estimation, namely, quantum tomography and quantum state certification. In the former, we are given n copies of an unknown mixed state rho, and the goal is to learn it to good accuracy in trace norm. In the latter, the goal is to distinguish if rho is equal to some specified state, or far from it. When we are allowed to perform arbitrary (possibly entangled) measurements on our copies, then the exact sample complexity of these problems is well-understood. However, arbitrary measurements are expensive, especially in terms of quantum memory, and impossible to perform on near-term devices. In light of this, a recent line of work has focused on understanding the complexity of these problems when the learner is restricted to making incoherent (aka single-copy) measurements, which can be performed much more efficiently, and crucially, capture the set of measurements that can be be performed without quantum memory. However, characterizing the copy complexity of such algorithms has proven to be a challenging task, and closing this gap has been posed as an open question in various previous papers.

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