# Cassandra GranadeMicrosoft · Quantum Architectures and Computation Group (QuArc)

Cassandra Granade

PhD, Theoretical Physics, UWaterloo

## About

41

Publications

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2,041

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Introduction

Additional affiliations

May 2010 - present

## Publications

Publications (41)

As Hamiltonian models underpin the study and analysis of physical and chemical processes, it is crucial that they are faithful to the system they represent. However, formulating and testing candidate Hamiltonians for quantum systems from experimental data is difficult, because one cannot directly observe which interactions are present. Here we prop...

This paper explores the utility of the quantum phase estimation (QPE) algorithm in calculating high-energy excited states characterized by the promotion of electrons occupying core-level shells. These states have been intensively studied over the last few decades, especially in supporting the experimental effort at light sources. Results obtained w...

This paper explores the utility of the quantum phase estimation (QPE) in calculating high-energy excited states characterized by promotions of electrons occupying inner energy shells. These states have been intensively studied over the last few decades especially in supporting the experimental effort at light sources. Results obtained with the QPE...

An isolated system of interacting quantum particles is described by a Hamiltonian operator. Hamiltonian models underpin the study and analysis of physical and chemical processes throughout science and industry, so it is crucial they are faithful to the system they represent. However, formulating and testing Hamiltonian models of quantum systems fro...

Developing novel quantum devices poses the problem of their efficient characterization. We introduce and experimentally demonstrate a methodology to automatically formulate and rank Hamiltonian models, learning the most appropriate in reproducing the observed system’s dynamics.

Iterative phase estimation has long been used in quantum computing to estimate Hamiltonian eigenvalues. This is done by applying many repetitions of the same fundamental simulation circuit to an initial state, and using statistical inference to glean estimates of the eigenvalues from the resulting data. Here, we show a generalization of this framew...

In this paper, we discuss the extension of the recently introduced subsystem embedding subalgebra coupled cluster (SES-CC) formalism to unitary CC formalisms. In analogy to the standard single-reference SES-CC formalism, its unitary CC extension allows one to include the dynamical (outside the active space) correlation effects in an SES induced com...

Nitrogen-vacancy (NV) centers in diamond are appealing nanoscale quantum sensors for temperature, strain, electric fields, and, most notably, magnetic fields. However, the cryogenic temperatures required for low-noise single-shot readout that have enabled the most sensitive NV magnetometry reported to date are impractical for key applications, e.g....

Fault-tolerant quantum computation promises to solve outstanding problems in quantum chemistry within the next decade. Realizing this promise requires scalable tools that allow users to translate descriptions of electronic structure problems to optimized quantum gate sequences executed on physical hardware, without requiring specialized quantum com...

Hamiltonian learning can be used to efficiently characterise quantum systems. Here we apply it to the estimation of magnetic fields with quantum sensors, achieving experimentally, room temperature sensing performance comparable to those of cryogenic set-ups.

Nitrogen-vacancy (NV) centres in diamond are appealing nano-scale quantum sensors for temperature, strain, electric fields and, most notably, for magnetic fields. However, the cryogenic temperatures required for low-noise single-shot readout that have enabled the most sensitive NV-magnetometry reported to date, are impractical for key applications,...

Quantum computing exploits quantum phenomena such as superposition and entanglement to realize a form of parallelism that is not available to traditional computing. It offers the potential of significant computational speed-ups in quantum chemistry, materials science, cryptography, and machine learning.
The dominant approach to programming quantum...

As commonly understood, the noise spectroscopy problem---characterizing the statistical properties of a noise process affecting a quantum system by measuring its response---is ill-posed. Ad-hoc solutions assume implicit structure which is often never determined. Thus it is unclear when the method will succeed or whether one should trust the solutio...

The analysis of photon count data from the standard nitrogen vacancy (NV) measurement process is treated as a statistical inference problem. This has applications toward gaining better and more rigorous error bars for tasks such as parameter estimation (eg. magnetometry), tomography, and randomized benchmarking. We start by providing a summary of t...

We demonstrate that small quantum memories, realized via quantum error correction in multi-qubit devices, can benefit substantially by choosing a quantum code that is tailored to the relevant error model of the system. For a biased noise model, with independent bit and phase flips occurring at different rates, we show that a single code greatly out...

Extrapolating physical error rates to logical error rates requires many assumptions and thus can radically under- or overestimate the performance of an error correction implementation. We introduce logical randomized benchmarking, a characterization procedure that directly assesses the performance of a quantum error correction implementation at the...

A major challenge facing existing sequential Monte-Carlo methods for parameter estimation in physics stems from the inability of existing approaches to robustly deal with experiments that have different mechanisms that yield the results with equivalent probability. We address this problem here by proposing a form of particle filtering that clusters...

Characterizing quantum systems through experimental data is critical to applications as diverse as metrology and quantum computing. Analyzing this experimental data in a robust and reproducible manner is made challenging, however, by the lack of readily-available software for performing principled statistical analysis. We improve the robustness and...

We propose a framework for the systematic and quantitative generalization of Bell's theorem using causal networks. We first consider the multi-objective optimization problem of matching observed data while minimizing the causal effect of nonlocal variables and prove an inequality for the optimal region that both strengthens and generalizes Bell's t...

We introduce a fast and accurate heuristic for adaptive tomography that addresses many of the limitations of prior methods. Previous approaches were either too computationally intensive or tailored to handle special cases such as single qubits or pure states. By contrast, our approach combines the efficiency of online optimization with generally ap...

We examine the question of whether quantum mechanics places limitations on
the ability of small quantum devices to learn. We specifically examine the
question in the context of Bayesian inference, wherein the prior and posterior
distributions are encoded in the quantum state vector. We conclude based on
lower bounds from Grover's search that an eff...

We provide a method for approximating Bayesian inference using rejection
sampling. We not only make the process efficient, but also dramatically reduce
the memory required relative to conventional methods by combining rejection
sampling with particle filtering. We also provide an approximate form of
rejection sampling that makes rejection filtering...

In recent years, Bayesian methods have been proposed as a solution to a wide range of issues in quantum state and process tomography. State-of-the-art Bayesian tomography solutions suffer from three problems: numerical intractability, a lack of informative prior distributions, and an inability to track time-dependent processes. Here, we address all...

We provide a new efficient adaptive algorithm for performing phase estimation
that does not require that the user infer the bits of the eigenphase in reverse
order; rather it directly infers the phase and estimates the uncertainty in the
phase directly from experimental data. Our method is highly flexible, recovers
from failures, and can be run in...

We present an efficient classical algorithm for training deep Boltzmann
machines (DBMs) that uses rejection sampling in concert with variational
approximations to estimate the gradients of the training objective function.
Our algorithm is inspired by a recent quantum algorithm for training DBMs. We
obtain rigorous bounds on the errors in the approx...

Noise mechanisms in quantum systems can be broadly characterized as either
coherent (i.e., unitary) or incoherent. For a given fixed average error rate,
coherent noise mechanisms will generally lead to a larger worst-case error than
incoherent noise. We show that the coherence of a noise source can be
quantified by the unitarity, which we relate to...

High fidelity coherent control of quantum systems is critical to building
quantum devices and quantum computers. We provide a general optimal control
framework for designing control sequences that account for hardware control
distortions while maintaining robustness to environmental noise. We demonstrate
the utility of our algorithm by presenting e...

Recent work has shown that quantum simulation is a valuable tool for learning
empirical models for quantum systems. We build upon these results by showing
that a small quantum simulators can be used to characterize and learn control
models for larger devices for wide classes of physically realistic
Hamiltonians. This leads to a new application for...

Producing useful quantum information devices requires efficiently assessing
control of quantum systems, so that we can determine whether we have
implemented a desired gate, and refine accordingly. Randomized benchmarking
uses symmetry to reduce the difficulty of this task.
We bound the resources required for benchmarking and show that with prior
in...

In this Letter, we strengthen and extend the connection between simulation and estimation to exploit simulation routines that do not exactly compute the probability of experimental data, known as the likelihood function. Rather, we provide an explicit algorithm for estimating parameters of physical models given access to a simulator which is only c...

Understanding the performance of realistic noisy encoded circuits is an
important task for the development of large-scale quantum computers. One
difficulty in approaching this is that classical simulation of arbitrary noisy
circuits is inefficient. Nevertheless, important classes of faulty circuits can
be simulated efficiently. These types of simul...

Identifying an accurate model for the dynamics of a quantum system is a
vexing problem that underlies a range of problems in experimental physics and
quantum information theory. Recently, a method called quantum Hamiltonian
learning has been proposed by the present authors that uses quantum simulation
as a resource for modeling an unknown quantum s...

In recent years quantum simulation has made great strides culminating in
experiments that operate in a regime that existing supercomputers cannot easily
simulate. Although this raises the possibility that special purpose analog
quantum simulators may be able to perform computational tasks that existing
computers cannot, it also introduces a major c...

We introduce the likelihood-free quantum inference algorithm (LFQIA), a
Bayesian learning algorithm which can estimate quantum states and processes
given access to a classical experiment simulator rather than to exact
likelihood functions. It has been shown recently that there exists interesting
classes of states and processes for which weak simula...

In this work we combine two distinct machine learning methodologies,
sequential Monte Carlo and Bayesian experimental design, and apply them to the
problem of inferring the dynamical parameters of a quantum system. We design
the algorithm with practicality in mind by including parameters that control
trade-offs between the requirements on computati...

Understanding fault-tolerant properties of quantum circuits is important for
the design of large-scale quantum information processors. In particular,
simulating properties of encoded circuits is a crucial tool for investigating
the relationships between the noise model, encoding scheme, and threshold
value. For general circuits and noise models, th...

We describe a method for coupling disjoint quantum bits (qubits) in different local processing nodes of a distributed node quantum information processor. An effective channel for information transfer between nodes is obtained by moving the system into an interaction frame where all pairs of cross-node qubits are effectively coupled via an exchange...

Using Bayesian experimental design techniques, we have shown that for a
single two-level quantum mechanical system under strong (projective)
measurement, the dynamical parameters of a model Hamiltonian can be estimated
with exponentially improved accuracy over offline estimation strategies. To
achieve this, we derive an adaptive protocol which find...

Projective measurements of a single two-level quantum mechanical system (a
qubit) evolving under a time-independent Hamiltonian produce a probability
distribution that is periodic in the evolution time. The period of this
distribution is an important parameter in the Hamiltonian. Here, we explore how
to design experiments so as to minimize error in...