Chris Cade
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Towards secondary structure prediction of longer mRNA sequences using a quantum-centric optimization scheme Open
Accurate prediction of mRNA secondary structure is critical for understanding gene expression, translation efficiency, and advancing mRNA-based therapeutics. However, the combinatorial complexity of possible foldings, especially in long se…
View article: Digital quantum magnetism at the frontier of classical simulations
Digital quantum magnetism at the frontier of classical simulations Open
The utility of near-term quantum computers for simulating realistic quantum systems hinges on the stability of digital quantum matter--realized when discrete quantum gates approximate continuous time evolution--and whether it can be mainta…
Non-zero noise extrapolation: accurately simulating noisy quantum circuits with tensor networks Open
Understanding the effects of noise on quantum computations is fundamental to the development of quantum hardware and quantum algorithms. Simulation tools are essential for quantitatively modelling these effects, yet unless artificial restr…
Complexity of Supersymmetric Systems and the Cohomology Problem Open
We consider the complexity of the local Hamiltonian problem in the context of fermionic Hamiltonians with supersymmetry and show that the problem remains -complete. Our main motivation for studying this is the well-known fact that the grou…
Quantum algorithms for community detection and their empirical run-times Open
We apply recent work~\cite{ourotherpaper} on empirical estimates of quantum speedups to the practical task of community detection in complex networks. We design several quantum variants of a popular classical algorithm -- the \textit{Louva…
Guidable Local Hamiltonian Problems with Implications to Heuristic Ansatz State Preparation and the Quantum PCP Conjecture Open
We study "Merlinized" versions of the recently defined Guided Local Hamiltonian problem, which we call "Guidable Local Hamiltonian" problems. Unlike their guided counterparts, these problems do not have a guiding state provided as a part o…
Quantifying Grover speed-ups beyond asymptotic analysis Open
Run-times of quantum algorithms are often studied via an asymptotic, worst-case analysis. Whilst useful, such a comparison can often fall short: it is not uncommon for algorithms with a large worst-case run-time to end up performing well o…
Quantum Motif Clustering Open
We present three quantum algorithms for clustering graphs based on higher-order patterns, known as motif clustering. One uses a straightforward application of Grover search, the other two make use of quantum approximate counting, and all o…
Towards quantum advantage via topological data analysis Open
Even after decades of quantum computing development, examples of generally useful quantum algorithms with exponential speedups over classical counterparts are scarce. Recent progress in quantum algorithms for linear-algebra positioned quan…
Complexity of the Guided Local Hamiltonian Problem: Improved Parameters and Extension to Excited States Open
Recently it was shown that the so-called guided local Hamiltonian problem -- estimating the smallest eigenvalue of a $k$-local Hamiltonian when provided with a description of a quantum state ('guiding state') that is guaranteed to have sub…
Quantum Algorithms for Community Detection and their Empirical Run-times Open
We apply our recent work on empirical estimates of quantum speedups to the practical task of community detection in complex networks. We design several quantum variants of a popular classical algorithm -- the Louvain algorithm for communit…
Quantifying Grover speed-ups beyond asymptotic analysis Open
Run-times of quantum algorithms are often studied via an asymptotic, worst-case analysis. Whilst useful, such a comparison can often fall short: it is not uncommon for algorithms with a large worst-case run-time to end up performing well o…
Quantum Motif Clustering Open
We present three quantum algorithms for clustering graphs based on higher-order patterns, known as motif clustering. One uses a straightforward application of Grover search, the other two make use of quantum approximate counting, and all o…
Complexity of Supersymmetric Systems and the Cohomology Problem Open
We consider the complexity of the local Hamiltonian problem in the context of fermionic Hamiltonians with $\mathcal N=2 $ supersymmetry and show that the problem remains $\mathsf{QMA}$-complete. Our main motivation for studying this is the…
Strategies for solving the Fermi-Hubbard model on near-term quantum computers Open
The Fermi-Hubbard model is of fundamental importance in condensed-matter\nphysics, yet is extremely challenging to solve numerically. Finding the ground\nstate of the Hubbard model using variational methods has been predicted to be\none of…
Towards quantum advantage for topological data analysis Open
A particularly promising line of quantum machine leaning (QML) algorithms with the potential to exhibit exponential speedups over their classical counterparts has recently been set back by a series of dequantization results, that is, quant…
Towards quantum advantage via topological data analysis Open
Even after decades of quantum computing development, examples of generally useful quantum algorithms with exponential speedups over classical counterparts are scarce. Recent progress in quantum algorithms for linear-algebra positioned quan…
Data from "Strategies for solving the Fermi-Hubbard model on near-term quantum computers" (v2) Open
Data corresponding to the results from the paper "Strategies for solving the Fermi-Hubbard model on near-term quantum computers" by Chris Cade, Lana Mineh, Ashley Montanaro, and Stasja Stanisic. Version 2.
The one clean qubit model without entanglement is classically simulable Open
Entanglement has been shown to be necessary for pure state quantum computation to have an advantage over classical computation. However, it remains open whether entanglement is necessary for quantum computers that use mixed states to also …
The Quantum Complexity of Computing Schatten p-norms Open
We consider the quantum complexity of computing Schatten p-norms and related quantities, and find that the problem of estimating these quantities is closely related to the one clean qubit model of computation. We show that the problem of a…
Post-selected Classical Query Complexity Open
We study classical query algorithms with post-selection, and find that they are closely connected to rational functions with nonnegative coefficients. We show that the post-selected classical query complexity of a Boolean function is equal…
Time and space efficient quantum algorithms for detecting cycles and testing bipartiteness Open
We study space and time-efficient quantum algorithms for two graph problems – deciding whether an n-vertex graph is a forest, and whether it is bipartite. Via a reduction to the s-t connectivity problem, we describe quantum algorithms for …
The Quantum Complexity of Computing Schatten p-norms Open
We consider the quantum complexity of computing Schatten p-norms and related quantities, and find that the problem of estimating these quantities is closely related to the one clean qubit model of computation. We show that the problem of a…
Time and Space Efficient Quantum Algorithms for Detecting Cycles and\n Testing Bipartiteness Open
We study space and time efficient quantum algorithms for two graph problems\n-- deciding whether an $n$-vertex graph is a forest, and whether it is\nbipartite. Via a reduction to the s-t connectivity problem, we describe quantum\nalgorithm…