Business Management Meets Quantum Computing

Motivated by supply chain, finance, technology, and health care applications, the Quantum Computing Group at the Tepper School aims to turn quantum computing as a service into industrial reality and help design practical quantum communication networks.

Quantum and quantum-inspired algorithms offer dramatically new possibilities to tackle practical problems previously considered intractable. Right now.

Quantum Computing Areas of Research

The research of the Quantum Computing Group (QCG) at the Tepper School focuses on the creation of radically different types of algorithms to optimize complex large-scale industrial problems startlingly faster, with the ultimate desired outcome of commercialized algorithms that are easily accessible for practical application. We are also exploring unconventional hardware and studying practical issues in quantum communications.

QCG research takes place in five parallel areas:

1. Solving practical problems using novel quantum and quantum-inspired algorithms.
2. Developing robust and efficient processes of translating a mathematical algorithm into physical instructions executed by the hardware — known as compilers — for quantum computers.
3. Understanding and enhancing quantum speedup: How and why speed is increased, and by how much.
4. Understanding quantum queue-channel capacities: How much classical information can be securely and reliably sent over a quantum channel in presence of inevitable buffering?
5. Hardware: How well can Photonic Ising Machines (PIM) solve benchmark combinatorial problems such as Max-Cut and Number Partitioning Problem?

Our Quantum and Quantum-inspired (classical) algorithms are novel approaches to tackle complex models that arise in areas such as finance, supply chain management, and cancer genomics.

By creatively advancing methods from geometry of numbers, computational integer programming, and algebraic geometry, QCG research has:

• Solved instances of real-world finance problems in seconds that can take hours by classical best-in-class commercial solvers, by developing hybrid quantum-classical algorithms and testing them on the D-Wave and Toshiba's Simulated Bifurcation Machine (SBM). 
  
  Research: Graver Bases Via Quantum Annealing With Application to Non-Linear Integer Programs
  

• Developed the Graver-Augmented Multi-Seed algorithm (GAMA), a Quantum-inspired classical algorithm that is two (and three) orders of magnitude faster than commercial best-in-class solvers. GAMA has been applied to solve problems in supply chain management involving integrated production, inventory, and logistics. These work on standard computer hardware and do not require access to digital annealers or quantum hardware.
  
  Research: GAMA: A Novel Algorithm for Non-Convex Integer Programs

To solve practical problems on a real quantum computer, we must translate the real-world problem into something that can be understood by the physical hardware — a process known as compiling.

There are two dominant computational models for quantum computing:

• Circuit (Gate) models, with hardware from Google, IBM, and Rigetti.
• Adiabatic Quantum Computing (AQC) with hardware from D-Wave.

QCG has developed two novel algorithms for compiling quantum circuits.

Research: Knuth-Bendix Completion Algorithm and Shuffle Algebras for Compiling NISQ Circuits

QCG has also developed a systematic computational approach to prepare a polynomial optimization problem for AQC.

Research: A Novel Algebraic Geometry Compiling Framework for Adiabatic Quantum Computations

Current QCG research on compiling enhances methods for Gate/circuit chips to account directly for the noise, incorporating models into our algorithms directly and adapts computational methods from Mixed-Integer Linear Programming to create open-source compilers for AQC. 

Research: Integer Programming Techniques for Minor-Embedding in Quantum Annealers 

Where does quantum speedup really come from? How can we enhance the speedup of quantum (and hybrid) algorithms? This is an exciting and deep area of research.

QCG research has helped provide algorithmic guidelines that enable further speedup in AQC.

Research: Enhancing the Efficiency of Adiabatic Quantum Computations

Research: Homological Description of the Quantum Adiabatic Evolution With a View Toward Quantum Computations

MyAmpleLife Blog: The Next Quantum Revolution 

Quantum queue-channels arise naturally in the context of buffering in quantum networks. We study the important practical case of symmetric Generalized Amplitude Damping, and extend our results to Unital qubit queue-channels: We show that the maximum classical capacity can be achieved without entanglement (in encoding and decoding)!

Research: Queue-Channel Capacities With Generalized Amplitude Damping 

Research: Unital Qubit Queue-channels: Classical Capacity and Product Decoding

My Ample Life Blog: Buffering of Flying Qubits

Photonic Ising Machines (PIMs) offer alternatives to quantum annealing and simulated annealing. An NP-hard problem is cast as a quadratic unconstrained binary optimization (QUBO) where the final spin configuration in the Ising model is adiabatically arrived at as a solution to a Hamiltonian, given a known set of interactions between spins.

The temporal multiplexed Ising machine uses the bistable response of an electro-optic modulator to mimic the spin up and down states and solves the Max-Cut problem on par with Gurobi for up to 1000 spins.

The spatial photonic Ising machine easily partitions an array of 2^14 integers, vastly outperforming both Gurobi and the state-of-the-art D-Wave annealer.

Research: Optimization With Photonic Wave-Based Annealers

MyAmpleLife Blog: 2020 Tayur Prize