By Dr. Chris Mansell

Shown below are summaries of a few interesting research papers related to quantum computing that have been published over the past month.

Title: Quantum machine learning models are kernel methods
Organization: Xanadu 
Kernel methods were very popular in classical machine learning before the advent of deep neural networks. Insightful researchers, including the author of the present paper, Maria Schuld, had previously noted a connection between kernels and the mathematical structure of quantum mechanics. In this paper, she clarifies and formalises the connection, before using it to arrive at some important results for the field. You can view the published paper here.
https://arxiv.org/abs/2101.11020

Title: Information Scrambling in Computationally Complex Quantum Circuits
Organizations: Google, NASA, KBR and others
A quantum processor undergoing quantum scrambling explores its Hilbert space in interesting and computationally powerful ways. Even though it is challenging to experimentally distinguish scrambling from decoherence and other imperfections, the researchers manage to do so by measuring out-of-time-order correlators. They obtain results for both operator spreading and operator entanglement. You can view the published paper here.
https://arxiv.org/abs/2101.08870

Title: Experimental demonstration of quantum advantage for NP verification with limited information
Organizations: QC Ware Corp and others
The authors use a remarkably simple linear optics set-up to perform instances of a computational task that, according to well-accepted assumptions, would take a classical computer an utterly infeasible length of time. Even though this task is not commercially useful, it is similar to classical zero-knowledge proof protocols that are used in authentication systems and blockchains. You can view the published paper here.
https://www.nature.com/articles/s41467-021-21119-1

Title: Classical algorithms for Forrelation 
Organization: IBM
The authors develop new classical algorithms for forrelation, which is a powerful computational primitive. They also provide an efficient classical method for calculating variational energies achieved by the some versions of the Quantum Approximate Optimization Algorithm (QAOA). This allows larger instances of QAOA to be investigated on classical computers. You can view the paper here.
https://arxiv.org/abs/2102.06963

Title: Exponential suppression of bit or phase flip errors with repetitive error correction
Organization: Google Quantum AI
The large team of researchers at Google used their “Sycamore” superconducting quantum computer to investigate the error correction properties of two stabilizer protocols: the repetition code and the stabilizer code. This work is the first demonstration of exponential error suppression with cyclic stabilizer measurements. You can view the paper here
https://arxiv.org/abs/2102.06132

Title: Qubit-efficient exponential suppression of errors
Organizations: Los Alamos National Laboratory and Quantum Science Center
Recently, two related papers have devised error mitigation protocols for NISQ devices which require controlled-SWAP gates to act on M copies of a quantum state. The error suppression performance of the protocols improves exponentially with M. With some clever adaptations, this latest work finds a way to reduce the required number of qubits at the expense of increased circuit depth. You can view the paper here.
https://arxiv.org/abs/2102.06056

Title: Strongly Universal Hamiltonian Simulators
Organizations: Harvard University and The Hebrew University
Universal simulators can encode and simulate any other quantum system. Efficient implementation of analog Hamiltonian simulators would allow one to probe many-body physics, develop new materials and drugs and improve the feasibility of adiabatic algorithms. However, known encoding strategies have exponential overheads. The authors overcome these overheads and make near-term simulators a much more exciting prospect. You can view the paper here.
https://arxiv.org/abs/2102.02991

Title: Capacity and quantum geometry of parametrized quantum circuits
Organization: Imperial College London and National University of Singapore 
Parameterized quantum circuits provide a flexible paradigm for programming near-term quantum computers. However, there are often trade-offs between the expressibility of a circuit and the magnitude of its gradients. The authors find a rage of parameters where this is not the case. You can view their paper and their Python code here.
https://arxiv.org/abs/2102.01659
https://github.com/txhaug/quantum-geometry/blob/main/Quantum%20Geometry.ipynb

Title: Efficient and Accurate Electronic Structure Simulation Demonstrated on a Trapped-Ion Quantum Computer
Organizations: 1QBit, Dow and IonQ
Electronic structure simulation is central to modern materials design and drug discovery. The researchers devise an end-to-end pipeline for reducing the number of qubits required for these calculations by close to an order of magnitude. They use IonQ’s 11-qubit trapped-ion quantum computer to simulate a ring of 10 hydrogen atoms with an accuracy sufficient for realistic chemical predictions. You can view the paper here.
https://arxiv.org/abs/2102.07045

Title: Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets
Organization: D-Wave Systems, Google and Simon Fraser University
D-Wave have improved upon the work in their 2018 Nature article on frustrated magnets, a topic of practical relevance to material design. By using a quantum annealer with less noise and introducing topological obstructions into the initial quantum state, they observe a three million fold advantage of their device over a CPU. Furthermore, the advantage increased with difficulty of the simulation. You can view the article and a breakdown of the results by the lead author here.
https://www.nature.com/articles/s41467-021-20901-5
https://medium.com/d-wave/d-wave-insights-simulation-research-e6c4f0fb5409

February 25, 2021