# Research Summary for October 2022

*By Dr. Chris Mansell*

### Material

**Title: Quantum and non-local effects offer a noise resilience advantage of more than 40 dB compared to quantum lidar Organization: University of Toronto**

LiDAR systems, such as those in some self-driving cars, can measure distances by shining a laser at an object and measuring the time it takes for the reflected light to return to a receiver. In this paper, quantum correlations between probe and reference photon times were used to improve the signal-to-noise ratio of the receiver by 43 decibels. The demonstrated system could also tolerate 1000 times more background noise than a comparable typical configuration. These impressive results were achieved in the lab, but given the performance and noise resistance of the system, it seems plausible that future upgrades could be tested in the real world.

**Link: https://www.nature.com/articles/s41467-022-33376-9**

**Title: A shuttle-based two-qubit logic gate for linking remote silicon quantum processors Organizations: RIKEN; Delft University of Technology; Netherlands Organization for Applied Scientific Research (TNO)**

Quantum logic gates between silicon quantum dots typically rely on short-range exchange coupling between nearest neighbors. This work demonstrated a phase-controlled gate between a stationary qubit and a qubit that was moved from point to point by a phase-coherent spin-shuttle process. The precision was 93%, but could potentially be increased by an additional barrier pulse and more frequent self-calibration. With these improvements in place, the next step will be to see if qubits can be moved longer distances.

**Link: https://www.nature.com/articles/s41467-022-33453-z**

**Title: Universal control of a silicon six-qubit quantum processor Organizations: Delft University of Technology; Netherlands Organization for Applied Scientific Research (TNO)**

Experiments involving four or fewer spin qubits in silicon quantum dots typically optimize either quantum logic gate fidelity or initialization and measurement fidelities. In this impressive paper, the researchers created six spin qubits in a linear array of quantum dots and introduced new techniques that allow the aforementioned fidelities to reach high values simultaneously. They demonstrated universal control over these qubits by preparing maximally entangled states and gave plans to improve and scale their device.

**Link: https://www.nature.com/articles/s41586-022-05117-x**

**Title: On the emerging potential of quantum annealing hardware for combinatorial optimizationOrganizations: Los Alamos National Laboratory; University of New Mexico**

D-Wave Systems’ newest quantum annealer can solve unconstrained quadratic optimization problems with over 5,000 binary decision variables and 40,000 quadratic terms. This study shows that there are classes of engineered problems where this quantum annealing provides an order of magnitude runtime advantage over state-of-the-art classical solving methods. The work has some limitations which are openly discussed, but the results are valid even taking into account practicalities and overheads.

**Link: https://arxiv.org/abs/2210.04291**

**Title: Protecting Fiber Optic Quantum Key Distribution Sources Against Light Injection AttacksOrganizations: Russian Quantum Center; National University of Science and Technology MISiS; University of Waterloo; Mahidol University; Quantum Technology Foundation (Thailand); ITMO University; SMARTS-Quanttelecom; University of Science and Technology of China; National University of Defense Technology, China**

Device-dependent quantum key distribution requires a light source that operates within well-defined parameters. If prying eyes inject bright light into the system, this can change the properties of the light source and thus ruin the safety of the installation. This paper proposed and tested a countermeasure in the form of a component that under lower light levels shielded the light source and under higher levels permanently and securely terminated the protocol. Importantly for the practicality of the proposal, the crucial component could be a standard fiber optic isolator or a simple circulator.

**Link: https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.3.040307**

**Title: Testing platform-independent quantum error mitigation on noisy quantum computersOrganizations: Unitary Fund; Federal Polytechnic School of Lausanne (EPFL); Goldman Sachs & Co.**

Noiseless extrapolation and probabilistic error cancellation are two important quantum error mitigation techniques. In this paper, they have been applied to two benchmark problems each running on IBM, IonQ, and Rigetti quantum computers. The benefit provided by these techniques is characterized by an improvement factor. The results varied depending on the underlying hardware, but the main finding was that, on average, error mitigation is beneficial compared to no mitigation. The authors expect error mitigation to feature in nearly every experiment of the NISQ era.

**Link: https://arxiv.org/abs/2210.07194**

### Software

**Title: A simplified quantum algorithm for the analysis of topological data with an exponential number of qubits Organizations: AWS; California Institute of Technology; Alfred Rényi Institute**ute of Mathematics; Imperial College

Analyzing the topological features of a dataset can be useful in many data science and machine learning contexts. This article presents a quantum algorithm that improves on its predecessors by being polynomially faster and requiring exponentially fewer qubits. It also has a roughly quintic speedup compared to rigorous classical algorithms and a roughly quadratic speedup compared to heuristic classical algorithms. Despite this, the authors suspect that the conditions required for their algorithm to show an advantage may not occur very frequently in real-world datasets.

**Link: https://arxiv.org/abs/2209.12887**

**Title: Quantum calculation of molecular structure using data from nuclear magnetic resonance experiments difficult to simulate classically Organizations: Google; University of Maryland**

Nuclear Magnetic Resonance (NMR) experiments are used by chemists and biologists to study the properties of molecules. However, the data generated is often difficult for conventional computers to analyze. In this paper, a quantum algorithm is presented to use this data to infer molecular nuclear spin Hamiltonians. The algorithm can be run on both current NISQ devices and future fault-tolerant quantum computers. The researchers used the protein ubiquitin as an example and hope their work will aid in the development of new NMR-based techniques for molecular structure analysis.

**Link: https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.3.030345**

**Title: Portfolio optimization via Quantum Zeno Dynamics on a Quantum processorOrganizations: JPMorgan Chase**

The quantum Zeno effect takes its name from Zeno’s arrow paradox and can be implemented using repeated projective measures. In this preprint on portfolio optimization with quantum algorithms, this effect is used to apply several constraints. This is done by introducing penalty terms into the objective function and slack variables into the inequality constraints. The methods require only a few auxiliary qubits and no post-selection, but they can be incorporated into the QAOA algorithm and variational quantum algorithms to obtain high-quality valid solutions. This was tested on the Quantinuum H1-2 trapped ion quantum processor with two-qubit gate depths of up to 148.

**Link: https://arxiv.org/abs/2209.15024**

**Title: The complexity of the NISQOrganizations: UC Berkeley; Harvard University; California Institute of Technology; Microsoft Search**

In this work, the authors define a complexity class intended to capture problems that can be efficiently solved by a classical computer combined with a NISQ device. Their analysis takes place in the circuit model of quantum computing where all the key steps are noisy: the initialization of the qubits; setting up logic gates; and the measurement process. Using quantum query complexity tools, they demonstrate that this complexity class is strictly more powerful than the complexity class describing classical computation and strictly less powerful than that of fault-tolerant quantum computation. Overall, their mathematical framework allowed them to draw very general conclusions about the current era of NISQ calculation.

**Link: https://arxiv.org/abs/2210.07234**

**Title: The quantum Fourier transform has a small entanglementOrganizations: University of California, Irvine; California Institute of Technology; Flatiron Institute**

Fourier transforms are extremely important in mathematics, physics, computer science, and engineering. In quantum computing, the quantum Fourier transform (QFT) plays a prominent role in quantum phase estimation and in Shor’s algorithm for integer factorization. It was already known that the QFT has a maximum entanglement of operators but the authors of this article have shown that this is mainly due to a step in the process where the order of the qubits is reversed. They found that this step is not necessary and that without it the QFT has a different entanglement structure which makes it easier to simulate on a classical computer. They called it a “classical quantum-inspired algorithm” and showed that it can outperform the ubiquitous Fast Fourier Transform.

**Link: https://arxiv.org/abs/2210.08468**

**Title: Exponentially tighter bounds on quantum error attenuation bounds Organizations: Freie Universität Berlin; University of Copenhagen; ENS Lyon; Helmholtz-Zentrum Berlin for Materials and Energy**

Quantum Error Mitigation (QEM) schemes are of great interest because they require few additional quantum resources and yet promise to enable useful quantum computations in the NISQ era. Their benefits have been demonstrated on small quantum processors available today. However, theoretical results can tell us what to expect as devices grow in their quantum volume and this work proves that QEM protocols (which fall within its scope) work exponentially both in depth and in circuit width. The theory is a worst case analysis and therefore further research is needed to see if the results apply to typical quantum circuits.

**Link: https://arxiv.org/abs/2210.11505**

October 29, 2022