By Dr Chris Mansell, Senior Scientific Writer at Terra Quantum

Shown below are summaries of a few interesting research papers in quantum computing and communications that we have seen over the past month.


Title: Fault-Tolerant Connection of Error-Corrected Qubits with Noisy Links
Organizations: MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics; University of Bristol
Qubit architectures are hard to scale: ions experience spectral crowding of their motional modes, superconductors have to fit inside a cryostat and arrays of ultracold atoms must stay within the field of view of an aspheric lens. One way to overcome this is to link patches of qubits together with optical interconnects, superconducting microwave links or by simply shuttling qubits from one patch to the next. Unfortunately, the noise involved in some of these operations is quite high. (Although see the first few articles in the hardware section of this Research Roundup for the latest developments.) In this software paper, the researchers show that even when the errors within a patch aren’t extremely low, perhaps about 1%, the operations between the patches can have errors as high as 10% while keeping the overall system fault-tolerant. 

Title: Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics
Organization: Google
Typically, quantum error correction codes do not include time as an important parameter. However, the codes are ultimately implemented in quantum circuits, which highlights the relevance of their temporal structure. By treating codes from a more dynamic, less static perspective, the authors of this paper find many advantages over prior state-of-the-art codes. For example, fewer nearest neighbour couplings are required for certain operations, which will make the code easier for experimentalists to implement. This research was focussed on the surface code, so future work could consider alternative schemes like the color code. Benchmarking these ideas against more realistic error models could be another next step.

Title: Linear-depth quantum circuits for loading Fourier approximations of arbitrary functions
Organizations: Cornell University; Purdue University; Princeton University
Loading functions on a quantum computer in an efficient way is an important task with lots of applications. The authors of this paper present a method to do this for Fourier series. The depth of their quantum circuit scales linearly with both the number of Fourier coefficients and the number of qubits. This scaling enables the circuit to use a sufficient number of coefficients to represent functions with high accuracy. They test their method on real and complex functions in one and two dimensions, with and without discontinuities. They do this with noiseless classical simulations and on the Quantinuum H1-1 and H1-2 trapped-ion quantum computers. They thoroughly compare their results with prior work on this topic and discuss a good number of future research directions. 

Title: Improved quantum algorithms for linear and nonlinear differential equations
Organization: Riverlane 
The laws of physics are written in the form of differential equations. For example, the Schrödinger equation is a linear homogeneous differential equation. Complex physical phenomena like ocean currents, solar flares and plasma dynamics are governed by nonlinear differential equations that are harder to solve. The evolution of these chaotic systems is therefore harder to predict, yet the benefits of improved predictions extend to weather forecasting, designing aerodynamic vehicles and maintaining nuclear fusion. In this paper, quantum algorithms for solving both linear and nonlinear differential equations are presented. Matrix exponentials are used to analyse the stability of the equations and the use of block encoded matrices enables the algorithm to work for singular and non-diagonalisable matrices. The presented algorithm is exponentially faster and has an exponentially better dependence on error than some prior algorithms.

Title: Optimization Applications as Quantum Performance Benchmarks
Organizations: Quantum Circuits Inc.; QED-C; Los Alamos National Laboratory; D-Wave Systems; University of California at Los Angeles; Universities Space Research Association; Indiana University; NASA Ames Research Center
Operations research involves using analytic methods to improve decision-making and plays an important role in both the private and public sectors. Experts in operations research have their own standards for, say, assessing and evaluating the trade-off between the runtime and the solution quality of an optimization algorithm. These standards may be quite different to those found in the academic quantum computing literature. In this work, quantum optimization algorithms are benchmarked in a way that deliberately makes their performance characteristics easy to understand by people whose expertise is not in the quantum domain. 

Title: Computing 256-bit Elliptic Curve Logarithm in 9 Hours with 126133 Cat Qubits
Organizations: Université Paris–Saclay; Alice & Bob; Sorbonne Université
Cat states are superpositions of coherent states with opposite phases. With these states, there is a way to exponentially suppress the bit-flip errors and then use a repetition code to take care of the remaining phase errors. In comparison to two-dimensional error correction codes, where the number of physical qubits per logical qubit scales quadratically with the code distance, cat states can instantiate a one-dimensional code where this scaling is only linear. In this preprint, a fault-tolerant approach to Shor’s algorithm based on cat states is given. Its performance is analysed for the task of computing the elliptic curve discrete logarithms used in Bitcoin signatures.


Title: A high-fidelity quantum matter-link between ion-trap microchip modules
Organizations: University of Sussex; Universal Quantum Ltd; University College London; University of Bristol
Ion trap quantum computers have recently demonstrated fault-tolerant logical gate operations and researchers are aiming to start incorporating repetitive cycles of quantum error correction. However, many physical qubits will be needed for the most important algorithms and this will require ions from one chip to interface with those from an adjacent chip. Ions can be coherently moved around a single chip but this new paper shows that they can also be quickly and deterministically shuttled between chips using electric fields. No ions were lost in 15 million shuttles. This impressive feat could be built upon by employing techniques to minimise the motional excitation of the ions. 

Title: Long-Distance Transmon Coupler with cz-Gate Fidelity above 99.8%
Organizations: IQM Quantum Computers; Quantum Technology Finland Center of Excellence; Aalto University
In this paper, waveguides are used to couple superconducting transmon qubits together. Compared to the usual approach of direct capacitive coupling, this lowers the unwanted crosstalk between the qubits and allows them to be placed four times further apart. This has the advantage that it makes room for each qubit to have its own set of components for high-fidelity readout. The long-distance coupling still performs its main role extremely well, as shown by the researchers’ demonstration of a controlled-Z gate with 99.8% fidelity and a duration of 33 nanoseconds.

Title: Low-loss interconnects for modular superconducting quantum processors
Organizations: Southern University of Science and Technology, Shenzhen; International Quantum Academy; Hefei National Laboratory; University of Chicago; Argonne National Laboratory
In this paper, low-loss interconnects between superconducting transmon qubits are made from aluminium coaxial cables and on-chip impedance transformers. These interconnects link together five separate quantum modules, each containing four capacitively coupled qubits. The experimentalists managed to create a Bell state between a qubit on one module and a qubit on an adjacent module with a fidelity of 99%. They characterised their interconnects and found that they have a linear loss rate of 0.15 decibels per kilometre (dB/km). Impressively, this is better than the 0.2 dB/km value for telecommunications standard optical fibers. 

Title: Entanglement of Trapped-Ion Qubits Separated by 
Organizations: Österreichische Akademie der Wissenschaften; Universität Innsbruck; Georgetown University; University of Geneva; Université Paris-Saclay
Entangling the electronic state of a trapped ion qubit with the polarisation state of a photon and then entangling that photon with another ion is an extremely challenging task. However, the authors of this paper, using optical cavities, photons with frequencies employed by the telecommunications industry and 230 meters of optical fiber, managed to create a Bell state between two ions located in separate buildings. They achieved a fidelity of 88% but the process was probabilistic, succeeding only forty times per million, with each success being heralded by the coincident detection of two photons.

Title: Quantum Optimization with Arbitrary Connectivity Using Rydberg Atom Arrays
Organizations: QuEra Computing Inc.; Harvard University; University of Innsbruck; Austrian Academy of Sciences
Rydberg atoms have some rather unique strengths as a platform for quantum algorithms. In particular, they can be placed in optical dipole traps that can be arranged into different geometrical patterns using spatial light modulators. As such, the atoms can represent the vertices of a graph theory problem and the interactions between the atoms can represent the edges. In this article, the authors provide a simple, unified and general framework for efficiently mapping a variety of problems into arrangements of Rydberg atoms. They give results for exactly solving quadratic unconstrained binary optimization problems with 2D arrangements of atoms. In the future, they plan to consider approximate solutions, higher-order optimization problems and placing the atoms in 3D geometries.

February 27, 2023