*By Dr Chris Mansell, Senior Scientific Writer at Terra Quantum*

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

### Hardware

**Title: Fault-Tolerant One-Bit Addition with the Smallest Interesting Colour CodeOrganizations: QuTech; University of Stuttgart; QuantinuumSummary: **To build a fault-tolerant circuit, you can select a quantum error-correcting code and then decide which operations to directly implement in a fault-tolerant way and which to perform via the code’s associated error-correction gadgets. For the colour code, the usual choice is for the Clifford gates to have a direct, fault-tolerant implementation with the non-Clifford gates being performed in a more complex way. In this paper, the reverse approach is taken and, at least for the task of one-bit addition, it led to a reduction in the logical error rate. That is, errors in the arithmetic occurred less frequently. Using the Quantinuum H1-1 quantum computer, the errors dropped from 9.5 in a thousand to 1.1 in a thousand.

Link: https://arxiv.org/abs/2309.09893

Link: https://arxiv.org/abs/2309.09893

**Title: High-fidelity optical readout of a superconducting qubit using a scalable piezo-optomechanical transducerOrganizations: QphoX; Rigetti Computing; QbloxSummary: **One way to scale up superconducting quantum processors is to use dilution refrigerators that are several times larger than those that are readily available today. Another is to convert microwave signals to the optical domain because optical fibers have a passive heat load that is about 1000 times smaller than coaxial cables (picowatts instead of nanowatts). This research investigated the latter option by using a piezo-optomechanical transducer to measure the state of a transmon qubit. The readout fidelity was comparable to microwave-only readout. Despite needing 10 times as many repetitions of the measurement, plans to optimize the optical approach could increase the signal-to-noise ratio by orders of magnitude and enable single-shot measurements. Additional optical fibers would then allow thousands of superconducting qubits to be cooled inside a standard-size dilution refrigerator.

Link: https://arxiv.org/abs/2310.06026

Link: https://arxiv.org/abs/2310.06026

**Title: High-fidelity parallel entangling gates on a neutral-atom quantum computerOrganizations: Harvard University; QuEra Computing; Massachusetts Institute of TechnologySummary: **In this paper on ultracold rubidium atoms, Rydberg interactions were used to perform two-qubit entangling gates with 99.5% fidelity. This is an improvement of two percentage points over the best prior work in neutral-atom quantum processors and puts such systems on par with state-of-the-art superconducting and ion trap platforms. Furthermore, it was performed on 60 atoms in parallel. The researchers also performed a three-qubit entangling gate, reporting data consistent with a 97.9% fidelity. It was performed across 21 atoms in parallel. When analysing the error sources, they found that high-weight correlated errors were largely absent. Overall, the high fidelities of the multi-qubit gates, the parallel operation and the low levels of unwanted correlation add to the argument that ultracold atoms are a highly scalable and valuable technology.

Link: https://www.nature.com/articles/s41586-023-06481-y

Link: https://www.nature.com/articles/s41586-023-06481-y

**Title(1): Erasure conversion in a high-fidelity Rydberg quantum simulatorOrganizations(1): California Institute of Technology; Stanford UniversityLink(1): https://www.nature.com/articles/s41586-023-06516-4 Title(2): High-fidelity gates and mid-circuit erasure conversion in an atomic qubitOrganizations(2): Princeton University; University of Strasbourg; CNRS; Yale UniversityLink: https://www.nature.com/articles/s41586-023-06438-1Summary of both papers: **Certain atomic species have richer energy-level structures than others. In the context of neutral-atom quantum computing, this presents certain opportunities, such as the ability to detect whenever an atom has decayed to an energy level that is not involved in the computation. It is possible to discard these instances while leaving the rest of the quantum system in the desired state. As experimentally demonstrated in the two papers, the resulting fidelities can be extremely high. For example, in one of the papers, Rydberg interactions were used to prepare a Bell-state with a fidelity of over 99.7%.

**Title: Supercharged two-dimensional tweezer array with more than 1000 atomic qubits Organization: Technische Universita ̈t DarmstadtSummary: **To set expectations about neutral-atom quantum computers, it is important to be quantitative about their scalability. Spatial light modulators can currently create about 1,000 trapping sites and fill just over 300 of them with atoms. Microfabricated lens arrays can create 10 times as many trapping sites with a similar filling fraction. In two dimensions, laser power can be a limiting factor, while for three-dimensional arrangements employing the Talbot effect, some of the planes of trapping sites are not as close together as is needed for the quantum computation to involve all the atoms. In this paper, the researchers show how more than one laser can be shone on a lens array. This demonstrates that laser power need not be a limitation. Instead, the number of trapped atoms can depend linearly on the number of available lasers.

Link: https://arxiv.org/abs/2310.09191

Link: https://arxiv.org/abs/2310.09191

**Title: QRAM architectures using superconducting cavitiesOrganization: Yale UniversitySummary: **Consider a quantum state that plays the role of a memory address and another that is in a simple fiducial state. A QRAM device can perform a unitary operation that keeps the address state constant and encodes data in the other state. It can even do this to a superposition of such states. In this work, two QRAM architectures were proposed and analysed. The researchers made use of a “dual-rail” encoding that was recently brought from the field of linear quantum optics to the domain of superconducting cavities. They helpfully put their findings in the context of important quantum algorithms that need access to a QRAM.

Link: https://arxiv.org/abs/2310.08288

Link: https://arxiv.org/abs/2310.08288

**Title: Purification-based quantum error mitigation of pair-correlated electron simulationsOrganizations: Google; Universiteit Leiden; Covestro Deutschland AG; PASQAL; University of Massachusetts Amherst; University of Connecticut; Auburn University; University of Technology Sydney; University of California; Columbia UniversitySummary: **A quantum simulation that finds the ground state of a chemical system must meet stringent accuracy requirements in order to be useful. In the NISQ era, this necessitates the use of error mitigation. In this paper, echo verification and postselected virtual distillation were used to mitigate errors in a quantum simulation run on up to 20 superconducting qubits. They reduced the errors by up to two orders of magnitude over the unmitigated implementations. The authors of the paper found that the techniques worked better in larger simulations. They also considered what capabilities the quantum processor would need to possess to run a beyond-classical experiment.

Link: https://www.nature.com/articles/s41567-023-02240-y

Link: https://www.nature.com/articles/s41567-023-02240-y

### Software

**Title: Advances in compilation for quantum hardware — A demonstration of magic state distillation and repeat-until-success protocolsOrganizations: Quantinuum; MicrosoftSummary: **The Quantum Intermediate Representation (QIR) allows compilers to process quantum and classical instructions in an optimised way. In this paper, the researchers used QIR to perform magic state distillation (MSD) on Quantinuum’s H1-1 ion-trap quantum computer. This marked the first ever implementation of MSD on a quantum processor. They also employed QIR to emulate a fault-tolerant repeat-until-success algorithm. They found that QIR could handle the feed-forward data processing required by these protocols almost as well as custom-written assembly code.

Link: https://arxiv.org/abs/2310.12106

Link: https://arxiv.org/abs/2310.12106

**Title: Complexity and order in approximate quantum error-correcting codesOrganizations: Perimeter Institute for Theoretical Physics; University of Waterloo; University of Maryland; Tsinghua UniversitySummary: **An approximate quantum error correction (AQEC) code is one where the protected quantum information can only be recovered approximately. The level of approximation is usually vanishingly small in the system size. The authors of this paper noticed that this can be achieved in a contrived fashion. This suggested to them that a more meaningful framework for AQEC codes could be established. They achieved this by focusing on quantum circuit complexity. They found connections to a wide range of physical scenarios where there is nontrivial quantum order. Given these relationships to other important areas of physics, the prospects for improved AQEC codes look bright.

Link: https://arxiv.org/abs/2310.04710

Link: https://arxiv.org/abs/2310.04710

**Title: Optimizing Space in Regev’s Factoring AlgorithmOrganizations: Massachusetts Institute of TechnologySummary: **In August of this year, Oded Regev devised a quantum factoring algorithm that improves upon the 1994 landmark result of Peter Shor. Instead of the number of quantum gates required to factor an n-bit integer scaling as n squared, it scales only as n to the power of 1.5. This could make it easier to build a cryptographically relevant quantum computer. However, one big downside of Regev’s approach is that it requires more qubits than Shor’s. Now, a new paper shows how to construct a quantum factoring algorithm that performs as well as Regev’s in terms of gates and as well as Shor’s in terms of qubits.

Link: https://arxiv.org/abs/2310.00899

Link: https://arxiv.org/abs/2310.00899

**Title: Quantum algorithms: A survey of applications and end-to-end complexitiesOrganizations: AWS; RWTH Aachen University; Imperial College London; Caltech; Alfréd Rényi Institute of Mathematics; IT University of Copenhagen; Harvard University; Amazon Quantum Solutions LabSummary: **This extremely comprehensive review paper covers quantum algorithms with scientific and industrial applications, as well as algorithmic primitives and fault-tolerant protocols. The algorithms are surveyed one by one. In addition to the usual headings, like “Overview,” each algorithm has a section completely dedicated to its technical caveats. In this way, subtleties that might otherwise require a great deal of expertise and effort to uncover are clearly laid out. As such, it is a very useful resource for the quantum technology community.

Link: https://arxiv.org/abs/2310.03011

Link: https://arxiv.org/abs/2310.03011

**Title: One Clean Qubit Suffices for Quantum Communication AdvantageOrganizations: IBM; Princeton University; Hebrew University of JerusalemSummary: **The one clean qubit model of quantum computation involves multiple qubits in the maximally mixed state and only one qubit in a pure state. Despite this unusual configuration, algorithms within this model can solve certain tasks exponentially faster than classical algorithms. In this paper, the model is considered from a perspective which has a successful history of establishing important results in theoretical computer science, that of communication complexity. The main result is that a certain problem, defined in terms of a parameter, N, can be solved in the one clean qubit model by exchanging log(N) qubits, while every classical, interactive, randomised protocol requires exchanging the square root of N qubits. This separation is unconditional in the sense that its proof does not rely on any complexity theoretic assumptions.

Link: https://arxiv.org/abs/2310.02406

Link: https://arxiv.org/abs/2310.02406

October 30, 2023