Noisy intermediate-scale quantum computing algorithm for solving an nn-vertex MaxCut problem with log(nn) qubits

Quantum computers are devices, which allow more efficient solutions of problems as compared to their classical counterparts. As the timeline to developing a quantum-error corrected computer is unclear, the quantum computing community has dedicated much attention to developing algorithms for currently available noisy intermediate-scale quantum computers (NISQ). Thus far, within NISQ, optimization problems are one of the most commonly studied and are quite often tackled with the quantum approximate optimization algorithm (QAOA). This algorithm is best known for computing graph partitions with a maximal separation of edges (MaxCut), but can easily calculate other problems related to graphs. Here, I present a novel quantum optimization algorithm, which uses exponentially less qubits as compared to the QAOA while requiring a significantly reduced number of quantum operations to solve the MaxCut problem. Such an improved performance allowed me to partition graphs with 32 nodes on publicly available 5 qubit gate-based quantum computers without any preprocessing such as division of the graph into smaller subgraphs. These results represent a 40% increase in graph size as compared to state-of-art experiments on gate-based quantum computers such as Google Sycamore. The obtained lower bound is 54.9% on the solution for actual hardware benchmarks and 77.6% on ideal simulators of quantum computers. Furthermore, large-scale optimization problems represented by graphs of a 128 nodes are tackled with simulators of quantum computers, again without any predivision into smaller subproblems and a lower solution bound of 67.9% is achieved. The study presented here paves way to using powerful genetic optimizer in synergy with quantum computersComment: 5 pages, 4 figures, 2 tables + Supplementary materia

Exactly solving the Kitaev chain and generating Majorana-zero-modes out of noisy qubits

Majorana-zero-modes (MZMs) were predicted to exist as edge states of a physical system called the Kitaev chain. MZMs should host particles that are their own antiparticles and could be used as a basis for a qubit which is robust-to-noise. However, all attempts to prove their existence gave inconclusive results. Here, the Kitaev chain is exactly solved with a quantum computing methodology and properties of MZMs are probed by generating eigenstates of the Kitev Hamiltonian on 3 noisy qubits of a publicly available quantum computer. After an ontological elaboration I show that two eigenstates of the Kitaev Hamiltonian exhibit eight signatures attributed to MZMs. The results presented here are a most comprehensive set of validations of MZMs ever conducted in an actual physical system. Furthermore, the findings of this manuscript are easily reproducible for any user of publicly available quantum computers, solving another important problem of research with MZMs-the result reproducibility crisis

Simulating Majorana zero modes on a noisy quantum processor

The simulation of systems of interacting fermions is one of the most anticipated applications of quantum computers. The most interesting simulations will require a fault-tolerant quantum computer, and building such a device remains a long-term goal. However, the capabilities of existing noisy quantum processors have steadily improved, sparking an interest in running simulations that, while not necessarily classically intractable, may serve as device benchmarks and help elucidate the challenges to achieving practical applications on near-term devices. Systems of non-interacting fermions are ideally suited to serve these purposes. While they display rich physics and generate highly entangled states when simulated on a quantum processor, their classical tractability enables experimental results to be verified even at large system sizes that would typically defy classical simulation. In this work, we use a noisy superconducting quantum processor to prepare Majorana zero modes as eigenstates of the Kitaev chain Hamiltonian, a model of non-interacting fermions. Our work builds on previous experiments with non-interacting fermionic systems. Previous work demonstrated error mitigation techniques applicable to the special case of Slater determinants. Here, we show how to extend these techniques to the case of general fermionic Gaussian states, and demonstrate them by preparing Majorana zero modes on systems of up to 7 qubits.Comment: 12 pages, 6 figure

Entangling Spins in Double Quantum Dots and Majorana Bound States

We study the coupling between a singlet-triplet qubit realized in a double quantum dot to a topological qubit realized by spatially well-separated Majorana bound states. We demonstrate that the singlet-triplet qubit can be leveraged for readout of the topological qubit and for supplementing the gate operations that cannot be performed by braiding of Majorana bound states. Furthermore, we extend our setup to a network of singlet-triplet and topological hybrid qubits that paves the way to scalable fault-tolerant quantum computing

Open Source Variational Quantum Eigensolver Extension of the Quantum Learning Machine (QLM) for Quantum Chemistry

Quantum Chemistry (QC) is one of the most promising applications of Quantum Computing. However, present quantum processing units (QPUs) are still subject to large errors. Therefore, noisy intermediate-scale quantum (NISQ) hardware is limited in terms of qubits counts and circuit depths. Specific algorithms such as Variational Quantum Eigensolvers (VQEs) can potentially overcome such issues. We introduce here a novel open-source QC package, denoted Open-VQE, providing tools for using and developing chemically-inspired adaptive methods derived from Unitary Coupled Cluster (UCC). It facilitates the development and testing of VQE algorithms. It is able to use the Atos Quantum Learning Machine (QLM), a general quantum programming framework enabling to write, optimize and simulate quantum computing programs. Along with Open-VQE, we introduce myQLM-Fermion, a new open-source module (that includes the key QLM ressources that are important for QC developments (fermionic second quantization tools etc...). The Open-VQE package extends therefore QLM to QC providing: (i) the functions to generate the different types of excitations beyond the commonly used UCCSD ans{\"a}tz;(ii) a new implementation of the "adaptive derivative assembled pseudo-Trotter method" (ADAPT-VQE), written in simple class structure python codes. Interoperability with other major quantum programming frameworks is ensured thanks to myQLM, which allows users to easily build their own code and execute it on existing QPUs. The combined Open-VQE/myQLM-Fermion quantum simulator facilitates the implementation, tests and developments of variational quantum algorithms towards choosing the best compromise to run QC computations on present quantum computers while offering the possibility to test large molecules. We provide extensive benchmarks for several molecules associated to qubit counts ranging from 4 up to 24

Self-controlled growth of highly uniform Ge/Si hut wires for scalable qubit devices

Semiconductor nanowires have been playing a crucial role in the development of nanoscale devices for the realization of spin qubits, Majorana fermions, single photon emitters, nanoprocessors, etc. The monolithic growth of site-controlled nanowires is a prerequisite towards the next generation of devices that will require addressability and scalability. Here, combining top-down nanofabrication and bottom-up self-assembly, we report on the growth of Ge wires on pre-patterned Si (001) substrates with controllable position, distance, length and structure. This is achieved by a novel growth process which uses a SiGe strain-relaxation template and can be generalized to other material combinations. Transport measurements show an electrically tunable spin-orbit coupling, with a spin-orbit length similar to that of III-V materials. Also, capacitive coupling between closely spaced wires is observed, which underlines their potential as a host for implementing two qubit gates. The reported results open a path towards scalable qubit devices with Si compatibility