Encoding Two-Qubit Logical States and Quantum Operations Using the Energy States of a Physical System

In this paper, we introduce a novel coding scheme, which allows single quantum systems to encode multi-qubit registers. This allows for more efficient use of resources and the economy in designing quantum systems. The scheme is based on the notion of encoding logical quantum states using the charge degree of freedom of the discrete energy spectrum that is formed by introducing impurities in a semiconductor material. We propose a mechanism of performing single qubit operations and controlled two-qubit operations, providing a mechanism for achieving these operations using appropriate pulses generated by Rabi oscillations. The above architecture is simulated using the Armonk single qubit quantum computer of IBM to encode two logical quantum states into the energy states of Armonk’s qubit and using custom pulses to perform one and two-qubit quantum operations.

Current biased gradiometric flux qubit in a circuit-QED architecture

We propose a scheme for controlling the gradiometric flux qubit (GFQ) by applying an ac bias current in a circuit-QED architecture. The GFQ is insensitive to the magnetic flux fluctuations, which at the same time makes it challenging to manipulate the qubit states by an external magnetic field. In this study, we demonstrate that an ac bias current applied to the $\alpha$-junction of the GFQ can control the qubit states. Further, the present scheme is robust against the charge fluctuation as well as the magnetic flux fluctuations, promising a long coherence time for quantum gate operations. We introduce a circuit-QED architecture to perform the single and two-qubit operations with a sufficiently strong coupling strength.

Double Electron Spin Resonance of Engineered Atomic Structures on a Surface

Atomic-scale control of multiple spins with individual addressability enables the bottom-up design of functional quantum devices. Tailored nanostructures can be built with atomic precision using scanning tunneling microscopes, but quantum-coherent driving has thus far been limited to a spin in the tunnel junction. Here we show the ability to drive and detect the spin resonance of a remote spin using the electric field from the tip and a single-atom magnet placed nearby. Read-out was achieved via a weakly coupled second spin in the tunnel junction that acted as a quantum sensor. We simultaneously and independently drove the sensor and remote spins by two radio frequency voltages in double resonance experiments, which provides a path to quantum-coherent multi-spin manipulation in customized spin structures on surfaces. One-Sentence Summary: Using a scanning tunneling microscope, we simultaneously control two spins using one tip, paving the way for multi-spin-qubit operations on surfaces.

Spin-valley coupling in single-electron bilayer graphene quantum dots

Understanding how the electron spin is coupled to orbital degrees of freedom, such as a valley degree of freedom in solid-state systems, is central to applications in spin-based electronics and quantum computation. Recent developments in the preparation of electrostatically-confined quantum dots in gapped bilayer graphene (BLG) enable to study the low-energy single-electron spectra in BLG quantum dots, which is crucial for potential spin and spin-valley qubit operations. Here, we present the observation of the spin-valley coupling in bilayer graphene quantum dots in the single-electron regime. By making use of highly-tunable double quantum dot devices we achieve an energy resolution allowing us to resolve the lifting of the fourfold spin and valley degeneracy by a Kane-Mele type spin-orbit coupling of ≈ 60 μeV. Furthermore, we find an upper limit of a potentially disorder-induced mixing of the $$K$$ K and $$K^{\prime}$$ K ′ states below 20 μeV.

3D topological quantum computing

In this paper, we will present some ideas to use 3D topology for quantum computing extending ideas from a previous paper. Topological quantum computing used “knotted” quantum states of topological phases of matter, called anyons. But anyons are connected with surface topology. But surfaces have (usually) abelian fundamental groups and therefore one needs non-Abelian anyons to use it for quantum computing. But usual materials are 3D objects which can admit more complicated topologies. Here, complements of knots do play a prominent role and are in principle the main parts to understand 3-manifold topology. For that purpose, we will construct a quantum system on the complements of a knot in the 3-sphere (see T. Asselmeyer-Maluga, Quantum Rep. 3 (2021) 153, arXiv:2102.04452 for previous work). The whole system is designed as knotted superconductor, where every crossing is a Josephson junction and the qubit is realized as flux qubit. We discuss the properties of this systems in particular the fluxion quantization by using the A-polynomial of the knot. Furthermore, we showed that 2-qubit operations can be realized by linked (knotted) superconductors again coupled via a Josephson junction.

Logical-qubit operations in an error-detecting surface code

Future fault-tolerant quantum computers will require storing and processing quantum data in logical qubits. We realize a suite of logical operations on a distance-two logical qubit stabilized using repeated error detection cycles. Logical operations include initialization into arbitrary states, measurement in the cardinal bases of the Bloch sphere, and a universal set of single-qubit gates. For each type of operation, we observe higher performance for fault-tolerant variants over non-fault-tolerant variants, and quantify the difference through detailed characterization. In particular, we demonstrate process tomography of logical gates, using the notion of a logical Pauli transfer matrix. This integration of high-fidelity logical operations with a scalable scheme for repeated stabilization is a milestone on the road to quantum error correction with higher-distance superconducting surface codes.

Leakage reduction in fast superconducting qubit gates via optimal control

Reaching high-speed, high-fidelity qubit operations requires precise control over the shape of the underlying pulses. For weakly anharmonic systems, such as superconducting transmon qubits, short gates lead to leakage to states outside of the computational subspace. Control pulses designed with open-loop optimal control may reduce such leakage. However, model inaccuracies can severely limit the usability of such pulses. We implemented a closed-loop optimization that simultaneously adapts all control parameters based on measurements of a cost function built from Clifford gates. We directly optimize the amplitude and phase of each sample point of the digitized control pulse. We thereby fully exploit the capabilities of the pulse generation electronics and create a 4.16 ns single-qubit pulse with 99.76 % fidelity and 0.044 % leakage. This is a sevenfold reduction of the leakage rate and a threefold reduction in standard errors of the best DRAG pulse we have calibrated at such short durations on the same system.

Circulator function in a Josephson junction circuit and braiding of Majorana zero modes

We propose a scheme for the circulator function in a superconducting circuit consisting of a three-Josephson junction loop and a trijunction. In this study we obtain the exact Lagrangian of the system by deriving the effective potential from the fundamental boundary conditions. We subsequently show that we can selectively choose the direction of current flowing through the branches connected at the trijunction, which performs a circulator function. Further, we use this circulator function for a non-Abelian braiding of Majorana zero modes (MZMs). In the branches of the system we introduce pairs of MZMs which interact with each other through the phases of trijunction. The circulator function determines the phases of the trijunction and thus the coupling between the MZMs to gives rise to the braiding operation. We modify the system so that MZMs might be coupled to the external ones to perform qubit operations in a scalable design.