Efficient Decomposition of Unitary Matrices in Quantum Circuit Compilers

Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for the translation of bigger unitary gates into elementary quantum operations, which is key to executing these algorithms on existing quantum computers. The decomposition can be used as an aggressive optimization method for the whole circuit, as well as to test part of an algorithm on a quantum accelerator. For the selection and implementation of the decomposition algorithm, perfect qubits are assumed. We base our decomposition technique on Quantum Shannon Decomposition, which generates O(344n) controlled-not gates for an n-qubit input gate. In addition, we implement optimizations to take advantage of the potential underlying structure in the input or intermediate matrices, as well as to minimize the execution time of the decomposition. Comparing our implementation to Qubiter and the UniversalQCompiler (UQC), we show that our implementation generates circuits that are much shorter than those of Qubiter and not much longer than the UQC. At the same time, it is also up to 10 times as fast as Qubiter and about 500 times as fast as the UQC.

Simulating of X-states and the two-qubit XYZ Heisenberg system on IBM quantum computer

Two qubit density matrices which are of X-shape, are a natural generalization of Bell Diagonal States (BDSs) recently simulated on the IBM quantum device. We generalize the previous results and propose a quantum circuit for simulation of a general two qubit X-state, implement it on the same quantum device, and study its entanglement for several values of the extended parameter space. We also show that their X-shape is approximately robust against noisy quantum gates. To further physically motivate this study, we invoke the two-spin Heisenberg XYZ system and show that for a wide class of initial states, it leads to dynamical density matrices which are X-states. Due to the symmetries of this Hamiltonian, we show that by only two qubits, one can simulate the dynamics of this system on the IBM quantum computer.

High-fidelity quantum gates for OAM single qudits on quantum memory

The application of high-dimensional quantum systems (qudits) in quantum computing and communications seems to be a promising avenue due to the possibility of increasing the amount of information encoded in one physical carrier. In this work, we propose a method for implementing single-qudit gates for qudits based on light modes with orbital angular momentum (OAM). Method for logical qudits encoding, which ensures the quasi-cyclicity of operations, is introduced. Based on the protocol for converting the OAM of light in the Raman quantum memory scheme (Vashukevich et al 2020 Phys. Rev. A 101 033830), we show that the considered gates provide an extremely high level of fidelity of single-qudit transformations. We also compare quantum gates’ properties for systems of different dimensions and find the optimal conditions for carrying out transformations in the protocol under consideration.

Many-Objective Quantum-Inspired Particle Swarm Optimization Algorithm for Placement of Virtual Machines in Smart Computing Cloud

Particle swarm optimization algorithm (PSO) is an effective metaheuristic that can determine Pareto-optimal solutions. We propose an extended PSO by introducing quantum gates in order to ensure the diversity of particle populations that are looking for efficient alternatives. The quality of solutions was verified in the issue of assignment of resources in the computing cloud to improve the live migration of virtual machines. We consider the multi-criteria optimization problem of deep learning-based models embedded into virtual machines. Computing clouds with deep learning agents can support several areas of education, smart city or economy. Because deep learning agents require lots of computer resources, seven criteria are studied such as electric power of hosts, reliability of cloud, CPU workload of the bottleneck host, communication capacity of the critical node, a free RAM capacity of the most loaded memory, a free disc memory capacity of the most busy storage, and overall computer costs. Quantum gates modify an accepted position for the current location of a particle. To verify the above concept, various simulations have been carried out on the laboratory cloud based on the OpenStack platform. Numerical experiments have confirmed that multi-objective quantum-inspired particle swarm optimization algorithm provides better solutions than the other metaheuristics.

Dynamical second-order noise sweetspots in resonantly driven spin qubits

Quantum dot-based quantum computation employs extensively the exchange interaction between nearby electronic spins in order to manipulate and couple different qubits. The exchange interaction, however, couples the qubit states to charge noise, which reduces the fidelity of the quantum gates that employ it. The effect of charge noise can be mitigated by working at noise sweetspots in which the sensitivity to charge variations is reduced. In this work we study the response to charge noise of a double quantum dot based qubit in the presence of ac gates, with arbitrary driving amplitudes, applied either to the dot levels or to the tunneling barrier. Tuning with an ac driving allows to manipulate the sign and strength of the exchange interaction as well as its coupling to environmental electric noise. Moreover, we show the possibility of inducing a second-order sweetspot in the resonant spin-triplet qubit in which the dephasing time is significantly increased.

Robustly decorrelating errors with mixed quantum gates

Coherent errors in quantum operations are ubiquitous. Whether arising from spurious environmental couplings or errors in control fields, such errors can accumulate rapidly and degrade the performance of a quantum circuit significantly more than an average gate fidelity may indicate. As shown by Hastings [1] and Campbell [2], by replacing the deterministic implementation of a quantum gate with a randomized ensemble of implementations, one can dramatically suppress coherent errors. Our work begins by reformulating the results of Hastings and Campbell as a quantum optimal control problem. We then discuss a family of convex programs able to solve this problem, as well as a set of secondary objectives designed to improve the performance, implementability, and robustness of the resulting mixed quantum gates. Finally, we implement these mixed quantum gates on a superconducting qubit and discuss randomized benchmarking results consistent with a marked reduction in the coherent error. [1] M. B. Hastings, Quantum Information & Computation 17, 488 (2017). [2] E. Campbell, Physical Review A 95, 042306 (2017).

Introduction to Quantum Gates : Implementation of Single and Multiple Qubit Gates

A quantum gate or quantum logic gate is an elementary quantum circuit working on a small number of qubits. It means that quantum gates can grasp two primary feature of quantum mechanics that are entirely out of reach for classical gates : superposition and entanglement. In simpler words quantum gates are reversible. In classical computing sets of logic gates are connected to construct digital circuits. Similarly, quantum logic gates operates on input states that are generally in superposition states to compute the output. In this paper the authors will discuss in detail what is single and multiple qubit gates and scope and challenges in quantum gates.