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A method for compiling quantum algorithms into specific braiding patterns for non-Abelian quasiparticles described by the so-called Fibonacci anyon model is developed. The method is based on the observation that a universal set of quantum gates acting on qubits encoded using triplets of these quasiparticles can be built entirely out of three-stranded braids (three-braids). These three-braids can then be efficiently compiled and improved to any required accuracy using the Solovay-Kitaev algorithm.
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Topological pumping and duality transformations are paradigmatic concepts in condensed matter and statistical mechanics. In this paper, we extend the concept of topological pumping of particles to topological pumping of quantum correlations. We propose a scheme to find pumping protocols for highly-correlated states by mapping them to uncorrelated ones. We show that one way to achieve this is to use dualities, because they are non-local transformations that preserve the topological properties of the system. By using them, we demonstrate that topological pumping of kinks and cluster-like excitations can be realized. We find that the entanglement of these highly-correlated excitations is strongly modified during the pumping process and the interactions enhance the robustness against disorder. Our work paves the way to explore topological pumping beyond the notion of particles and opens a new avenue to investigate the relation between correlations and topology.
The architecture of circuital quantum computers requires computing layers devoted to compiling high-level quantum algorithms into lower-level circuits of quantum gates. The general problem of quantum compiling is to approximate any unitary transformation that describes the quantum computation, as a sequence of elements selected from a finite base of universal quantum gates. The existence of an approximating sequence of one qubit quantum gates is guaranteed by the Solovay-Kitaev theorem, which implies sub-optimal algorithms to establish it explicitly. Since a unitary transformation may require significantly different gate sequences, depending on the base considered, such a problem is of great complexity and does not admit an efficient approximating algorithm. Therefore, traditional approaches are time-consuming tasks, unsuitable to be employed during quantum computation. We exploit the deep reinforcement learning method as an alternative strategy, which has a significantly different trade-off between search time and exploitation time. Deep reinforcement learning allows creating single-qubit operations in real time, after an arbitrary long training period during which a strategy for creating sequences to approximate unitary operators is built. The deep reinforcement learning based compiling method allows for fast computation times, which could in principle be exploited for real-time quantum compiling.
A two-component fermion model with conventional two-body interactions was recently shown to have anyonic excitations. We here propose a scheme to physically implement this model by transforming each chain of two two-component fermions to the two capacitively coupled chains of superconducting devices. In particular, we elaborate how to achieve the wanted operations to create and manipulate the topological quantum states, providing an experimentally feasible scenario to access the topological memory and to build the anyonic interferometry.
Read-Rezayi fractional quantum Hall states are among the prime candidates for realizing non-Abelian anyons which in principle can be used for topological quantum computation. We present a prescription for efficiently finding braids which can be used to carry out a universal set of quantum gates on encoded qubits based on anyons of the Read-Rezayi states with $k>2$, $k eq4$. This work extends previous results which only applied to the case $k = 3$ (Fibonacci) and clarifies why in that case gate constructions are simpler than for a generic Read-Rezayi state.
Quantum compiling aims to construct a quantum circuit V by quantum gates drawn from a native gate alphabet, which is functionally equivalent to the target unitary U. It is a crucial stage for the running of quantum algorithms on noisy intermediate-scale quantum (NISQ) devices. However, the space for structure exploration of quantum circuit is enormous, resulting in the requirement of human expertise, hundreds of experimentations or modifications from existing quantum circuits. In this paper, we propose a variational quantum compiling (VQC) algorithm based on reinforcement learning (RL), in order to automatically design the structure of quantum circuit for VQC with no human intervention. An agent is trained to sequentially select quantum gates from the native gate alphabet and the qubits they act on by double Q-learning with epsilon-greedy exploration strategy and experience replay. At first, the agent randomly explores a number of quantum circuits with different structures, and then iteratively discovers structures with higher performance on the learning task. Simulation results show that the proposed method can make exact compilations with less quantum gates compared to previous VQC algorithms. It can reduce the errors of quantum algorithms due to decoherence process and gate noise in NISQ devices, and enable quantum algorithms especially for complex algorithms to be executed within coherence time.
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