The Solovay-Kitaev theorem allows us to approximate any single-qubit gate to arbitrary accuracy with a finite sequence of fundamental operations from a universal set of gates. Inspired by this decomposition, we present a quantum channel simulator capable of implementing any completely positive trace-preserving map. Our realization consists of one ancillary qubit, encoded in the transverse mode of a laser beam (orbital degree of freedom), one qubit system, encoded in its polarization (spin), one spin-orbit CNOT gate and four single-qubit operations performed with prisms and polarization components. Our results describe the implementation of arbitrary single-qubit channels on the photon polarization using the transverse mode as the ancillary qubit.
High-Fidelity Universal Quantum Gate Compilation for Non-semisimple Ising Anyons via Genetic Algorithm-Optimized Solovay-Kitaev Decomposition
School of Physics and Optoelectronics, Xiangtan University（湘潭大学物理与光电工程学院）；School of Physics and Electronic Science, Hunan Institute of Science and Technology（湖南理工学院物理与电子科学学院）；Center for Quantum Science and Technology, Department of Physics, Shanghai University（上海大学物理学部量子科学与技术中心）
The Solovay-Kitaev algorithm is a fundamental result in quantum computation. It gives an algorithm for efficiently compiling arbitrary unitaries using universal gate sets: any unitary can be approximated by short gates sequences, whose length scales merely poly-logarithmically with accuracy. As a consequence, the choice of gate set is typically unimportant in quantum computing. However, the Solovay-Kitaev algorithm requires the gate set to be inverse-closed. It has been a longstanding open question if efficient algorithmic compilation is possible without this condition. In this work, we provid…
Numerical Evaluation of ZX Calculus Optimization for Solovay Kitaev Quantum Circuit Synthesis
University of Colombo（科伦坡大学）；The University of Western Australia（西澳大学）；University Paris City and University of Reunion（巴黎城市大学与留尼汪大学）；PEACCEL, AI for Biologics（PEACCEL生物制剂人工智能）
We investigate the energy-constrained (EC) diamond norm distance between unitary channels acting on possibly infinite-dimensional quantum systems, and establish a number of results. Firstly, we prove that optimal EC discrimination between two unitary channels does not require the use of any entanglement. Extending a result by Acín, we also show that a finite number of parallel queries suffices to achieve zero error discrimination even in this EC setting. Secondly, we employ EC diamond norms to study a novel type of quantum speed limits, which apply to pairs of quantum dynamical semigroups. We …
The Gottesman-Kitaev-Preskill encoding of a qubit in a harmonic oscillator is a promising building block towards fault-tolerant quantum computation. Recently, this encoding was experimentally demonstrated for the first time in trapped-ion and superconducting circuit systems. However, these systems lack some of the Gaussian operations which are critical to efficiently manipulate the encoded qubits. In particular, homodyne detection, which is the preferred method for readout of the encoded qubit, is not readily available, heavily limiting the readout fidelity. Here, we present an alternative rea…
Quantum resource theories are a powerful framework to characterize and quantify relevant quantum phenomena and identify processes that optimize their use for different tasks. Here, we define a resource measure for magic, the sought-after property in most fault-tolerant quantum computers. In contrast to previous literature, our formulation is based on bosonic codes, well-studied tools in continuous-variable quantum computation. Particularly, we use the Gottesman-Kitaev-Preskill code to represent multi-qubit states and consider the resource theory for the Wigner negativity. Our techniques are us…
Gottesman-Kitaev-Preskill (GKP) qubit is a promising ingredient for fault-tolerant quantum computation (FTQC) in optical continuous variables due to its advantage of noise tolerance and scalability. However, one of the main problems in the preparation of the optical GKP qubit is the difficulty in obtaining the nonlinearity. Cross-Kerr interaction is one of the promising candidates for this nonlinearity. There is no existing scheme to use the cross-Kerr interaction to generate the optical GKP qubit for FTQC. In this work, we propose a generation method of the GKP qubit by using a cross-Kerr int…
We study the Chern-Simons approach to the topological quantum computing. We use quantum $\mathcal{R}$-matrices as universal quantum gates and study the approximations of some one-qubit operations. We make some modifications to the known Solovay-Kitaev algorithm suitable for our particular problem.
Graph states are a central resource in measurement-based quantum information processing. In the photonic qubit architecture based on Gottesman-Kitaev-Preskill (GKP) encoding, the generation of high-fidelity graph states composed of realistic, finite-energy approximate GKP-encoded qubits thus constitutes a key task. We consider the finite-energy approximation of GKP qubit states given by a coherent superposition of shifted finite-squeezed vacuum states, where the displacements are Gaussian distributed. We present an exact description of graph states composed of such approximate GKP qubits as a …
The Gottesman-Kitaev-Preskill (GKP) encoding of a qubit into a bosonic mode is a promising bosonic code for quantum computation due to its tolerance for noise and all-Gaussian gate set. We present a toolkit for phase-space description and manipulation of GKP encodings that includes Wigner functions for ideal and approximate GKP states, for various types of mixed GKP states, and for GKP-encoded operators. One advantage of a phase-space approach is that Gaussian unitaries, required for computation with GKP codes, correspond to simple transformations on the arguments of Wigner functions. We use t…
We introduce a new approach to Gottesman-Kitaev-Preskill (GKP) states that treats their finite-energy version in an exact manner. Based on this analysis, we develop new qubit-oscillator circuits that autonomously stabilize a GKP manifold, correcting errors without relying on qubit measurements. Finally, we show numerically that logical information encoded in GKP states is very robust against typical oscillator noise sources when stabilized by these new circuits.
Quantum repeaters are a promising platform for realizing long-distance quantum communication and thus could form the backbone of a secure quantum internet, a scalable quantum network, or a distributed quantum computer. Repeater protocols that encode information in single- or multi-photon states are limited by transmission losses and the cost of implementing entangling gates or Bell measurements. In this work, we consider implementing a quantum repeater protocol using Gottesman-Kitaev-Preskill (GKP) qubits. These qubits are natural elements for quantum repeater protocols, because they allow for…
Nies and Scholz defined quantum Martin-Löf randomness (q-MLR) for states (infinite qubitstrings). We define a notion of quantum Solovay randomness and show it to be equivalent to q-MLR using purely linear algebraic methods. Quantum Schnorr randomness is then introduced. A quantum analogue of the law of large numbers is shown to hold for quantum Schnorr random states. We introduce quantum-K, ($QK$) a measure of the descriptive complexity of density matrices using classical prefix-free Turing machines and show that the initial segments of weak Solovay random and quantum Schnorr random states are…
Modeling Logical Gates and Read-Out of Superconducting Gottesman-Kitaev-Preskill Qubits
ARC Centre of Excellence for Engineered Quantum Systems, School of Physics, The University of Sydney（悉尼大学工程量子系统卓越研究中心物理学院）；QuTech, Delft University of Technology（代尔夫特理工大学QuTech）；Faculty of EEMCS, Delft University of Technology（代尔夫特理工大学EEMCS学院）；AWS Center for Quantum Computing（亚马逊云科技量子计算中心）；California Institute of Technology（加州理工学院）
Robust Spin Qubit Coupler via Minimal Kitaev Chain
Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Beijing Key Laboratory of Quantum Devices and School of Electronics, Peking University（北京大学电子学院）
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 …
Remote Gottesman-Kitaev-Preskill Entanglement Generation between Trapped Ions
School of Mathematical and Physical Sciences, Keio University（庆应义塾大学数理科学学院）；Department of Electronics and Electrical Engineering, Keio University（庆应义塾大学电子电气工程系）；Advanced ICT Research Institute, National Institute of Information and Communications Technology (NICT)（信息通信研究机构高级ICT研究所）
Topological quantum computation based on anyons is a promising approach to achieve fault-tolerant quantum computing. The Majorana zero modes in the Kitaev chain are an example of non-Abelian anyons where braiding operations can be used to perform quantum gates. Here we perform a quantum simulation of topological quantum computing, by teleporting a qubit encoded in the Majorana zero modes of a Kitaev chain. The quantum simulation is performed by mapping the Kitaev chain to its equivalent spin version, and realizing the ground states in a superconducting quantum processor. The teleportation tran…
In this work, we study the Wigner phase-space representation of qubit states encoded in continuous variables (CV) by using the Gottesman-Kitaev-Preskill (GKP) mapping. We explore a possible connection between resources for universal quantum computation in discrete-variable (DV) systems, i.e. non-stabilizer states, and negativity of the Wigner function in CV architectures, which is a necessary requirement for quantum advantage. In particular, we show that the lowest Wigner logarithmic negativity of qubit states encoded in CV with the GKP mapping corresponds to encoded stabilizer states, while t…
Simulation of depolarizing channel exploring maximally non separable spin-orbit mode
Universidade Federal Fluminense（弗鲁米嫩塞联邦大学）；Instituto Federal de Educação, Ciência e Tecnologia do Paraná（巴拉那联邦教育、科学和技术学院）；Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；Instituto Federal de Educação, Ciência e Tecnologia do Rio de Janeiro - IFRJ（里约热内卢联邦教育、科学和技术学院）
The Gottesman-Kitaev-Preskill (GKP) encoding of a qubit within an oscillator is particularly appealing for fault-tolerant quantum computing with bosons because Gaussian operations on encoded Pauli eigenstates enable Clifford quantum computing with error correction. We show that applying GKP error correction to Gaussian input states, such as vacuum, produces distillable magic states, achieving universality without additional non-Gaussian elements. Fault tolerance is possible with sufficient squeezing and low enough external noise. Thus, Gaussian operations are sufficient for fault-tolerant, uni…
