Demonstration of two-dimensional connectivity for a scalable error-corrected ion-trap quantum processor architecture
Marco Valentini, Martin W. van Mourik, Friederike Butt, Jakob Wahl, Matthias Dietl, Michael Pfeifer, Fabian Anmasser, Yves Colombe, Clemens Rössler, Philip Holz… 展开作者
Marco Valentini, Martin W. van Mourik, Friederike Butt, Jakob Wahl, Matthias Dietl, Michael Pfeifer, Fabian Anmasser, Yves Colombe, Clemens Rössler, Philip Holz, Rainer Blatt, Alejandro Bermudez, Markus Müller, Thomas Monz, Philipp Schindler
备注：
35 pages, 27 figures (19 in main text, 8 in appendices), 6 appendices
构建大规模量子计算机的主要障碍是在增加量子比特数量的同时保持它们之间的连通性。在离子阱设备中，这种连通性可以通过在处理器上移动由几个离子组成的子寄存器来实现。本文聚焦于一种称为量子弹簧阵列（Quantum Spring Array，QSA）的架构，该架构基于离子线性串的矩形二维晶格。相邻离子串之间的连通性可以通过调整它们的间距来控制，这需要沿两个方向控制俘获势：一个沿离子串的轴线方向，另一个沿其径向方向。本研究中，我们沿这两个方向研究了QSA架构的关键元素：我们发现相邻晶格位点之间的耦合速率随每位点离子数量的增加而提高，且耦合系统的运动对电噪声具有韧性，这两者都是快速、高保真量子门操作的关键要求。我们评估了耦合的相干性，并演示了径向分离俘获区域中存储的量子比特之间的纠缠门；此外，我们演示了通过控制射频信号来调整离子串之间的径向间距，从而调整耦合速率；我们还提出了并行化横向门操作的实现构造，并将QSA架构映射到容错量子纠错的代码原语，为迈向优化大规模操作的量子处理器架构迈出了一步。
英文摘要：
A major hurdle for building a large-scale quantum computer is increasing the number of qubits while maintaining connectivity between them. In trapped-ion devices, this connectivity can be achieved by moving subregisters consisting of a few ions across the processor. Here, we focus on an architecture, which we refer to as the Quantum Spring Array (QSA), that is based on a rectangular two-dimensional lattice of linear strings of ions. Connectivity between adjacent ion strings can be controlled by adjusting their separation. This requires control of trapping potentials along two directions, one along the axis of the ion string and one radial to it. In this work, we investigate key elements of the QSA architecture along both directions: We show that the coupling rate between neighboring lattice sites increases with the number of ions per site and the motion of the coupled system can be resilient to electrical noise, both being key requisites for fast and high-fidelity quantum gate operations. The coherence of the coupling is assessed and an entangling gate between qubits stored in radially separated trapping regions is demonstrated. Moreover, we demonstrate control over radio-frequency signals to adjust the radial separation, and thus the coupling rate, between strings. We further present constructions for the implementation of parallelized, transversal gate operations, and map the QSA architecture to code primitives for fault-tolerant quantum error correction, providing a step towards a quantum processor architecture that is optimized for large-scale operation.
Quantum simulation of complex quantum systems and their properties often requires the ability to prepare initial states in an eigenstate of the Hamiltonian to be simulated. In addition, to compute the eigenvalues of a Hamiltonian is in general a non-trivial problem. Here, we propose a hybrid quantum-classical probabilistic method to compute eigenvalues and prepare eigenstates of Hamiltonians which are simulatable with a trapped-ion quantum processor.
We investigate theoretically the speed limit of quantum gate operations for ion trap quantum information processors. The proposed methods use laser pulses for quantum gates which entangle the electronic and vibrational degrees of freedom of the trapped ions. Two of these methods are studied in detail and for both of them the speed is limited by a combination of the recoil frequency of the relevant electronic transition, and the vibrational frequency in the trap. We have experimentally studied the gate operations below and above this speed limit. In the latter case, the fidelity is reduced, in …
A quantitative assessment of the progress of small prototype quantum processors towards fault-tolerant quantum computation is a problem of current interest in experimental and theoretical quantum information science. We introduce a necessary and fair criterion for quantum error correction (QEC), which must be achieved in the development of these quantum processors before their sizes are sufficiently big to consider the well-known QEC threshold. We apply this criterion to benchmark the ongoing effort in implementing QEC with topological color codes using trapped-ion quantum processors and, more…
Two techniques are described that simplify the experimental requirements for measuring and manipulating quantum information stored in trapped ions. The first is a new technique using electron shelving to measure the populations of the Zeeman sublevels of the ground state, in an ion for which no cycling transition exists from any of these sublevels. The second technique is laser cooling to the vibrational ground state, without the need for a trap operating in the Lamb-Dicke limit. This requires sideband cooling in a sub-recoil regime. We present a thorough analysis of sideband cooling on one or…
Quantum computers hold the promise to solve certain problems exponentially faster than their classical counterparts. Trapped atomic ions are among the physical systems in which building such a computing device seems viable. In this work we present a small-scale quantum information processor based on a string of $^{40}$Ca${^+}$ ions confined in a macroscopic linear Paul trap. We review our set of operations which includes non-coherent operations allowing us to realize arbitrary Markovian processes. In order to build a larger quantum information processor it is mandatory to reduce the error rate…
Error-Corrected Memory and Logic on a Heavy-Hex Superconducting-Qubit Processor
The University of Sydney（悉尼大学）；Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Sungkyunkwan University（成均馆大学）；IBM Quantum, T. J. Watson Research Center（IBM量子T.J.沃森研究中心）；IBM Denmark（IBM丹麦）
So far, only the results on 3 qubit spaces (both on superconducting and ion-trap realisations of quantum processors) have beaten the classical unstructured search in the expected number of oracle calls using optimal protocols in both settings. We present experimental results on running unstructured search in spaces defined by 4, 5 and 6 qubits on ion-trapped quantum processor. Our best circuits obtained respectively 66\%, 26\% and 6\% average probability of measuring the marked element. In the case of 4 and 5 qubit spaces we obtained fewer expected number of oracle calls required to find a mar…
An introductory review of the linear ion trap is given, with particular regard to its use for quantum information processing. The discussion aims to bring together ideas from information theory and experimental ion trapping, to provide a resource to workers unfamiliar with one or the other of these subjects. It is shown that information theory provides valuable concepts for the experimental use of ion traps, especially error correction, and conversely the ion trap provides a valuable link between information theory and physics, with attendant physical insights. Example parameters are given for…
Large-scale quantum computers will require quantum gate operations between widely separated qubits. A method for implementing such operations, known as quantum gate teleportation (QGT), requires only local operations, classical communication, and shared entanglement. We demonstrate QGT in a scalable architecture by deterministically teleporting a controlled-NOT (CNOT) gate between two qubits in spatially separated locations in an ion trap. The entanglement fidelity of our teleported CNOT is in the interval [0.845, 0.872] at the 95% confidence level. The implementation combines ion shuttling wi…
In this tutorial we review physical implementation of quantum computing using a system of cold trapped ions. We discuss systematically all the aspects for making the implementation possible. Firstly, we go through the loading and confining of atomic ions in the linear Paul trap, then we describe the collective vibrational motion of trapped ions. Further, we discuss interactions of the ions with a laser beam. We treat the interactions in the travelling-wave and standing-wave configuration for dipole and quadrupole transitions. We review different types of laser cooling techniques associated wit…
Using optical Ramsey interferometry, we precisely measure the laser-induced AC-stark shift on the $S_{1/2}$ -- $D_{5/2}$ "quantum bit" transition near 729 nm in a single trapped $^{40}$Ca$^+$ ion. We cancel this shift using an additional laser field. This technique is of particular importance for the implementation of quantum information processing with cold trapped ions. As a simple application we measure the atomic phase evolution during a $n \times 2π$ rotation of the quantum bit.
Active quantum error correction has been identified as a crucial ingredient of future quantum computers, motivating the recent experimental efforts to encode logical quantum bits using small topological codes. In addition to the demonstration of the beneficial role of the encoding, a break-even point in the progress towards large-scale quantum computers will be the implementation of a universal set of gates. This mid-term challenge will soon be faced by various quantum technologies, which urges the need of realistic assessments of their prospects. In this work, we pursue this goal by assessing…
Scalable suppression of heating errors in large trapped-ion quantum processors
Center on Frontiers of Computing Studies, School of Computer Science, Peking University（北京大学计算机学院前沿计算研究中心）；Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University（华南师范大学物理学院原子与亚原子结构及量子控制教育部重点实验室、广东省物质结构与基本相互作用卓越基础研究基地）；Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University（华南师范大学前沿物理研究院广东量子工程与量子材料重点实验室、粤港澳量子物质联合实验室）
Quantum information processing offers dramatic speedups, yet is famously susceptible to decoherence, the process whereby quantum superpositions decay into mutually exclusive classical alternatives, thus robbing quantum computers of their power. This has made the development of quantum error correction an essential and inescapable aspect of both theoretical and experimental quantum computing. So far little is known about protection against decoherence in the context of quantum annealing, a computational paradigm which aims to exploit ground state quantum dynamics to solve optimization problems …
We report a proof-of-principle experimental demonstration of the quantum speed-up for learning agents utilizing a small-scale quantum information processor based on radiofrequency-driven trapped ions. The decision-making process of a quantum learning agent within the projective simulation paradigm for machine learning is implemented in a system of two qubits. The latter are realized using hyperfine states of two frequency-addressed atomic ions exposed to a static magnetic field gradient. We show that the deliberation time of this quantum learning agent is quadratically improved with respect to…
Revealing Noise in Axial Motion Through Quantum Noise Spectroscopy on a Trapped Ion Processor
Johns Hopkins University Applied Physics Laboratory（约翰斯·霍普金斯大学应用物理实验室）；HRL Laboratories, LLC（HRL实验室有限责任公司）；Sandia National Laboratories（桑迪亚国家实验室）；Department of Physics and Astronomy, University of New Mexico（新墨西哥大学物理与天文系）；Center for Quantum Information and Control, CQuIC, University of New Mexico（新墨西哥大学量子信息与控制中心）；Quantinuum；Johns Hopkins University（约翰斯·霍普金斯大学）
The quest of demonstrating beneficial quantum error correction in near-term noisy quantum processors can benefit enormously from a low-resource optimization of fault-tolerant schemes, which are specially designed for a particular platform considering both state-of-the-art technological capabilities and main sources of noise. In this work, we show that flag-qubit-based fault-tolerant techniques for active error detection and correction, as well as for encoding of logical qubits, can be leveraged in current designs of trapped-ion quantum processors to achieve this break-even point of beneficial …
The performance of quantum gate operations is experimentally determined by how correct operational parameters can be determined and set, and how stable these parameters can be maintained. In addition, gates acting on different sets of qubits require unique sets of control parameters. Thus, an efficient multi-dimensional parameter estimation procedure is crucial to calibrate even medium sized quantum processors. Here, we develop and characterize an efficient calibration protocol to automatically estimate and adjust experimental parameters of the widely used Molmer-Sorensen entangling gate opera…
We develop holographic quantum simulation techniques to prepare correlated electronic ground states in quantum matrix product state (qMPS) form, using far fewer qubits than the number of orbitals represented. Our approach starts with a holographic technique to prepare a compressed approximation to electronic mean-field ground-states, known as fermionic Gaussian matrix product states (GMPS), with a polynomial reduction in qubit- and (in select cases gate-) resources compared to existing techniques. Correlations are then introduced by augmenting the GMPS circuits in a variational technique which…
Several errors in Refs. [1, 2] are corrected related to the optical trapping potentials for a state-insensitive, compensated nanofiber trap for the D2 transition of atomic Cesium. Section I corrects our basic formalism in Ref. [1] for calculating dipole-force potentials. Section II corrects erroneous values for a partial lifetime and a transition wavelength in Ref. [1]. Sections III and IV present corrected figures for various trapping configurations considered in Refs. [1] and [2], respectively.
We propose a new design for a quantum information processor where qubits are encoded into Hyperfine states of ions held in a linear array of individually tailored microtraps and sitting in a spatially varying magnetic field. The magnetic field gradient introduces spatially dependent qubit transition frequencies and a type of spin-spin interaction between qubits. Single and multi-qubit manipulation is achieved via resonant microwave pulses as in liquid-NMR quantum computation while the qubit readout and reset is achieved through trapped-ion fluorescence shelving techniques. By adjusting the mic…
A quantum information processor is proposed that combines experimental techniques and technology successfully demonstrated either in nuclear magnetic resonance experiments or with trapped ions. An additional inhomogenenous magnetic field applied to an ion trap i) shifts individual ionic resonances (qubits), making them distinguishable by frequency, and, ii) mediates the coupling between internal and external degrees of freedom of trapped ions. This scheme permits one to individually address and coherently manipulate ions confined in an electrodynamic trap using radiation in the radiofrequency …
Quantum gates in experiment are inherently prone to errors that need to be characterized before they can be corrected. Full characterization via quantum process tomography is impractical and often unnecessary. For most practical purposes, it is enough to estimate more general quantities such as the average fidelity. Here we use a unitary 2-design and twirling protocol for efficiently estimating the average fidelity of Clifford gates, to certify a 7-qubit entangling gate in a nuclear magnetic resonance quantum processor. Compared with more than $10^8$ experiments required by full process tomogr…
