Suppressing quantum errors by scaling a surface code logical qubit

Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical qubits, where increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low in order for logical performance to improve with increasing code size. Here, we report the measurement of logical qubit performance scaling across multiple code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, both in terms of logical error probability over 25 cycles and logical error per cycle ($2.914\%\pm 0.016\%$ compared to $3.028\%\pm 0.023\%$). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a $1.7\times10^{-6}$ logical error per round floor set by a single high-energy event ($1.6\times10^{-7}$ when excluding this event). We are able to accurately model our experiment, and from this model we can extract error budgets that highlight the biggest challenges for future systems. These results mark the first experimental demonstration where quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation.Comment: Main text: 6 pages, 4 figures. v2: Update author list, references, Fig. S12, Table I

Measurement-induced entanglement and teleportation on a noisy quantum processor

Measurement has a special role in quantum theory: by collapsing the wavefunction it can enable phenomena such as teleportation and thereby alter the "arrow of time" that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space-time that go beyond established paradigms for characterizing phases, either in or out of equilibrium. On present-day NISQ processors, the experimental realization of this physics is challenging due to noise, hardware limitations, and the stochastic nature of quantum measurement. Here we address each of these experimental challenges and investigate measurement-induced quantum information phases on up to 70 superconducting qubits. By leveraging the interchangeability of space and time, we use a duality mapping, to avoid mid-circuit measurement and access different manifestations of the underlying phases -- from entanglement scaling to measurement-induced teleportation -- in a unified way. We obtain finite-size signatures of a phase transition with a decoding protocol that correlates the experimental measurement record with classical simulation data. The phases display sharply different sensitivity to noise, which we exploit to turn an inherent hardware limitation into a useful diagnostic. Our work demonstrates an approach to realize measurement-induced physics at scales that are at the limits of current NISQ processors

Non-Abelian braiding of graph vertices in a superconducting processor

Indistinguishability of particles is a fundamental principle of quantum mechanics. For all elementary and quasiparticles observed to date - including fermions, bosons, and Abelian anyons - this principle guarantees that the braiding of identical particles leaves the system unchanged. However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions. Hence, it can change the observables of the system without violating the principle of indistinguishability. Despite the well developed mathematical description of non-Abelian anyons and numerous theoretical proposals, the experimental observation of their exchange statistics has remained elusive for decades. Controllable many-body quantum states generated on quantum processors offer another path for exploring these fundamental phenomena. While efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasi-particles, superconducting quantum processors allow for directly manipulating the many-body wavefunction via unitary gates. Building on predictions that stabilizer codes can host projective non-Abelian Ising anyons, we implement a generalized stabilizer code and unitary protocol to create and braid them. This allows us to experimentally verify the fusion rules of the anyons and braid them to realize their statistics. We then study the prospect of employing the anyons for quantum computation and utilize braiding to create an entangled state of anyons encoding three logical qubits. Our work provides new insights about non-Abelian braiding and - through the future inclusion of error correction to achieve topological protection - could open a path toward fault-tolerant quantum computing

New Family of Six Stable Metals with a Nearly Isotropic Triangular Lattice of Organic Radical Cations and Diluted Paramagnetic System of Anions: κ(κ_⊥)‑(BDH-TTP)₄MX₄·Solv, where M = Co^II, Mn^II; X = Cl, Br, and Solv = (H₂O)₅, (CH₂X₂)

A new family of six paramagnetic metals, namely, κ-(BDH-TTP)₄­CoCl₄­·(H₂O)₅ (<b>I</b>), κ-(BDH-TTP)₄­Co_0.54Mn_0.46Cl₄­·(H₂O)₅ (<b>II</b>), κ-(BDH-TTP)₄­MnCl₄­·(H₂O)₅ (<b>III</b>), κ_⊥-(BDH-TTP)₄­CoBr₄­·(CH₂Cl₂) (<b>IV</b>), κ_⊥-(BDH-TTP)₄­MnBr₄­·(CH₂Cl₂) (<b>V</b>), and κ_⊥-(BDH-TTP)₄­MnBr₄­·(CH₂Br₂) (<b>VI</b>), has been synthesized and characterized by X-ray crystallography, four-probe conductivity measurements, SQUID magnetometry, and calculations of electronic structure. The newly discovered κ_⊥-type packing motif of organic layers differs from the parent κ-type by a series of longitudinal shifts of BDH-TTP radical cations in the crystal structure. Salts <b>I</b>–<b>VI</b> form two isostructural groups: <b>I</b>–<b>III</b> (κ) and <b>IV</b>–<b>VI</b> (κ_⊥). Salts <b>I</b>–<b>III</b> are isostructural to the previously discovered κ-(BDH-TTP)₂­Fe^IIIX₄ (X = Cl, Br) even though the charge of FeX₄^– anions is half that of the MX₄^2– (M = Co, Mn) anions. The tetrahedral anions are disordered in <b>I</b>–<b>III</b> but completely ordered in <b>IV</b>–<b>VI</b>. The type of included solvent molecule is solely determined by the anion size. The paramagnetic subsystem is effectively spin diluted either by anion disorder (<b>I</b>–<b>III</b>) or by spatial separation (<b>IV</b>–<b>VI</b>). The Weiss constants are virtually zero for all compounds (e.g., θ­(<b>III</b>) = 0.0056 K, θ­(<b>V</b>) = −0.076 K). Curie constants are dominated by anion paramagnetic centers indicating high spin states 5/2 for Mn^II and 3/2 for Co^II with large spin–orbital coupling. All compounds retain metallic properties down to 4.2 K. There is a magnetic breakdown gap of width (<i>w</i>) in the chiral salts <b>IV</b>–<b>VI</b>: <i>w</i>(<b>IV</b>) > <i>w</i>(<b>V</b>) ≈ <i>w</i>(<b>VI</b>) but no gap in the centrosymmetric salts <b>I</b>–<b>III</b>. Electronic structure calculations at room temperature revealed a nearly isotropic triangular lattice in <b>I</b>–<b>III</b> and a honeycomb lattice in <b>IV</b>–<b>VI</b> with an extreme geometric spin frustration exceeding the level reported for the quantum “spin liquid” κ-(BEDT-TTF)₂­Cu₂(CN)₃

Metal-insulator interplays rendered by lattice transformations and structural disorder in DOEO salts

Three salts, β-DOEONO(HO) (I), β″-DOEONO(HO) (II), and β″-DOEOHSO(HO) (III), have been synthesized and characterized by means of four-probe conductivity measurements from room temperature down to 4.2 K and X-ray single crystal analysis at room temperature and 100 K. Salt I shows dielectric properties below room temperature, and salts II and III are stable metals. The DOEO molecules in I-III are packed into organic (conductive) layers expanding along the ab plane. The layer packing in II and III is the same in the projection along the long molecular axis and is of the β″ type, but differs noticeably in the perpendicular direction. Salts I and II are not isostructural, but their structures are very similar. However, the electronic structures of II and III are very similar, which leads to quantitatively comparable conductivities for II and III. The upper bands of II and III are 1/4-filled, whereas strong dimerization and band splitting leads to effective 1/2-filling of the upper band in I, which predetermines stable metallic properties for the former and renders strong electronic correlations in the latter. A superstructure of I is formed at room temperature. The Fermi surface obtained by means of extended Hückel tight-binding (EHTB) calculations is essentially altered by the superstructure: Two parallel 1D chains instead of a set of 1D chains and closed 2D pockets visible on the substructure are realized. The Fermi surface of I consists of flattened sections that could be a source of nesting instability. In contrast, the appearance of a superstructure of II at 100 K does not alter the Fermi surface that significantly, leaving the 2D conduction system intact and the Fermi surface with enough curvature to be stable against nesting effects. The DOEO terminal ethylene groups are strongly disordered in I with position occupancies (PO) of 0.6/0.4, less disordered in III (PO: 0.8/0.2), and fully ordered in II at room temperature. All these factors together with the very large value of the dimensionless ratio U/W = 1.66, where U is an on-site Coulomb repulsion and W is a bandwidth, indicate that I most likely is a Mott insulator. Two polymorphs were observed for DOEONO(HO): β and β″.The β polymorph is a Mott insulator with U/W = 1.66, where U is an on-site Coulomb repulsion and W is a bandwidth, whereas β″ is a stable metal with a wide 1/4-filled (W = 1 eV) upper band. DOEOHSO(HO) also shows β″ packing. Electronic structures and conductivities of both β″ compounds are nearly the same. Their X-ray structures are similar, however not isostructural

Electrochemically-Driven Water Oxidation by a Highly Active Ruthenium-Based Catalyst

Herein is described a highly active ruthenium-based water oxidation catalyst [RuX(mcbp)(OHn)(py)2] (5, mcbp2− = 2,6-bis(1- methyl-4-(carboxylate)benzimidazol-2-yl)pyridine; n = 2, 1, and 0 for X = II, III, and IV, respectively), which can be generated in a mixture of RuIII/RuIV states from either [RuII(mcbp)(py)2] (4II) or [RuIII(Hmcbp)(py)2]2+ (4III). Complexes 4II and 4III were isolated and characterized by single crystal X-ray analysis, NMR, UV-vis, FT-IR, ESI-HRMS, EPR, and elemental analysis, and their redox properties were studied in detail by electrochemical and spectroscopic methods. Unlike for the parent catalyst [Ru(tda)(py)2] (1, tda2− = [2,2′:6′,2′′- terpyridine]-6,6′′-dicarboxylate), for which full transformation to the catalytically active species [RuIV(tda)(O)(py)2] (2) could not be carried out — stoichiometric generation of the catalytically active Ru-aqua complex 5 from 4II was achieved under mild conditions (pH 7.0) and short reaction times. The redox properties of the catalys were studied and its activity for electrocatalytic water oxidation was evaluated, reaching TOFmax ≈ 40 000 s−1 at pH 9.0 (from the foot-of- the-wave analysis, FOWA), which is comparable to the activity of the state-of-the-art catalyst 2

ILC Reference Design Report Volume 1 - Executive Summary

The International Linear Collider (ILC) is a 200-500 GeV center-of-mass high-luminosity linear electron-positron collider, based on 1.3 GHz superconducting radio-frequency (SCRF) accelerating cavities. The ILC has a total footprint of about 31 km and is designed for a peak luminosity of 2x10^34 cm^-2s^-1. This report is the Executive Summary (Volume I) of the four volume Reference Design Report. It gives an overview of the physics at the ILC, the accelerator design and value estimate, the detector concepts, and the next steps towards project realization.The International Linear Collider (ILC) is a 200-500 GeV center-of-mass high-luminosity linear electron-positron collider, based on 1.3 GHz superconducting radio-frequency (SCRF) accelerating cavities. The ILC has a total footprint of about 31 km and is designed for a peak luminosity of 2x10^34 cm^-2s^-1. This report is the Executive Summary (Volume I) of the four volume Reference Design Report. It gives an overview of the physics at the ILC, the accelerator design and value estimate, the detector concepts, and the next steps towards project realization