Weyl semimetals provide the realization of Weyl fermions in solid-state physics. Among all the physical phenomena that are enabled by Weyl semimetals, the chiral anomaly is the most unusual one. Here, we report signatures of the chiral anomaly in the magneto-transport measurements on the first Weyl semimetal TaAs. We show negative magnetoresistance under parallel electric and magnetic fields, that is, unlike most metals whose resistivity increases under an external magnetic field, we observe that our high mobility TaAs samples become more conductive as a magnetic field is applied along the direction of the current for certain ranges of the field strength. We present systematically detailed data and careful analyses, which allow us to exclude other possible origins of the observed negative magnetoresistance. Our transport data, corroborated by photoemission measurements, first-principles calculations and theoretical analyses, collectively demonstrate signatures of the Weyl fermion chiral anomaly in the magneto-transport of TaAs.

Generating quantum entanglement in large systems on time scales much shorter than the coherence time is key to powerful quantum simulation and computation. Trapped ions are among the most accurately controlled and best isolated quantum systems [1] with low-error entanglement gates operated via the vibrational motion of a few-ion crystal within tens of microseconds [2]. To exceed the level of complexity tractable by classical computers the main challenge is to realise fast entanglement operations in large ion crystals [3,4]. The strong dipole-dipole interactions in polar molecule [5] and Rydberg atom [6,7] systems allow much faster entangling gates, yet stable state-independent confinement comparable with trapped ions needs to be demonstrated in these systems [8]. Here, we combine the benefits of these approaches: we report a 700 ns two-ion entangling gate which utilises the strong dipolar interaction between trapped Rydberg ions and produce a Bell state with 78% fidelity. The sources of gate error are identified and a total error below 0.2% is predicted for experimentally-achievable parameters. Furthermore, we predict that residual coupling to motional modes contributes ∼ 10 −4 gate error in a large ion crystal of 100 ions. This provides a new avenue to significantly speed up and scale up trapped ion quantum computers and simulators. Trapped atomic ions are one of the most promising architectures for realizing a universal quantum computer [1]. The fundamental single-and two-qubit quantum gates have been demonstrated with errors less than 0.1% [2], sufficiently low for fault-tolerant quantum errorcorrection schemes [10]. Nevertheless, a scalable quantum computer requires a large number of qubits and a large number of gate operations to be conducted within the coherence time.Most established gate schemes using a common motional mode are slow (typical gate times are between 40 and 100 µs) and difficult to scale up since the motional spectrum becomes more dense with increasing ion number. Many new schemes have been proposed [11][12][13][14], with the fastest experimentally-achieved gate being 1.6 µs (99.8% fidelity) and 480 ns (60% fidelity) [15], realised by driving multiple motional modes simultaneously. Although the gate speed is not limited by the trap frequencies, the gate protocol requires the phase-space trajectories of all modes to close simultaneously at the end of the pulse sequence [15]. In long ion strings with a large number of vibrational modes, it becomes increasingly challenging to find and implement laser pulse parameters that execute this gate with a low error. Thus, a slow-down of gate speed appears inevitable.Two-qubit entangling gates in Rydberg atom systems are substantially faster, owing to strong dipole-dipole interactions. The gate fidelities in recent experiments using neutral atoms are fairly high [16,17]. However, the atom traps need to be turned off during Rydberg excitation. This can cause unwanted coupling between qubits and atom motion as well as atom loss [8,18]. Employing blue-detune...

We study the efficiency of algorithms simulating a system evolving with Hamiltonian H = m j=1 H j . We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number of exponentials required to approximate e −iHt with error ε. Moreover, we derive the order of the splitting method that optimizes the cost of the resulting algorithm. We show significant speedups relative to previously known results.

Trapped Rydberg ions are a promising novel approach to quantum computing and simulations [1][2][3]. They are envisaged to combine the exquisite control of trapped ion qubits [4] with the fast two-qubit Rydberg gates already demonstrated in neutral atom experiments [5][6][7]. Coherent Rydberg excitation is a key requirement for these gates. Here, we carry out the first coherent Rydberg excitation of an ion and perform a single-qubit Rydberg gate, thus demonstrating basic elements of a trapped Rydberg ion quantum computer.Systems of trapped ion qubits have set numerous benchmarks for single-qubit preparation, manipulation, and readout [8]. They can perform low error entanglement operations [9,10] with up to 14 ion qubits [11]. Still, a major limitation towards realizing a large-scale trapped ion quantum computer or simulator is the scalability of entangling quantum logic gates [12].Arrays of neutral atoms in dipole traps offer another promising approach to quantum computation and simulation. Here, qubits are stored in electronically low-lying states and multi-qubit gates may be realized by exciting atoms to Rydberg states [6,7,13,14]. Rydberg states are exotic states of matter in which the valence electron is excited to high principal quantum numbers. They can have extremely high dipole moments and may interact strongly with each other, which has allowed entanglement generation [15,16] and fast two-qubit Rydberg gates [5] in neutral atom systems.A system of trapped Rydberg ions may combine the advantages of both technologies. Electronically lowlying states may be used as qubit states and fast multiqubit gates are envisaged by coherently exciting ions to Rydberg states and employing dipolar interactions between them [1,17]. Multi-qubit gates commonly used in trapped ion systems suffer scalability restrictions due to spectral crowding of motional modes [12]. This issue does not affect multi-qubit Rydberg gates thus a trapped Rydberg ion quantum computer offers an alternate approach to a scalable system. An unanswered question was whether trapped ions can be excited to Rydberg states in a coherent fashion as is required for multi-qubit Rydberg gates. In our experiment we study a single 88 Sr + ion confined in a linear Paul trap. Three atomic levels in a ladder configuration are coupled using two UV lasers (Fig. 1). The qubit state |0 is coupled to the excited state |e by the pump laser at 243 nm with Rabi frequency Ω P . |e is coupled in turn to the Rydberg state |r (42S 1/2 , m J = −1/2) using the Stokes laser at 307 nm with Rabi frequency Ω S . The experimental setup is described in detail in the Methods section and in [3].We can use the two-photon coupling for coherent control of the Rydberg excitation. At two-photon resonance (|0 to |r ) the coupling Hamiltonian has a "dark" eigenstate |Φ dark ∼ Ω S e iφ |0 − Ω P |r (Methods), which is named so because it does not contain any component of |0-|rRydberg excitation by STIRAP shown by comparing application of the single and the double STIRAP pulse sequences. The sin...