Esteban A. Martinez

Spallation neutron production by 0.8, 1.2, and 1.6 GeV protons on various targets

Spallation neutron production in proton induced reactions on Al, Fe, Zr, W, Pb and Th targets at 1.2 GeV and on Fe and Pb at 0.8, and 1.6 GeV measured at the SATURNE accelerator in Saclay is reported. The experimental double-differential cross-sections are compared with calculations performed with different intra-nuclear cascade models implemented in high energy transport codes. The broad angular coverage also allowed the determination of average neutron multiplicities above 2 MeV. Deficiencies in some of the models commonly used for applications are pointed out.

Quantum computations on a topologically encoded qubit

Fault-tolerant quantum computing Quantum states can be delicate. Attempts to process and manipulate quantum states can destroy the encoded information. Nigg et al. encoded the quantum state of a single qubit (in this case, a trapped ion) over the global properties of a series of trapped ions. These so-called stabilizers protected the information against noise sources that can degrade the single qubit. The protocol provides a route to fault-tolerant quantum computing. Science, this issue p. 302 A protocol is implemented that allows for fault-tolerant quantum computing. The construction of a quantum computer remains a fundamental scientific and technological challenge because of the influence of unavoidable noise. Quantum states and operations can be protected from errors through the use of protocols for quantum computing with faulty components. We present a quantum error-correcting code in which one qubit is encoded in entangled states distributed over seven trapped-ion qubits. The code can detect one bit flip error, one phase flip error, or a combined error of both, regardless on which of the qubits they occur. We applied sequences of gate operations on the encoded qubit to explore its computational capabilities. This seven-qubit code represents a fully functional instance of a topologically encoded qubit, or color code, and opens a route toward fault-tolerant quantum computing.

Real-time dynamics of lattice gauge theories with a few-qubit quantum computer

Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. This has recently stimulated theoretical effort, using Feynman’s idea of a quantum simulator, to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron–positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which can be directly and efficiently implemented on an ion trap architecture. We explore the Schwinger mechanism of particle–antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulation of high-energy theories using atomic physics experiments—the long-term intention is to extend this approach to real-time quantum simulations of non-Abelian lattice gauge theories.

Realization of a scalable Shor algorithm.

Reducing quantum overhead A quantum computer is expected to outperform its classical counterpart in certain tasks. One such task is the factorization of large integers, the technology that underpins the security of bank cards and online privacy. Using a small-scale quantum computer comprising five trapped calcium ions, Monz et al. implement a scalable version of Shors factorization algorithm. With the function of ions being recycled and the architecture scalable, the process is more efficient than previous implementations. The approach thus provides the potential for designing a powerful quantum computer, but with fewer resources. Science, this issue p. 1068 Integer factorization is implemented in a scalable trapped-ion–based quantum computer. Certain algorithms for quantum computers are able to outperform their classical counterparts. In 1994, Peter Shor came up with a quantum algorithm that calculates the prime factors of a large number vastly more efficiently than a classical computer. For general scalability of such algorithms, hardware, quantum error correction, and the algorithmic realization itself need to be extensible. Here we present the realization of a scalable Shor algorithm, as proposed by Kitaev. We factor the number 15 by effectively employing and controlling seven qubits and four “cache qubits” and by implementing generalized arithmetic operations, known as modular multipliers. This algorithm has been realized scalably within an ion-trap quantum computer and returns the correct factors with a confidence level exceeding 99%.

Quantum simulation of dynamical maps with trapped ions

Dynamical maps are well known in the context of classical nonlinear dynamics and chaos theory. A trapped-ion quantum simulator can be used to study the generalized version of dynamical maps for many-body dissipative quantum systems.

Measurement-based quantum computation with trapped ions.

Measurement-based quantum computation represents a powerful and flexible framework for quantum information processing, based on the notion of entangled quantum states as computational resources. The most prominent application is the one-way quantum computer, with the cluster state as its universal resource. Here we demonstrate the principles of measurement-based quantum computation using deterministically generated cluster states, in a system of trapped calcium ions. First we implement a universal set of operations for quantum computing. Second we demonstrate a family of measurement-based quantum error correction codes and show their improved performance as the code length is increased. The methods presented can be directly scaled up to generate graph states of several tens of qubits.

Compiling quantum algorithms for architectures with multi-qubit gates

In recent years, small-scale quantum information processors have been realized in multiple physical architectures. These systems provide a universal set of gates that allow one to implement any given unitary operation. The decomposition of a particular algorithm into a sequence of these available gates is not unique. Thus, the fidelity of the implementation of an algorithm can be increased by choosing an optimized decomposition into available gates. Here, we present a method to find such a decomposition, where a small-scale ion trap quantum information processor is used as an example. We demonstrate a numerical optimization protocol that minimizes the number of required multi-qubit entangling gates by design. Furthermore, we adapt the method for state preparation, and quantum algorithms including in-sequence measurements.

Undoing a quantum measurement.

In general, a quantum measurement yields an undetermined answer and alters the system to be consistent with the measurement result. This process maps multiple initial states into a single state and thus cannot be reversed. This has important implications in quantum information processing, where errors can be interpreted as measurements. Therefore, it seems that it is impossible to correct errors in a quantum information processor, but protocols exist that are capable of eliminating them if they affect only part of the system. In this work we present the deterministic reversal of a fully projective measurement on a single particle, enabled by a quantum error-correction protocol in a trapped ion quantum information processor. We further introduce an in-sequence, single-species recooling procedure to counteract the motional heating of the ion string due to the measurement.

U(1) Wilson lattice gauge theories in digital quantum simulators

Lattice gauge theories describe fundamental phenomena in nature, but calculating their real-time dynamics on classical computers is notoriously difficult. In a recent publication [Nature 534, 516 (2016)], we proposed and experimentally demonstrated a digital quantum simulation of the paradigmatic Schwinger model, a U(1)-Wilson lattice gauge theory describing the interplay between fermionic matter and gauge bosons. Here, we provide a detailed theoretical analysis of the performance and the potential of this protocol. Our strategy is based on analytically integrating out the gauge bosons, which preserves exact gauge invariance but results in complicated long-range interactions between the matter fields. Trapped-ion platforms are naturally suited to implementing these interactions, allowing for an efficient quantum simulation of the model, with a number of gate operations that scales polynomially with system size. Employing numerical simulations, we illustrate that relevant phenomena can be observed in larger experimental systems, using as an example the production of particle--antiparticle pairs after a quantum quench. We investigate theoretically the robustness of the scheme towards generic error sources, and show that near-future experiments can reach regimes where finite-size effects are insignificant. We also discuss the challenges in quantum simulating the continuum limit of the theory. Using our scheme, fundamental phenomena of lattice gauge theories can be probed using a broad set of experimentally accessible observables, including the entanglement entropy and the vacuum persistence amplitude.

Iterative Phase Optimization of Elementary Quantum Error Correcting Codes

M. Müller, A. Rivas, E. A. Mart́ınez, D. Nigg, P. Schindler, T. Monz, R. Blatt, and M. A. Martin-Delgado Department of Physics, Swansea University, Singleton Park, Swansea SA2 8PP, United Kingdom Departamento de F́ısica Teórica I, Universidad Complutense, Avenida Complutense s/n, 28040 Madrid, Spain Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, A–6020 Innsbruck, Austria Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften,Technikerstrasse 21A, 6020 Innsbruck, Austria (Dated: January 22, 2018)