Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future. Quantum computers with 50-100 qubits may be able to perform tasks which surpass the capabilities of today's classical digital computers, but noise in quantum gates will limit the size of quantum circuits that can be executed reliably. NISQ devices will be useful tools for exploring many-body quantum physics, and may have other useful applications, but the 100-qubit quantum computer will not change the world right away --- we should regard it as a significant step toward the more powerful quantum technologies of the future. Quantum technologists should continue to strive for more accurate quantum gates and, eventually, fully fault-tolerant quantum computing.

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Quantum Computing in the NISQ era and beyond

Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the
near future. Quantum computers with 50-100 qubits may be able to perform tasks
which surpass the capabilities of today's classical digital computers, but
noise in quantum gates will limit the size of quantum circuits that can be
executed reliably. NISQ devices will be useful tools for exploring many-body
quantum physics, and may have other useful applications, but the 100-qubit
quantum computer will not change the world right away --- we should regard it
as a significant step toward the more powerful quantum technologies of the
future. Quantum technologists should continue to strive for more accurate
quantum gates and, eventually, fully fault-tolerant quantum computing.

/pdf/quantum-computing-in-the-nisq-era-and-beyond-3utyn832f7.pdf

One of the most promising suggested applications of quantum computing is solving classically intractable chemistry problems. This may help to answer unresolved questions about phenomena such as high temperature superconductivity, solid-state physics, transition metal catalysis, and certain biochemical reactions. In turn, this increased understanding may help us to refine, and perhaps even one day design, new compounds of scientific and industrial importance. However, building a sufficiently large quantum computer will be a difficult scientific challenge. As a result, developments that enable these problems to be tackled with fewer quantum resources should be considered important. Driven by this potential utility, quantum computational chemistry is rapidly emerging as an interdisciplinary field requiring knowledge of both quantum computing and computational chemistry. This review provides a comprehensive introduction to both computational chemistry and quantum computing, bridging the current knowledge gap. Major developments in this area are reviewed, with a particular focus on near-term quantum computation. Illustrations of key methods are provided, explicitly demonstrating how to map chemical problems onto a quantum computer, and how to solve them. The review concludes with an outlook on this nascent field.

Quantum computational chemistry

Quantum technologies exploit entanglement to revolutionize computing, measurements, and communications. This has stimulated the research in different areas of physics to engineer and manipulate fragile many-particle entangled states. Progress has been particularly rapid for atoms. Thanks to the large and tunable nonlinearities and the well-developed techniques for trapping, controlling, and counting, many groundbreaking experiments have demonstrated the generation of entangled states of trapped ions, cold, and ultracold gases of neutral atoms. Moreover, atoms can strongly couple to external forces and fields, which makes them ideal for ultraprecise sensing and time keeping. All these factors call for generating nonclassical atomic states designed for phase estimation in atomic clocks and atom interferometers, exploiting many-body entanglement to increase the sensitivity of precision measurements. The goal of this article is to review and illustrate the theory and the experiments with atomic ensembles that have demonstrated many-particle entanglement and quantum-enhanced metrology.

Quantum metrology with nonclassical states of atomic ensembles

Universal logic gates for two quantum bits (qubits) form an essential ingredient of quantum computation. Dynamical gates have been proposed in the context of trapped ions; however, geometric phase gates (which change only the phase of the physical qubits) offer potential practical advantages because they have higher intrinsic resistance to certain small errors and might enable faster gate implementation. Here we demonstrate a universal geometric pi-phase gate between two beryllium ion-qubits, based on coherent displacements induced by an optical dipole force. The displacements depend on the internal atomic states; the motional state of the ions is unimportant provided that they remain in the regime in which the force can be considered constant over the extent of each ion's wave packet. By combining the gate with single-qubit rotations, we have prepared ions in an entangled Bell state with 97% fidelity-about six times better than in a previous experiment demonstrating a universal gate between two ion-qubits. The particular properties of the gate make it attractive for a multiplexed trap architecture that would enable scaling to large numbers of ion-qubits.

Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate*

The highest two-qubit gate fidelities have been demonstrated in two experiments that use scalable trapped ion platforms.

High-Fidelity Quantum Logic Gates Using Trapped-Ion Hyperfine Qubits.

We demonstrate a two-qubit logic gate driven by near-field microwaves in a room-temperature microfabricated surface ion trap. We introduce a dynamically decoupled gate method, which stabilizes the qubits against fluctuating energy shifts and avoids the need to null the microwave field. We use the gate to produce a Bell state with fidelity 99.7(1)%, after accounting for state preparation and measurement errors. The gate is applied directly to ^{43}Ca^{+} hyperfine "atomic clock" qubits (coherence time T_{2}^{*}≈50  s) using the oscillating magnetic field gradient produced by an integrated microwave electrode.

High-Fidelity Trapped-Ion Quantum Logic Using Near-Field Microwaves

Individual addressing of qubits is essential for scalable quantum computation. Spatial addressing allows unlimited numbers of qubits to share the same frequency, while enabling arbitrary parallel operations. We demonstrate addressing of long-lived $^{43}\mathrm{Ca}^{+}$ ``atomic clock'' qubits held in separate zones ($960\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{m}$ apart) of a microfabricated surface trap with integrated microwave electrodes. Such zones could form part of a ``quantum charge-coupled device'' architecture for a large-scale quantum information processor. By coherently canceling the microwave field in one zone we measure a ratio of Rabi frequencies between addressed and nonaddressed qubits of up to 1400, from which we calculate a spin-flip probability on the qubit transition of the nonaddressed ion of $1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. Off-resonant excitation then becomes the dominant error process, at around $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. It can be prevented either by working at higher magnetic field, or by polarization control of the microwave field. We implement polarization control with error $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, which would suffice to suppress off-resonant excitation to the $\ensuremath{\sim}{10}^{\ensuremath{-}9}$ level if combined with spatial addressing. Such polarization control could also enable fast microwave operations.

High-fidelity spatial and polarization addressing of Ca-43 qubits using near-field microwave control

Robust qubit memory is essential for quantum computing, both for near-term devices operating without error correction, and for the long-term goal of a fault-tolerant processor. We directly measure the memory error ${\ensuremath{\epsilon}}_{m}$ for a $^{43}{\mathrm{Ca}}^{+}$ trapped-ion qubit in the small-error regime and find ${\ensuremath{\epsilon}}_{m}l{10}^{\ensuremath{-}4}$ for storage times $t\ensuremath{\lesssim}50\text{ }\text{ }\mathrm{ms}$. This exceeds gate or measurement times by three orders of magnitude. Using randomized benchmarking, at $t=1\text{ }\text{ }\mathrm{ms}$ we measure ${\ensuremath{\epsilon}}_{m}=1.2(7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, around ten times smaller than that extrapolated from the ${T}_{2}^{*}$ time, and limited by instability of the atomic clock reference used to benchmark the qubit.

Probing qubit memory errors at the part-per-million level

Quantum computers offer great potential for significant speedup in executing certain algorithms compared to their classical counterparts. One of the most promising physical systems in which implementing such a device seems viable are trapped atomic ions. All of the fundamental operations needed for quantum information processing have already been experimentally demonstrated in trapped ion systems. Today, the remaining two obstacles are to improve the fidelities of these operations up to the point where quantum error correction techniques can be successfully applied, as well as to scale up the present systems to a higher number of quantum bits (qubits). This thesis addresses both issues. On the one hand, it decribes the experimental implementation of a high-fidelity two-qubit quantum logic gate, which is the most technically demanding fundamental operation to realise in practice. On the other hand, the presented work is carried out in a microfabricated surface ion trap – an architecture that holds the promise of scalability. The gate is applied directly to hyperfine "atomic clock" qubits in 43Ca+ ions using the near-field microwave magnetic field gradient produced by an integrated trap electrode. To protect the gate against fluctuating energy shifts of the qubit states, as well as to avoid the need to null the microwave field at the position of the ions, a dynamically decoupled Molmer-Sorensen scheme is employed. After accounting for state preparation and measurement errors, the achieved gate fidelity is 99.7(1)p. In previous work, the same apparatus has been used to demonstrate coherence times of Ta2 ≈ 50 s and all single-qubit operations with fidelity > 99.95p. To gain access to the "atomic clock" qubit transition in 43Ca+, a static magnetic field of 146G is applied. The resulting energy level Zeeman-structure is spread over many times the linewidth of the atomic transition used for Doppler cooling. This thesis presents a simple and robust method for Doppler cooling and obtaining high fluorescence from this qubit in spite of the complicated level structure. A temperature of 0.3mK, slightly below the Doppler limit, is reached.

M. A. Sepiol

Papers

High-Fidelity Quantum Logic Gates Using Trapped-Ion Hyperfine Qubits.

High-Fidelity Trapped-Ion Quantum Logic Using Near-Field Microwaves

High-fidelity spatial and polarization addressing of Ca-43 qubits using near-field microwave control

Probing qubit memory errors at the part-per-million level

A high-fidelity microwave driven two-qubit quantum logic gate in 43Ca+