Glossary of Quantum Computing terms

Trapped-ion quantum devices employ atomic ions to store and manipulate quantum information. For quantum computation and simulation applications, but also in quantum network and clock applications, one typically chooses atomic ions with a simple, hydrogen-like energy level scheme. All singly-ionized alkaline earth metals – Beryllium, Magnesium, Calcium, Strontium, Barium, Radium (typically not used as it is radioactive) – fall into this category, but also other elements, in particular singly-ionized Ytterbium are often used. Common properties of all these atomic ion species is the availability of energy levels that allow for efficient laser cooling, fluorescence detection and storage ofquantum information, see e.g. C. Roos, PhD thesis (2000). Other important parameters are the availability of highly stable lasers at the respective atomic transition wavelengths and a suitable charge to mass ratio.

ARNICA is the name of AQT’s cloud access to trapped ion quantum computers built and operated by AQT. It allows users to submit quantum circuits and retrieve the results through a publicly-available API. For more details see here.

BEECH is the name of AQT’s laser frequency stabilisation module for quantum optics applications. BEECH is fully digital, remotely controllable and rack-compatible. Due to its ultra low frequency drift for multiple wavelengths, BEECH is an indispensable device in quantum optic experiments and quantum computers. For details see here.

Coherence is a key property of physical systems described by a wave equation, such as water waves, electromagnetic waves, and also quantum mechanical systems, and describes the ability of two objects two interfere with each other. Two objects are said to be coherent if they have a fixed phase relation to each other, such that one can observe interference fringes between them. Noise effects causing uncontrolled or unknown shifts of the relative phase of two waves will lead to a gradual decoherence. The time over which a system is coherent is called the coherence time, often quantified by a 1/e decrease in the contrast of interference fringes.

For instance, ion-qubits in trapped-ion quantum computers need to be coherent with the control fields driving quantum gates on these qubits, otherwise the gates will have a random effect on the qubit state. Quantum algorithms make use of interference of the qubit states to arrive at a computation result, and if the time to execute the algorithm on a given quantum computer exceeds the coherence time of the qubits in this computer the computation result will be random.

For a spatially extended wave such as a laser beam, one can also define a coherence length, which quantifies the length after which the phase of the light is still well defined with respect to the initial position.

Decoherence is the effect of loss of coherence of a physical system due to noise effects acting on this system. For instance, a laser field may experience decoherence due to random shifts in the optical phase of the light induced by slight changes in the refractive index of the medium through which the laser propagates, e.g. air turbulence or acoustic vibrations in an optical fiber. In the context of trapped-ion or neutral atom quantum computing, the time evolution of the qubit phase depends on the energy level splitting of electronics states in the single atoms forming the qubits. This energy level splitting may fluctuate due to a noisy magnetic field via the Zeeman effect, causing the qubits to experience decoherence. Similar, the motional state of a trapped ion in the confining potential of the ion trap may be affected by decoherence due to random motional excitations by electric field noise, quantified by the so-called ion heating rate.

Entanglement is a central property of quantum systems describing a correlation in the states of two quantum objects that surpasses any correlation achievable in classical systems. The presence of entanglement therefore allows one to distinguish between classical and quantum mechanical systems. Arguably the most prominent example of entanglement is one of the so-called Bell states: for two qubits with states “0” and “1”, this state is a superposition of both qubits being in the “0” state and both qubits being in the “1” state. Upon measuring the first qubit with outcome “0”, one can immediately infer that the other qubit is now in the “0” state as well (and similar for the “1” state), even if the two qubits were to be located at different ends of the universe!

For quantum information devices, such as quantum computers, entanglement can be seen as the fundamental resource that enables quantum devices to arrive at computation results that cannot be achieved on classical devices due to execution time or memory limitations.

IBEX Q1 is the name of AQT’s universal quantum computer which is available to you via the AQT cloud service ARNICA. IBEX Q1 is based on trapped ions, it features Europe’s highest Quantum Volume and many more exceptional specifications, see here.

An ion trap is a device for the storage of charged particles, e.g. singly charged atoms (atomic ions). Ion traps utilize electric fields, sometimes in combination with magnetic fields, to manipulate the ion motion such that ions with a specific charge to mass ratio are trapped in a small spatial volume around the center of the trap. Ion traps using a combination of static magnetic and static electric fields are called “Penning traps”, for details see H. Dehmelt, Phys. Scr. 1988, 102 (1988). Traps We Paul et al.,, “Ein Ionenkäfig” (1958). A different way of classifying ion traps is the spatial arrangement of the electrodes, which either surround the trap center from all sides forming a so-called “3D trap”, or which may also be realized on the surface of a microchip forming a “surface trap”, for details see S. Seidelin et al., Phys. Rev. Lett. 96, 253003 (2006). In the latter case, the ions are trapped at some distance above the trap surface. Paul traps use a combination of DC and AC electric fields to create ion confinement, and for trapping of atomic ions the AC voltage drive frequency is typically in the radiofrequency domain, hence the AC drive is often called RF drive. The motion of ions in a Paul trap is described by the Matthieu equations (R. E. March et al., Encyclopedia of Spectroscopy and Spectrometry, Elsevier, p. 1000-1009 (1999)) and can typically be decomposed into a fast motion oscillating at the RF drive frequency, referred to as “micromotion”, and a slower motion called “secular motion”, which for stable trap operation has roughly a factor 7 smaller oscillation frequency than the micromotion. The amplitude of the micromotion is minimal at the trap center, which in practice is often the desired trapping location for the ions, and the process of moving ions to the trap center by compensating of electric stray fields with suitable control fields is often referred to as “micromotion compensation” or “stray field compensation”. The motion of ions in the trap may be cooled using laser cooling methods and once sufficiently close to the motional ground state, the ion motion may be effectively described by a quantum mechanical harmonic oscillator in all three spatial dimensions, for details see D. Leibfried et al., Rev. Mod. Phys. 75, 281 (2003).ul traps”, for details see https://doi.org/10.1103/RevModPhys.75.281

Laser cooling is one of the key technologies in modern atomic, molecular, and optical physics experiments. Laser cooling describes the reduction of the temperature of matter particles, such as single atoms, trapped ions, or levitated nanospheres, due to their interaction with laser light. Several different laser cooling techniques have been developed over the past years: from Doppler cooling to ground state cooling techniques, these techniques allow one to cool the motion of trapped particles close to the quantum mechanical ground state of motion, for more information see D/ Wineland et al., Physr Revs A Re, 4 (1979).1521 or J. Eschner et al., J. Opt. Soc. Am. B 20, 5 (2003).

In quantum computers based on trapped ions, laser cooling is used to prepare the ions in a well-defined motional state. Therefore, it is typically an essential component in the state initialization at the beginning of any quantum computation. In addition, it is used to re-cool ions and remove errors that appear during the quantum computation. In ion trap architectures that utilize ion transportation, laser cooling is an essential tool to remove undesired motional excitations that occur due to the transport.

Native gates are the set of quantum gates that can be directly run on a given quantum computer. Each quantum computer has its own set of native gates, which not hardware-agnostic. Arbitrary quantum circuits, typically composed of hardware agnostic gates such as  CNOT and Hadamard gates therefore need to be transpiled into a sequence of native gates before they are run on a given quantum computer. way the quantum computer is realized and are thus https://www.aqt.eu/products/

For instance, in a specific quantum computer realization based on trapped ions, the native gate set may consist of a laser driven Mølmer-Sørensen entangling gate and laser driven single-qubit gates, which together form a universal set of gates, see e.g. Philipp Schindler et al., New J. Phys. 15 123012 (2013 ).