Glossary of Quantum Computing terms

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 retrieving the results through a publicly available API (see also quantum as a service). For more details see here.

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 of  quantum 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.

The barium ion (Ba⁺) is a highly compelling qubit candidate for trapped-ion quantum computing due to its unique atomic structure. Like all alkaline-earth metal elements (second group of the periodic table), it features a relatively simple level scheme, and in addition uniquely provides the longest cooling wavelengths among commonly used species, allowing researchers to utilize convenient visible light rather than challenging (near-) ultraviolet lasers. Furthermore, barium has exceptionally long meta-stable state lifetimes (specifically in the D_5/2 state), which significantly reduces decoherence during quantum operations. For high-fidelity quantum information processing, specific isotopes of barium provide a suitable nuclear spin (such as ¹³⁷Ba⁺ with I = 3/2); these allow for encoding the qubit into magnetic-field-insensitive ground-state “clock” transitions, ensuring robust protection against environmental noise.

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.

The calcium ion (Ca⁺) serves as highly controllable atomic species for storing and processing quantum information within trapped-ion quantum computers. Like all ion-qubits, calcium ions can be trapped at precisely defined positions in space by utilizing electromagnetic fields, enabling high-fidelity manipulation of the qubit states with tightly focused laser beams. Historically, calcium became a foundational staple in the early quantum computing landscape because the necessary laser technology was readily available for its required wavelengths. As the lightest element in the second group of the periodic table that provides closed cooling transitions entirely within the convenient visible and infrared spectrum, it eliminates the need for complex, deep-ultraviolet optics. This favorable energy level structure allows researchers to achieve efficient laser cooling, state preparation, and readout using robust, commercially available diode lasers, making calcium a highly practical and enduring choice for scalable quantum architectures.

Cloud-based quantum computing enables organisations to access quantum computers remotely without investing in their own hardware infrastructure. Such a low-threshold entry point for using real quantum hardware allows teams to develop valuable quantum expertise at an early stage, positioning organisations for future innovation and competitive advantage.  AQT’s quantum computer systems can be accessed via the ARNICA cloud service from AQT directly, or through one of our cloud partners, such as AWS, Scaleway, Horizion Quantum, or Classiq.

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 to 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 a trapped-ion quantum computer 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 fibre. 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 fluctuations of the trapping frequency due to voltage noise, and also by 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 thus 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.

Fault tolerance describes the ability of a quantum computer to continue operating correctly (i.e. producing meaningful results) through application of quantum error correction techniques. Any real-world implementation of a quantum computer inevitably produces faulty quantum gates due to the inherent fragility of quantum information. Errors in quantum operations are one of the largest bottlenecks to a societally and commercially beneficial implementation of real-world applications on quantum computers.  Therefore, an important feature of next-generation quantum computer hardware is the ability to deal with errors. A fault tolerant architecture includes the design of quantum operations (state preparation, gates, readout, …) in a way such that errors do not spread uncontrolled and that errors can effectively be suppressed.

AQT products and QC systems are designed to achieve a quality and error rates that are compatible with fault tolerance concepts, see https://www.aqt.eu/solution/pine-system-fault-tolerant .

Hybrid computing describes an approach where a supercomputer and a quantum computer work together to solve a computational problem. The classical computer handles regular data processing providing the large memory and high clock rate benefits of classical computing technology, while specific calculations that perform better on quantum hardware are taken over by a quantum computer to achieve an overall quantum speed-up when solving the problem.

AQT has successfully integrated several of its quantum computers into HPC facilities to realize such hybrid computing systems, together with partners at the University of Innsbruck (see https://www.aqt.eu/solution/hpc-qc-integration/), the Poznan Supercomputing and Networking Center in Poland (see  https://www.aqt.eu/inauguration-of-piast-q/), or the Leibniz Rechenzentrum in Germany (see https://www.aqt.eu/ion-trap-quantum-computer-ready-for-novel-research-and-development-at-the-lrz-press/).

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 a high quantum volume and many more exceptional specifications, see https://www.aqt.eu/qc-systems.

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 centre of the trap.

Ion traps using a combination of static magnetic and static electric fields are called “Penning traps”, for details see H. Dehmelt (1988), Phys. Scr. 1988, 102. Traps that utilize static and time-varying electric fields are called “Paul traps”, see W. Paul et. al. (1958). A different way of classifying ion traps is the spatial arrangement of the electrodes, which either surround the trap centre 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 J. Eschner et. al. (2003), J. Opt. Soc. Am. B 20, 1003-1015, S. Seidelin et al. (2006), Phys. Rev. Lett. 96, 253003. 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. (1999), Encyclopedia of Spectroscopy and Spectrometry, Elsevier, p. 1000-1009) 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”. The secular 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. (2003), Rev. Mod. Phys. 75, 281.

Ion traps form the core of a trapped-ion quantum computer as they allow to confine the ions qubits.

Ionization is the process of removing (or adding) electrons from a neutral atom or molecule, thereby creating a charged particle. There are various methods to ionize neutral atoms, like e.g. laser-based ionization, where photons are absorbed from the atoms and the energy of the photon(s) is transferred to an electron such that the electron is excited into the continuum, i.e. it  is no longer bound by the interaction with the nucleus and the electron can leave the atom. Once ionized, and atomic ions can be stored in an ion trap.

IVY is the name of an optical filter cavity module provided by AQT for suppression of high frequency laser phase noise – IVY provides you with the spectral purity your experiment needs in a compact, rack-mountable solution. Read more https://www.aqt.eu/products/ivy/

Precision laser systems serve as the foundational backbone for operating quantum computers. Utilizing fundamental light-matter interactions, lasers allow one to manipulate the ions’ internal electronic states and external motion. A high degree of control over multiple laser systems operating at different wavelengths is thereby essential: The laser frequency needs to be precisely tuned to specific atomic transitions e.g. to implement laser cooling techniques such as Doppler-, or EIT- cooling. High fidelity state preparation, used to initialize the qubits into a well-defined quantum state, as well as quantum gate operations in addition often require lasers which are spectrally narrow and have extremely low noise performance. During quantum gates, tightly focused laser beams are amplitude and/or phase modulated to execute single- and multi-qubit quantum gates. Finally, laser beams are also used for quantum state readout, projecting the qubit’s final state onto certain basis states via state-dependent fluorescence measurement to determine the result of the quantum algorithm with near-perfect accuracy.

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 decades: 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. (1979). Phys Revs A Re, 4 or J. Eschner et al. (2003), J. Opt. Soc. Am. B 20, 5.

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 and is therefore a major component of quantum error correction procedures. In ion trap architectures that utilize ion transportation (e.g. the quantum charged-coupled device QCCD architecture), laser cooling is an essential tool to remove undesired motional excitations that occur due to the transport.

AQT’s LYNX Series is a new generation of 19-inch rack-mounted quantum computers that has achieved a record-breaking quantum volume of 2¹⁵=32768. This is the highest quantum volume ever achieved by a quantum computer system that is designed, built, and located in Europe. AQT quantum computer systems can be accessed via the ARNICA cloud service from AQT directly, or through one of our cloud partners.

Native gates are the set of quantum gates that can be directly run on a quantum computer. Each computer has its own set of native gates, which is hardware specific. 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.

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. P. Schindler et al., New J. Phys. 15 123012 (2013).

The AQT quantum computing systems each provide their individual native gate set as can be found here: https://www.aqt.eu/qc-systems.

In quantum computing applications, one often distinguishes between physical qubits and logical qubits. Logical qubits are the qubits defined in a high-level quantum circuit. In a way, users will almost always deal with logical qubits when they write and define quantum circuits in quantum SDKs that are hardware-agnostic. Physical qubits, on the other hand, are the actual physical carriers of the quantum information (such as the individual ions in a trapped-ion quantum computer). When using quantum error correction, the logical qubits are encoded in a set of physical qubits. See also qubit.

The PINE SET-UP is a modular vacuum chamber assembly and the foundation of many AQT quantum computing systems, such as MARMOT, IBEX and LYNX. The heart of the set-up is AQT’s ion trap unit PINE. The trap is located inside an ultra-high vacuum chamber facilitating a low background-gas collision rate of < 0.02 1/s. Optical interfaces for qubit manipulation, cooling and detection is provided via fibre ports. Single-qubit operations on a fault-tolerant level as well as fast detection can be implemented via the provided high-NA objective. The setup can be used to host more than 50 ions in a highly controlled fashion in industry standardised 19 inch racks as well as in laboratory table top experiments. More information on the PINE SET-UP can be found here: https://www.aqt.eu/products/pine-set-up/.

PINE is the name of AQT’s macroscopic 3D ion trap. Our PINE TRAP features a well proven design with high optical access and low ion heating rate, enabling the storage and manipulation of long strings of ions for quantum optics applications, such as quantum computation or quantum simulation.

The power consumption of a quantum computer is an important aspect when evaluating the overall energy efficiency and sustainability of the technology. Power consumption and dissipation is also relevant when considering the integration of quantum computers with high-performance computing systems (see hybrid computing).

The power consumption of a quantum computer is platform dependent. For instance, superconducting qubits or single-photon detectors in photonic quantum computers need to be operated at sub-Kelvin temperatures, requiring high power consumption for the cryogenic cooling. Other platforms, such as trapped-ions or neutral atoms, may be operated at moderate cryogenic temperatures or even room temperature, significantly lowering the demands on power consumption.

AQT’s quantum computing systems are designed for low power consumption. Each quantum computer fits into two custom 19-inch racks, the quantum processor runs in a room temperature environment and the entire systems consume less than 2 kW of power in total. Due to the modular and efficient architecture, the systems are easy to integrate into existing datacenter infrastructure.

A quantum algorithm is an algorithm or program that is designed to be implemented on a quantum computer. A large number of quantum algorithms have been developed so far, as listed for instance in the “Quantum Algorithm Zoo”. A quantum algorithm typically offers a computational speed-up compared to its classical counter-part. A prominent example is Shor’s “period finding” algorithm, which offers a super-polynomial speed-up, i.e. the number of computational steps when executing the quantum algorithm is by a super-polynomial factor smaller than for a classical algorithm. With increasing size of the computational problem (and given that no classical algorithm with similar efficiency will be found), a quantum computer will thus eventually outperform classical computers. For Shor’s algorithm that means that a sufficiently powerful quantum computer will be able to find the period of a large number (as in e.g. RSA-2048), which is considered infeasible for classical computers using currently available classical algorithms.

Quantum as a service (QaaS) is a (commercial) offering that allows users to remotely access quantum computers via the cloud enabling them to test and develop quantum algorithms and applications without owning quantum hardware.

AQT’s ARNICA service makes our cutting-edge quantum computers accessible to customers allowing them to transform their business with the simplicity of the cloud.

Quantum benchmarks are procedures that are used to assess the performance of quantum information processors. There exists a large variety of benchmarks from low level (on the component level) to top level (on the system level) benchmarks (see e.g. the “Quantum Benchmark Zoo“).

Component level benchmarks include for example standard randomized benchmarking (see J. Emerson et al (2005). J. Opt. B: Quantum Semiclass. Opt. 7 S347, E. Knill et. al. (2008). Phys. Rev. A 77, 012307, E. Magesan et. al. (2011). Phys. Rev. Lett. 106, 180504), interleaved randomized benchmarking (see E. Magesan et. al. (2012). Phys. Rev. Lett. 109, 080505), cycle benchmarking (see A. Erhard et. al. (2019). Nature communications, 10(1), 5347) or gate set tomography (see R. Blume-Kohout (2013). arXiv preprint arXiv:1310.4492). Such component level benchmarks rigorously test the performance of individual components using minimal assumptions on the underlying hardware.

System level benchmarks on the other hand are designed to test how the basics components work together. An example is the quantum volume (see A. W. Cross et. al. (2019). Phys. Rev. A 100, 032328), where a specific but quite generic type of random circuits is implemented to test the performance of a quantum computer using two major performance indicators: the qubit number and the error rate of the quantum operations.

Another type of system level benchmarks are application benchmarks (see T. Lubinski et. al. (2023). IEEE Transactions on Quantum Engineering, 4, 1-32, Z. Zimborás et. al. (2025). arXiv preprint arXiv:2512.19653) which test the performance of a quantum computer for specific applications. Currently available application benchmarks are not that rigorous since they involve a variety of details that do not test the actual quantum hardware, such as classical optimization methods. Nevertheless, application benchmarks still provide useful insights for users regarding the performance that can be expected when solving a given application on a certain quantum device.

The quantum charged-coupled device (QCCD) is a trap architecture for a trapped-ion quantum computer that is conceptually scalable to a large number of qubits, see D. Kielpinski et al., Nature 417, 709–711 (2002). The basic idea is to break down the quantum register into smaller sub-registers, i.e. sub-groups of ion-qubits, which can be reconfigured by moving ions across a complex trap array with comprises multiple linear segments connected by junctions. In this architecture, at any given moment, only a sub-set of qubits can interact with one another (e.g. interacting qubit pairs), although all these local interactions may happen in parallel. Between the interactions the qubits can be rearranged into new groups by ion transport operations, also called ion shuttling.  The reordering of the qubit register can typically be done with significantly lower error rates compared to quantum gate operations. This architecture therefore follows a “divide and conquer” strategy, in which operations on small qubit registers allow for the implementation of gates with low errors rates, while keeping all-to-all connectivity via high-fidelity shuttling. In addition, a QCCD-type trap array can comprise of different regions, as e.g. one region where ionic qubits are loaded and prepared, one region where quantum gates are implemented, one region where the qubit state is detected, one region that serves as qubit memory, etc. Due to this flexibility, the QCCD approach is believed to be one major building block for scalable quantum computers based on trapped ions.

A quantum circuit is a general description of a program that can be executed on a quantum computer. It consists of a series of (quantum-) operations applied to a number of qubits. These operations comprise for example 1-qubit and 2-qubit gates, measurements, or qubit reset operations. After initializing the qubits in a specific state, the quantum operations are defined in chronological order. In addition to the qubit register, it is often useful to define a classical register in which the measured classical information can be stored. Therefore, a quantum circuit comprises a qubit register (containing qubits), a classical register (containing bits), and a list of operations applied to these bits and qubits. Since the quantum state of a qubit “collapses” upon measurement resulting in a classical state 0 or 1 with given probabilities, quantum circuits or parts thereof are repeated several times to determine this probability distribution of the classical result with the desired precision. If a quantum computer has what is known as a universal quantum gate set, it is possible to implement any conceivable program or unitary operation using the quantum circuit model.

Alternatively to the quantum circuit model, there are complementary descriptions of programs for quantum computers that can be just as universal but offer a different type of information processing, such as measurement-based quantum computation (see H. J. Briegel et al (2009), Nature Physics 5, 19–26).

A quantum computer (or quantum information processor) is a device that can process information using programmable operations that obey the laws of quantum mechanics. The basic instructions that are used to program the quantum computer are called quantum gates. These quantum gates are often arranged and visualized using the quantum circuit model.  In analogy to a classical computer, also a quantum computer is able to calculate any conceivable mathematical problem. For this, the quantum computer in particular needs a universal gate set (see quantum gate). The minimal requirements for a physical implementation of a quantum computer were collected in David DiVincenzo’s list of criteria (see also arXiv:cond-mat/9612126). Quantum computers may be implemented on different physical platforms, e.g. trapped-ions, neutral atoms, superconducting circuits, or photons.

In any quantum device there are fluctuations and drifts in system parameters, unwanted couplings to the surrounding environment, etc. that lead to errors during quantum operations. If the accumulated errors become too large, the result of a quantum computation becomes essentially random and cannot be used any more. Quantum error correction (QEC) is an important method (and open research topic) that allows one to suppress errors occurring during quantum computation. Similar to classical error correction, QEC is based on redundancy (see e.g. P. W. Shor (1995). Phys. Rev. A 52, R2493(R) or A. M. Steane (1996). Phys. Rev. Lett. 77(5), 793 or D. Nigg et. al. (2014). Science, 345(6194), 302-305). By encoding the quantum information that is otherwise stored in a single physical qubit into several physical qubits (where certain groups of physical qubits are called a logical qubit, see also physical and logical qubit), errors can be detected and corrected. Importantly, QEC only works if certain criteria are met: e.g. not all physical qubits may exhibit the same error, errors may not spread uncontrolled in the qubit register, errors may not occur more frequently than they can be corrected for, etc. In practice, one needs complex QEC schemes or recipes, that specify how information is encoded, what operations are allowed where and when, how error syndromes are calculated and mapped back to the qubit register and so on.The specific QEC architecture (i.e. codes and algorithms) depends on the physical hardware and the specific types of errors that occur in a given system and therefore more hardware specific QEC protocols will likely be developed in the future. For more details see e.g. Bermudez, A. et. al (2017). Phys. Rev. X 7, 041061 or D. Gottesman (2022). arXiv preprint arXiv:2210.15844.

It is important to note, that QEC cannot provide that quantum programs can run for an infinite time, since this would require an infinite number of qubits. Therefore, QEC cannot prohibit errors, but QEC can help to suppress or reduce errors and hence allow for larger and more complex problems to be solved.

A quantum gate is a quantum operation acting on one or more qubits at a time. Mathematically, a quantum gate can be described by a unitary operation acting on a qubit state. A so-called 1-qubit gate acts on the state of a single qubit. For example, similar to a NOT gate in classical computation, there exists an X gate that brings the qubit state |0> to the state |1> and vice versa.

In addition to 1-qubit gates, there are 2-qubit gates that can be used to create entanglement and highly non-classical states. Since there are infinitely many unitary operations conceivable, there are also many different quantum gate realization used in practice and every quantum computing hardware has it’s individual “native” gate set, that works best on the respective physical implementation. A set of quantum gates that allows one to implement any possible quantum circuit, is called a universal gate set. The AQT LYNX device for example offers a native gate set comprising 1-qubit gates R(θ,φ)_i on qubit i and 2-qubit gates R_zz(θ)_(i,j) acting on qubit pair (i,j), which together form a universal gate set.

A quantum network is a network consisting of several quantum nodes that contain “stationary qubits”, such as trapped ions, atoms or NV centres. These nodes are interconnected by means of “flying qubits”, typically photons. Important components of a quantum network are the interfaces that physically connect and convert the information from stationary to flying qubits. A quantum network can be used to exchange information securely via Quantum-Key-Distribution (QKD) protocols or to scale quantum computers by connecting multiple quantum processors.

Quantum optics is a field of research that studies elementary interactions between matter and light. The advances in this field enable a high degree of control of the external and internal degrees of freedom of individual quantum particles, such as single atoms and single photons. The ability to control individual elementary quantum mechanical particles and the interactions between them forms the basis of modern  quantum devices such as trapped-ion quantum computers.

A quantum processing unit (QPU) serves as the fundamental computing core of a quantum computer, acting as the quantum equivalent to a classical CPU or GPU. A QPU can be engineered using a variety of underlying physical platforms – such as superconducting qubits, trapped ions, neutral atoms, or photonic circuits – depending on the hardware manufacturer’s approach. To achieve large-scale computational power, separate QPUs can be interconnected using advanced communication networks, such as photonic links, which facilitate the high-fidelity transfer of quantum information between modules and enable them to work together as a cohesive, powerful system.

A quantum software development kit (quantum SDK) is a highly abstracted and hardware agnostic framework for programming a quantum computer. Quantum SDKs provide a set of programming tools, such as libraries for quantum gates or even full algorithms, that allows developers to write, debug and execute quantum circuits without requiring them to know details about the physical implementation of the quantum computer on which the circuit is executed.

AQT quantum computers can be accessed via the cloud using the available connectors for popular quantum SDKs like Qiskit, Cirq, and pytket. Learn more about AQT’s cloud service interfaces https://www.aqt.eu/quantum-sdk-connectors/.

The quantum volume (QV) test is a holistic benchmark metric that is used to measure the overall performance of a quantum computer and characterize it with a single number. Importantly, the QV does not only include the number of qubits, but also factors in the quality and reliability of the qubits and quantum operations. Therefore, the QV metric basically describes how many “good”, i.e. usable, qubits a quantum computer contains. A given QV corresponds to the exponential of a number of such good qubits, with which the success probability of running a standardized quantum circuit exceeds a specific threshold. As the circuit size increases with the qubit number, the quality of the quantum operations must also  increase in order to  pass the tests successfully. Hence, the higher the QV benchmark value, the more powerful the computer. Originally proposed by IBM (see Cross, A. W. et. al. (2019). Physical Review A, 100(3), 032328) the QV test is now an internationally recognised benchmark rigorously assessing and describing the computational power of a quantum computer, see e.g. the QV tests for the AQT LYNX device.

A quantum binary digit (Qubit) is the fundamental building block of most quantum devices. A qubit is a quantum mechanical two-level system comprising the states |0> and |1> and may be represented by any physical system that can encode such a two-level system. Prime examples of qubits are two electronic states in a single atom or atomic ion, or the two polarizations states of a photon. The quantum state |ψ> of a qubit is in general a superposition of the two quantum states |0> and |1>, i.e. |ψ>= α|0>+β|1>. A common visualization of a qubit state is a vector pointing to any point on the surface of a sphere (the so-called Bloch-sphere), where the poles of the sphere are the states |0> and |1>. For details see e.g. https://doi.org/10.1017/CBO9780511976667.

In quantum computing applications, one often distinguishes between physical qubits, which are the actual physical carriers of the quantum information (such as the individual ions in a trapped-ion quantum computer), and logical qubits, which are mathematical abstractions and may be represented by a single physical qubit or a group of physical qubits (see also quantum error correction and physical and logical qubit).

Qubit connectivity describes how qubits in a quantum computer can interact with one another to perform quantum gate operations. It determines which qubits can directly execute two-qubit (or multi-qubit) gates and create entanglement.

Connectivity is a key factor for comparing quantum computing hardware, alongside other factors such as qubit number, gate fidelity, gate speed, and coherence time (see quantum benchmarks). Higher connectivity in general improves the overall fidelity of executing a quantum algorithm by reducing circuit complexity, reducing gate count and simplifying quantum circuit compilation.

Different quantum computing platforms offer different qubit connectivities. For instance, superconducting quantum processors typically rely on nearest-neighbour interactions, meaning qubits can only directly communicate with a limited number of adjacent qubits. In order to entangle two distant qubits, many operations on qubits that are located between the qubits of interest need to be implemented, which induces more errors. In contrast, trapped-ion quantum computers typically provide all-to-all connectivity, allowing any qubit to directly interact with any other qubit in the processor. This all-to-all connectivity is a major advantage of the trapped-ion platform.

Qubit state discrimination is a process where the quantum information of a qubit is being measured and mapped to a classical outcome. The measurement of qubits is typically done at the end of each quantum circuit, but it can also be implemented within a circuit, which is known as mid-circuit-measurement (MCM).

In a trapped-ion quantum computer the state of the ions is often measured using a technique known as electron shelving, followed by fluorescence detection. When atoms or ions are excited, they can decay into a lower energy state. This decay is accompanied by the emission of light, a phenomenon known as fluorescence. A detection laser is used to excite only one of the two possible qubit states, where we “see” either a dark or a bright atom, depending on the state (0 or 1) of the qubit. For details see D. Leibfried et al. (2003). Rev. Mod. Phys. 75(1), 281.

In analogy to the qubit, that is used to describe a quantum-mechanical two-level system, a qudit describes a system of d levels. Just like for qubits, a general qudit state is a superposition of these d levels. For example, a qudit with d=3 can be used to encode the state |ψ>=α|0>+β|1>+γ|2>. For details see M. A. Nielsen and I. L. Chuang (2010). Cambridge university press.

A rack-mounted quantum computer is a quantum computer that fits the form factor of standardised IT equipment cabinets. AQT has pioneered the shift to standardized form factors by shrinking originally room-sized laboratory physics experiments into two standard 19-inch data-center racks, see Pogorelov, I et al. (2021). PRX Quantum 2, 020343. Our systems were the first commercial 19-inch rack-mounted quantum computers, with a total footprint of less than 2m² and operated at room-temperature. Read more about AQT’s quantum computers.

Standard randomized benchmarking is a simple and efficient tool to rigorously characterize the average gate fidelity of basic quantum gate operations, such as 1-qubit and 2-qubit gates. The implementation of circuits comprising of randomly selected Clifford gates offers several important features. It is scalable, because the usage of Clifford operations allows for classical simulation of the expected outcome. The output of the quantum computer can therefore be cross-checked with a classical computer. The implementation of randomly chosen gates converts many types of errors into what might be described as an “average” error (depolarizing noise channel), which relaxes the assumptions regarding hardware errors and provides an estimate of the errors to be expected in many quantum circuits that have similar structure. In addition, the estimate of the average gate error is independent of state preparation and measurement (SPAM) errors. See also quantum benchmark.

The ROWAN modules by AQT are used in our quantum computers for controlling coherent laser pulses.  The product employs a double pass acousto-optic modulator (AOM) configuration and can be used for shaping laser light with arbitrary amplitude, frequency and phase for your research applications. ROWAN furthermore features a small footprint (3 RU) and simple integration in a standard 19-inch rack  – perfectly suitable for AMO experiments. Read more https://www.aqt.eu/rowan/

In general, a quantum state can be described as a superposition, i.e. a linear combination, of basis states. For example, a general qubit state |ψ> can be expressed as a superposition of two basis states |0> and |1> as |ψ>= α|0>+β|1>, where α and β are complex numbers. For details see Nielsen, M. A., & Chuang, I. L. (2010). Cambridge university press.

A trapped ion is a charged atom, created by an ionisation process, that is stored in an ion trap. The atom can be singly ionized (one electron removed) or also highly charged (if multiple electrons are removed). The important figure of merit that determines the trapping conditions is the charge-to-mass ratio. Trapped-ions may be used as ion-qubits in a trapped-ion quantum computer. (see also atomic ion species).

Trapped ions are one of several platforms suited for building quantum computing hardware. In a trapped-ion quantum computer, atomic ions are utilized to encode qubits and quantum operations are realized using laser or microwave radiation to drive transition between dedicated atomic levels. The concept of a trapped-ion quantum computer has originally been conceived in 1995 by I. Cirac and P. Zoller at the University of Innsbruck (see Cirac, J. I.; Zoller, P. (1995-05-15). “Quantum Computations with Cold Trapped Ions”. Physical Review Letters. 74 (20): 4091–4094.), and jump-started efforts worldwide in the academic and private sector to develop and build quantum computing systems based on trapped ions.

Today, trapped-ion quantum computers hold many major world-records as e.g. for high-fidelity gate operations ( Smith, M. C. et. al. (2025) Physical Review Letters, 134(23), 230601, Ransford, al. (2025).arXiv:2511.05465, Hughes, A. C et. al (2025). arXiv:2510.17286), long coherence times (Wang, P. et. al. (2021). Nature communications, 12(1), 233), as well as rigorous benchmarks like e.g. the quantum volume (QV=2²⁵). With multiple concepts to scale to larger qubit numbers (see e.g. QCCD), trapped-ion quantum computers are one of the leading candidates for utility scale quantum computers.

A two-qubit gate is a quantum operation that acts on two qubits simultaneously. Certain types of two-qubit gates can be used to create entanglement between two qubits. Such two-qubit gates in addition to a set of suitable single-qubit gates can form a universal set of gates and are therefore the building blocks of a universal quantum computer. Typically, two-qubit gates are the most challenging to implement with high-fidelity, since two (otherwise very well shielded and protected) qubits need to interact in a precisely controlled way. (see also quantum gate).

Ion traps for quantum applications such as trapped-ion quantum computers need to be operated in an ultra-high vacuum (UHV) environment to avoid collisions of the trapped ions with background gas atoms which can lead to disturbances of the ion crystal or even ion loss. Typical pressures obtained in state-of-the-art room temperature setups are 10^-10 to 10^-11 mbar, and can be even lower for cryogenic setups.