# Quantinuum Glossary

Here are some definitions to commonly used terms used in this emerging technology.

Curious about qubits and quantum computing? Here are some definitions that will help you learn about this emerging technology.

Not long ago, discussions about quantum computing occurred primarily in technical journals or at scientific conferences.

Today, mainstream media outlets and business publications are covering quantum topics and speculating about “quantum advantage” — the point at which quantum computers can perform calculations that today’s computers cannot.

Here are definitions to help explain quantum computing and Quantinuum’s trapped-ion technology:

## Quantum Computing Explained: Terms to Know

All-to-all connectivity

This characteristic of trapped ion quantum computers means that all qubits can be rearranged via ion transport to perform operations with other qubits in the trap. This improves the efficiency of the system and provides other benefits, including higher fidelity and less noise.

Bit flips and phase flips

In classical computing, bit flip errors occur when a binary digit or bit inadvertently switches from a zero to one or vice versa. Quantum computers experience this error as well as phase flips. Phase flips are when the “phase”, or sign, of a qubit gets inadvertently switched; you can think of it as if a right-handed qubit had suddenly become left-handed. Both errors cause qubits to lose their quantum state – or decohere. Classical computers get around this by cloning data to correct errors. However, this method does not work in quantum computing, so instead we need quantum error correction.

Bloch Sphere

Qubit states live on the Bloch sphere, which is a geometrical representation of the qubit’s state. The Bloch Sphere may be thought of as analogous to the unit sphere in geometry, but includes an axis with complex numbers. The spherical coordinates represent the quantum information as a degree of superposition between 0 and 1.

Break-even

The goal of creating logical qubits and applying quantum error correction to a quantum computer is to have lower error rates than one would have using individual physical qubits. However, if the physical qubits have an error rate that is too high, applying quantum error correction will actually exacerbate the physical errors, instead of making them worse. The “break-even” point is the physical error rate below which QEC helps, and above which QEC hurts. Different quantum error correction codes will have different “break-even” points.

Circuit

This computational routine is a sequence of operations performed on qubits, including gates, measurements and resets. A circuit may be conditioned on real-time classical computation.

Circuit depth

This is the longest path in the circuit from the data input to the output, representing the maximum number of gates executed on a single qubit.

Coherence

In quantum computing, coherence refers to qubits being entangled in the quantum state necessary to complete a calculation. Maintaining this quantum state longer is essential for running more complex calculations.

Eigensolver

This program or algorithm calculates eigenvalues or eigenvectors. The Variational Quantum Eigensolver (VQE) is a promising method to conduct ground-state calculations on current noisy intermediate-scale (NISQ) quantum computers.

Entanglement

Quantum particles can link across large distances and share a quantum state, a phenomenon known as entanglement. Quantum computers utilize this phenomenon by entangling qubits and then encoding them with information to run calculations while they share a quantum state. When a qubit is measured, its observed state will be correlated with the states of every other qubit with which it was entangled.

Error-Correcting Codes

Once a logical qubit is formed, researchers apply codes to detect and correct errors, which reduces noise. This is not the same as writing software code. These are mathematical protocols or processes that help protect quantum information. Some of the more popular quantum error correction codes are the color code and surface code.

Fault-tolerant computing

Fault tolerance is a design principle that prevents errors from cascading throughout a system and corrupting circuits. Today’s supercomputers are fault-tolerant and quantum computers must be as well to handle complex calculations.

Fidelity

Computers perform calculations by manipulating the states of bits – changing the bits from 0s to 1s and 1s to 0s, like flipping a switch. Quantum computers must similarly be able to manipulate qubits from 0s to 1s, and so on. The accuracy of the calculation depends on our ability to perform these “bit-flips” with very high success rate, or “fidelity.” Fidelity is the measure of how often an attempted flip results in the correct qubit state. The higher the fidelity the better.

Gates

This basic building block of a quantum computer is an operation on a qubit that changes its state. Unlike gates for conventional computers, quantum gates are reversible. The most common quantum gates operate on one or two qubits.

Logical qubit

To get around the issues of errors, researchers create “logical” qubits. A logical qubit is a collection of entangled physical qubits on which quantum information is distributed, stored, and protected. Logical qubits are structured in such a way that researchers can detect errors on outlying physical qubits known as ancillas without disrupting the qubits encoded with information and that are running calculations.

Magic state

What makes a quantum computer faster than a classical computer? The answer is a special resource state known as a magic state. Of the most commonly studied quantum universal gate sets, a subset of these gates (i.e., the ones that do not rely on magic states) can be efficiently simulated on a classical computer. If our quantum computer can only perform the gates in this subset, then we are no better off than a classical computer. Even the runtime of such algorithms is approximately the same. This is why this subset of gates does not constitute a quantum universal gate set. Adding gates based on these special magic states, completes the quantum universal gate set and are the “magic” that allow quantum computers to run faster than their classical counterparts.

Measurement

The process of observing the quantum state of a qubit is known as measurement. When a quantum state is measured, it collapses from a value on the Bloch sphere to either a 0 or 1 following the probability defined by its state. This illustrates one of the puzzling mysteries of quantum mechanics: if one measures a quantum state, the quantum information in that state is destroyed. While this may make one wonder how useful information can still be extracted if the information is destroyed, the patterns of 0s and 1s output give insight to the quantum state of interest, and, if run many times will build up to the answer of interest.

Mid-circuit measurement

With this feature, qubits can be selectively measured at a point other than the end of a quantum circuit. The quantum information of a measured qubit collapses to a classical state (zero or one), but the non-measured qubits retain their quantum state. Based on the measured qubit, users can decide what actions to take further in the circuit, enabling much more dynamic and flexible quantum computer programming than would otherwise be possible. We were the first to incorporate this type of measurement into our commercial offerings.

NISQ

Articles about quantum computing sometimes reference this current phase of quantum computing as the “NISQ era.” Pronounced “nis-k,” this acronym stands for Noisy Intermediate-Scale Quantum Computing. It refers to near-term quantum computers on which full quantum error correction cycles have not been applied. All commercial quantum computers operating today are considered NISQ-era machines.

Noise

Quantum bits or qubits are the smallest unit of data in quantum computers. Qubits are delicate and fragile and tend to interact with their environment and one another, which creates “noise” or interference. This noise causes errors to accumulate, corrupts information stored in and between physical qubits, and disrupts the quantum state in which qubits must exist to run calculations. This phenomenon is called decoherence.

Post-processing

There are different methods of removing “noise” from quantum data. One is called post processing where results from a quantum calculation are compared against data from classical computers so “noise” can be identified and removed after a computation is completed. This is a useful technique during this early stage of quantum computing to verify and validate calculations. But this will not be feasible as quantum computers scale and begin tackling calculations too complex for classical computers.

Quantum Annealer

These machines are set up specifically to perform adiabatic quantum algorithms to find good solutions for optimization problems. The quantum state is set up at the beginning, and the final configuration following the natural evolution represents a solution. Quantum annealers contrast with universal quantum computers that, as the name suggests, can be set up to run any quantum algorithm for a much broader range of problems by controlling the evolution of the quantum state over time.

Quantum Approximate Optimization Algorithm (QAOA)

QAOA is a quantum algorithm for solving combinatorial optimization problems on quantum computers. It is suitable for using on NISQ devices since it is a variational method. Quantinuum’s scientists created another algorithm called the Filtering Variational Quantum Eigensolver (F-VQE) to solve combinatorial optimization problems that has been shown to take fewer iterations than QAOA.

Quantum algorithm

An algorithm is a defined set of calculations to be followed, usually to solve a problem. A quantum algorithm is a set of calculations that follows the laws of quantum mechanics, including the properties of superposition, entanglement, and interference. Multiple quantum algorithms have been created to solve problems such as factoring for encryption or state of a Hamiltonian.

Quantum charged coupled device (QCCD)

In 1998, researchers at the National Institute of Standards and Technology laid out a proposal for building a quantum computer that uses movable ions as qubits. This is analogous to a charge-coupled device (CCD) camera, which stores and processes imaging information as movable electrical charges in coupled pixels. The QCCD computer, instead, stores quantum information in the internal state of electrically charged ions that are transported between different processing zones using dynamic electric fields. The Quantinuum H-Series devices follow the QCCD architecture, which enables the low error rates of these devices and all-to-all connectivity.

Quantum compiler

Compilers used in classical computing translate code written in a high-level language understandable by a programmer to a lower-level language of instructions that get executed on the computer. Similarly, a quantum compiler translates code written in the language of quantum circuits and translates these to the set of instructions that will run on the quantum computer. On trapped ion devices such as Quantinuum’s, the compiler translates the quantum circuit to the to the gate-pulse sequence performed on the qubits, along with the physical movement of qubits in the device.

Quantum error correction

Quantum error correction is the process of correcting errors that arise in quantum computers while running circuits. Many schemes have been proposed to do this, usually referred to as “quantum correction codes”. Most quantum correction codes assemble multiple physical qubits into a single “logical qubit”. Without quantum error correction, small decoherence errors can snowball over the course of a long circuit, until the result of the circuit is random nonsense.

Quantum error correction cycle

Quantum researchers have developed a multi-step process known as a quantum error correction cycle to detect and correct errors and eliminate noise as calculations are running. The QEC cycle starts with 1) measuring what are known as syndromes to pinpoint errors; 2) sending these error measurements to a decoder that identifies a mathematical correction; 3) updating these syndromes and implementing corrections. Applying full cycles of quantum error correction is tricky. In systems with error above the chosen QEC code’s break-even point *[link to definition]*, correction cycles can inject noise into the system, which causes the physical qubits to lose their quantum state. As such, it’s important to select a QEC code with a break-even point above the error rate of the physical system, to ensure that QEC cycles improve the accuracy of circuit outputs

Quantum volume

Remember the old saying “you can’t judge a book by its cover?” The same is true in quantum computing. You can’t judge a quantum computer solely on the number of qubits it has. Other factors such as number of operations, fidelity, and qubit connectivity also affect performance. The Quantum Volume (QV) benchmark was developed to measure performance in a comparable way across all quantum computing technologies. QV is measured through a series of carefully designed tests. The higher the quantum volume the more powerful the system.

Qubit

In classical computing, the smallest unit of data is a binary digit or bit. A bit is a stream of electrical pulses that each exist in either a “0”- off – or “1” -on- position. A quantum bit or qubit is the smallest unit of data in quantum computing. Qubits can exist as 0s and 1s simultaneously, a phenomenon called superposition, or anything in between. This ability to be in multiple positions at once is one of the reasons quantum computing is potentially so powerful.

Qubit reuse

Mid-circuit measurement is a feature of quantum computing devices that allows users to measure the result of a qubit and reset it, enabling that qubit to be used for further computations in the quantum circuit. This “qubit reuse” enables quantum error correction as well as re-writing quantum circuits to use fewer qubits than would otherwise be necessary.

State preparation and measurement (SPAM)

Typically, a quantum algorithm is designed to put a set of qubits on a quantum computer into a desired quantum state, usually to solve a problem of interest. At the end of this, the qubits are measured to retrieve the answer of interest. The process of preparing the qubits in the quantum state and measuring them is known as State Preparation and Measurement (SPAM).

Superposition

Another puzzling feature of quantum mechanics, superposition is the ability of qubits to be in multiple states (both 0 and 1) at one time. The quantum information held by the qubit lives somewhere on the Bloch sphere, and when observed will collapse to either 0 or 1 as defined by its state.

Trapped-ion technology

At Quantinuum, we develop trapped-ion quantum technologies. Our systems “trap” charged ytterbium atoms (ions) with electromagnetic fields so they can be manipulated and encoded with information using microwave signals and lasers. This design offers some distinct advantages, including high fidelities and longer coherence times (qubits maintain their quantum state longer) than other quantum computing technologies.

Universal gate set

All computers, whether classical or quantum, should be able to perform arbitrary computations. Given an algorithm, the computer should be able to break or compile the algorithm down into smaller and smaller, simpler pieces. These small, simple pieces are the instruction set or gate set that the computer knows how to do well. The smallest gate set that is able to perform any algorithm given has a special name: a universal gate set. For example, if one wants to calculate 3^{2}, rather than calculating the exponent directly, we can first break it down into multiplication: 3^{2} = 3*3. We can then further break this down into addition: 3*3 = (3+3+3). To calculate the square of three, we only need to understand how to break this equation down (compiling) and perform simple addition (native instructions).

Variational Quantum Algorithm

Today’s quantum devices have few numbers of qubits and are error-prone. To get around this, quantum algorithm developers are using something known as the variational method to solve problems on today’s devices. The variational method is a hybrid quantum-classical technique that uses a combination of quantum circuits and classical optimization techniques to enable the quantum computer to find the answer being sought. As quantum computers get bigger, the long-term feasibility of this method is debated, but in the near-term, it is enabling discoveries to inform long-term quantum algorithm development.

Zones

In the QCCD architecture, quantum operations (gates) occur within specified zones on the device. Additional auxiliary zones exist for storing qubits not involved in computation or for loading ions into the device.