# Resource - More About Quantum Computers

At Qfinity Labs, we are committed to developing the greatest Quantum Algorithms for our clients and business partners.

## Qubits - From 2 dimensions to 3 dimensions

At Qfinity Labs, we are committed to developing the very best Quantum Algorithms for our clients and business partners.

All computing systems rely on a fundamental ability to store and manipulate information. Current computers manipulate individual bits, which store information as binary 0 and 1 states. Quantum computers leverage quantum mechanical phenomena to manipulate information. To do this, they rely on quantum bits, or qubits.

Learn here about the quantum properties leveraged by qubits, how they’re used to compute, and how quantum systems scale.

## Scalable Quantum Systems

At the heart of our Quantum System is the transmon qubit. Successive generations of our Quantum processors have demonstrated the potential of superconducting transmon qubits as the basis for electrically controlled solid-state quantum computers. With a scalable approach to chip architecture and research into error correction and mitigation, Qfinity Labs is at the forefront of developing systems which gives us an edge in real world applications.

## Documentation

## Interview

## White Paper

Applications of Quantum Computing in Finance

by Dr David Moche

“This book gently eases computer scientists into the hybrid world of continuous qubits and discrete measurements from the ground up, covering all the essential mathematical prerequisites before diving into everything quantum in Finance: from algorithms and programming languages to protocols and hardware.”

*Vaughan Pratt, Professor, Department of Computer Science, Stanford University*

## Glossary

### Amplitude

Amplitudes are complex numbers, and each possible outcome has a corresponding amplitude. Amplitudes are analogous to conventional probabilities, as the magnitude of the amplitude is correlated to the chance of measuring that outcome. Unlike conventional probabilities, amplitudes have phase and can interfere with each other.

### Auxiliary qubit

Certain quantum operations require, or can be made more efficient using, extra qubits that do not store the inputs or outputs of the operation. Since these extra qubits do not contain useful information before or after the operation, their role is auxiliary. If the state of the auxiliary qubits is known before the operation, they are known as ‘clean’ qubits (and are usually set to ). If the state is unknown, they are referred to as ‘dirty’ qubits.

### Backend

The term backend can refer to either a quantum system or a high-performance classical simulator of a quantum system.

### Bloch sphere

The Bloch sphere (named after Felix Bloch) is a visual representation of the state of a qubit. Note that the Bloch sphere is different from the q-sphere. Multiple states can also be simultaneously displayed (see below). The components of the Bloch representation of the qubit state are found from the expectation values of the , , and gates. A qubit described by a statevector has unit length and is found on the surface of the Bloch sphere. Qubits characterized by a density matrix will in general have length less than one, as determined by the purity of the state, and lie within the Bloch sphere.

Evolution of a qubit statevector after applying a series of gates.

### Coherence

The coherence of a qubit, roughly speaking, is its ability to maintain superposition over time. It is therefore the absence of “decoherence”, which is any process that collapses the quantum state into a classical state, for instance by interaction with an environment.

### DiVincenzo Criteria

The DiVincenzo criteria are a list of conditions that are necessary to construct a quantum computer, and they were first proposed by the theoretical physicist David P. DiVincenzo in his 2000 paper “The Physical Implementation of Quantum Computation”. The DiVincenzo criteria consist of 5+2 conditions that an experimental setup must satisfy in order to successfully implement quantum algorithms, such as Grover’s search algorithm, or Shor factorisation. The two additional conditions are necessary to implement quantum communication, such as that used in the quantum key distribution.

1 – A scalable physical system with well characterized qubits.

2 – The ability to initialize the state of the qubits to a simple fiducial state.

3 – Long relevant decoherence times.

4 – A “universal” set of quantum gates.

5 – A qubit-specific measurement capability.

6 – The ability to interconvert stationary and flying qubits.

7 – The ability to faithfully transmit flying qubits between specified locations.

### Entanglement

Entanglement is a property of quantum systems comprised of more than one subsystem (i.e., qubits), where the quantum state of any one subsystem cannot be uniquely described independently of the remaining subsystems. Mathematically an entangled state is one that can not be written as as product of subsystem states. Subsystems of entangled states are mixed states requiring a density matrix representation. For a bipartite quantum system, the entanglement is equal to the entropy of the subsystems.

### Fair-share queue

Fair-share queuing executes jobs on a quantum system in a dynamic order so that no provider can monopolize the system. The shares in fair-share queuing represent the fraction of system time that is allocated to a given provider. Providers with the most device time have the highest priority in the fair-share algorithm. A provider’s dynamic priority depends on how much of the provider’s allotted system time has been consumed over a given floating window of time. When you send a job, it will be executed by the provider with the highest dynamic priority (or lowest fraction of allotted time used) at that moment. For more information, see the Fair-share queuing section.

### Global phase

A phase applied to a statevector as a whole, . States related by a global phase are equivalent in quantum mechanics; global phases can be ignored. This is a consequence of the fact that only energy differences, as opposed to absolute values, matter in determining the dynamics of physical systems. See An aside on global phase.

### Job

A job ties together all of the relevant information about a computation on QFinity Labs: a quantum circuit, choice of backend, the choice of how many shots to execute on the backend, and the results upon executing the quantum circuit on the backend.

### Majorana Fermions

Elementary particles, (the “fermions”) which form the matter, are described by an equation formulated in 1928 by Paul Dirac, the Dirac Equation. It implies that every fundamental particle in the universe has an antiparticle, which has the same mass but the opposite charge. In 1932 was found the first antiparticle: the positron, associated with the electron.

The electron and the other elementary particles have distinct antiparticles and they acquire mass through Higgs mechanism: in physics they are called “Dirac fermions”.

In 1937, the Italian physicist Ettore Majorana found out a more general equation (Majorana Equation) that predicts the existence of neutral fermions (without electric charge) that are their own antiparticles. Majorana fermions are exotic particles because they acquire the mass, not through Higgs mechanism, but interacting with themselves, because they are their own antiparticles.

This kind of interaction happens without annihilation, because Majorana fermions are very stable and interact very little with “ordinary” matter.

### Measurement

Measurement is the act of observing a quantum state. This observation will yield classical information, such as a bit. It is important to note that this measurement process will change the quantum state. For instance, if the state is in superposition, this measurement will ‘collapse’ it into a classical state: zero or one. This collapse process takes place randomly. Before a measurement is done, there is no way of knowing what the outcome will be. However, it is possible to calculate the probability of each outcome. This probability is a prediction about the quantum state, a prediction that we can test by preparing the state several times, measuring it and then counting the fraction of each outcome.

### No Cloning Theorem

The no-cloning principle is a fundamental property of quantum mechanics which states that, given an unknown quantum state, there is no reliable way of producing extra copies of that state. This means that information encoded in quantum states is essentially unique. This is sometimes very annoying, such as when you want to protect quantum information from outside influences, but it is also sometimes very useful, such as when you want to communicate securely with someone else.

### OpenQASM

A quantum assembly language dialect (see QASM). For more information, see the OpenQASM code topic.

### Provider

Access to the various services offered by QFinity Labs is controlled by the providers to which you are assigned. A provider is defined by a hierarchical organization of hub, group, and project. A hub is the top level of a given hierarchy (organization) and contains within it one or more groups. These groups are in turn populated with projects. The combination of hub/group/project is called a provider. Users can belong to more than one provider at any given time.

### QASM

QASM is an abbreviation for quantum assembly language. It is a set of text-based instructions to describe and visualize quantum circuits. QFinity Labs uses a dialect called OpenQASM; see more in the OpenQASM code topic.

### Quantum Advantage

For a given problem, the improvement in run time for a quantum computer versus a conventional computer running the best known conventional algorithm.

### Quantum Algorithm

An algorithm is a collection of instructions that allows you to compute a function, for instance the square of a number. A quantum algorithm is exactly the same thing, but the instructions also allow superpositions to be made and entanglement to be created. This allows quantum algorithms to do certain things that cannot be done efficiently with regular algorithms.

### Quantum Circuit

A quantum circuit is a computational routine consisting of coherent quantum operations on quantum data, such as qubits, and concurrent real-time classical computation. It is an ordered sequence of quantum gates, measurements, and resets, which may be conditioned on and use data from the real-time classical computation. A set of quantum gates is said to be universal if any unitary transformation of the quantum data can be efficiently approximated arbitrarily well as a sequence of gates in the set. Any quantum program can be represented by a sequence of quantum circuits and non-concurrent classical computation.

### Quantum Computer

A quantum computer is a device capable of executing coherent controlled quantum dynamics.

### Quantum Dot

Quantum dots are effectively “artificial atoms.” They are nanocrystals of semiconductor wherein an electron-hole pair can be trapped. The nanometer size is comparable to the wavelength of light and so, just like in an atom, the electron can occupy discrete energy levels. The dots can be confined in a photonic crystal cavity, where they can be probed with laser light.

### Quantum Error Correction

Quantum computers are always in contact with the environment. This environment can disturb the computational state of the system, thereby causing information loss. Quantum error correction combats this loss by taking the computational state of the system and spreading it out over an entangled state over many qubits. This entanglement allows outside classical observers to observe and remedy disturbances

without observing the computational state itself, which would collapse it.

### Quantum Internet

Researchers at QFinity Labs are trying to build the world’s first quantum internet. Quantum Internet is like the regular Internet but it can send quantum states and establish entanglement. Building a full-scale quantum internet is of course very hard. So they will begin by establishing a small four-node network by 2020. This four-node network would serve as a testbed for the larger network.

### Quantum Gate

A quantum gate is a reversible (unitary) operation applied to one or more qubits.

### Quantum Logic Gates

Quantum Logic Gates are analogous to conventional electronic logic gates in conventional computers but different in that the system follows the strange rules of quantum mechanics. An early realization of a quantum logic gate used a single trapped beryllium ion to demonstrate a two-bit quantum logic gate. One qubit, the control qubit, is specified by the (quantized) external vibrations of the ion in the atom trap; the two lowest vibrational levels correspond to values of 0 and 1. The other qubit (the target qubit) is specified by an internal state of one of the ion’s electrons; it has a “spin-down” state (0) and a “spin-up” state (1). Shooting laser pulses at a single ion causes it to act as a two-bit “controlled NOT” gate. If the control qubit is 0, the target bit is left alone. If the control qubit is 1, the target bit flips its spin.

### Quantum Indeterminacy

The fundamental condition of existence, supported by all empirical evidence, in which an isolated quantum system, such as a free electron, does not possess fixed properties until observed in experiments designed to measure those properties. That is, a particle does not have a specific mass, or position, or velocity, or spin, until those properties are measured. Indeed, in a strict sense the particle does not exist until observed.

### Quantum Key Distribution (QKD)

Quantum key distribution (QKD) is a method that leverages the properties of quantum mechanics, such as the no cloning theorem, to allow two people to securely agree on a key (OTP – One Time Pad). A key in this context is a secret code-word that is shared only between you and the person you are trying to communicate with. This secret code-word can then be used to encrypt messages such that they can be transmitted without being read by a malicious third party.

### Quantum Repeater

Quantum repeaters enable long distance communication over a quantum network. An optical fiber can transmit a qubit over roughly 100 kilometers. If you want to send a quantum information over an very long distance just a fiber is not good enough. To send information over this long distances we need quantum repeaters. Quantum repeaters can be thought of as a series of short entangled links connecting the two points. The quantum information can then be teleported through these links and arrive safely at its destination.

### Quantum Sensors

A quantum sensor is a device that exploits quantum correlations, such as quantum entanglement, to achieve a sensitivity or resolution that is better than can be achieved using only classical systems. A quantum sensor can measure the effect of the quantum state of another system on itself. The mere act of measurement influences the quantum state and alters the probability and uncertainty associated with its state during measurement. Quantum sensor is also a term used in other settings where entangled quantum systems are exploited to make better atomic clocks or more sensitive magnetometers. If you have a super sensitive detector, its killer app is surely in measuring the smallest effects you could possibly imagine. This might mean be the tiny disturbances in space as a gravitational wave goes by; or a small change in a magnetic field, perhaps that of the Earth itself; or even overcoming the shortcomings of conventional radar systems, to build a quantum radar for detecting stealth planes.

### Quantum Tunneling

Quantum Tunnelling is the quantum mechanical effect in which particles have a finite probability of crossing an energy barrier, or transitioning through an energy state normally forbidden to them by classical physics, due to the wave-like aspect of particles. The probability wave of a particle represents the probability of finding the particle in a certain location, and there is a finite probability that the par

### Quantum Simulators

Quantum simulation, which originated to a great extent with Richard Feynman’s 1982 proposal, has evolved into a field where scientists use a controllable quantum system to study a second, less experimentally feasible quantum phenomenon. In short, a full-scale quantum computer does not yet exist, and classical computers often cannot solve quantum problems, thus a “quantum simulator” presents an attractive alternative to gain insight into, for example, complex material properties.ticle is located on the other side of the barrier.

### Quantum Supremacy

A calculation on a quantum computer that cannot be in practice be performed on any foreseeable conventional computer. Either the number of CPU steps required or the necessary computer memory increases exponentially with the size of the input. This means that for all but the simplest cases, the calculation becomes unfeasible on a real machine using only conventional digital hardware.

### Qubit

A qubit (pronounced “cue-bit” and short for quantum bit) is the basic unit of quantum information. A qubit consists of two-levels that can be expressed using the “computational basis” states , and . Unlike a classical bit, the state of a qubit can be a linear combination (superposition) of both computational states.

### Register

A quantum register is a collection of qubits on which gates and other operations act. A classical register consists of bits that can be written to and read within the coherence time of the quantum circuit.

### Relative phase

A phase difference between components of a superposition state. By convention, the first term in a superposition is made to be real, and the remaining states have phase values relative to this, e.g., .

shot

Because the measurement of a qubit in a superposition state is random — the outcome is sometimes 0 and sometimes 1 — you must repeat the measurement multiple times to determine the likelihood that a qubit is in a particular state. When performing the experiment, you will be asked how many shots, or executions, to run in order to determine the qubit state probabilities.

### Simulator

For a quantum computer comprised of a small number of qubits , we can simulate its behavior on a classical computer. In general such a computation requires storing complex numbers, where is the number of qubits. For circuits composed solely of Clifford gates, or circuits generating quantum states that are weakly entangled, special simulation techniques allow for simulating a greater number of qubits.

### Statevector

Any single realization of a quantum system can be described through a complex vector known as its statevector. In a gate-based quantum computer the state of qubits has elements; the dimension of the statevector grows exponentially with.

### Superconducting Quantum Computing

Superconducting quantum computing is an implementation of a quantum computer in superconducting electronic circuits. Research in superconducting quantum computing is conducted by IBM, Google, Rigetti Computing, Microsoft and Intel. The devices are typically designed in the radio-frequency spectrum, cooled down in dilution refrigerators below 100mK and addressed with conventional electronic instruments, e.g. frequency synthesizers and spectrum analyzers. The typical dimensions, of a scale of micrometers, with sub-micrometer resolution, allow a convenient design of a quantum Hamiltonian with the well-established integrated circuit technology.

### Superposition

A superposition in quantum mechanics is a weighted sum, or linear combination, of two or more quantum states. A quantum computer with qubits can exist in a superposition of all of its computational basis states , through . Exploiting this ability is fundamental to most quantum algorithms.

### Transpilation

Transpilation is the process where a quantum circuit is transformed into a new quantum circuit that performs the same task, but is restructured to be compatible with the physical layout of a particular quantum system and, where possible, optimize its performance.

### Teleportation

Quantum teleportation is a method to send qubits using entanglement. Teleportation works as follows: first Alice and Bob need to establish an entangled pair of qubits between them. Alice then takes the qubit that she wants to send and the qubit that is entangled with Bob’s qubit and performs a measurement on them. This measurement collapses the qubits and destroys the entanglement, but gives her two classical outcomes in the form of two classical bits. Alice takes this two classical bits and sends them over the classical Internet to Bob. Bob then applies a correction operation that depends on these two classical bits to his qubit. This allows him to recover the qubit that was originally in Alice’s possession. Note that we have now transmitted a qubit without really using a physical carrier

that is capable of transmitting qubits. But of course you already need entanglement to do this. It is also important to note that quantum teleportation does not allow for faster than light communication. This is so because Bob cannot make sense of the qubit in her possession before he gets the classical measurement outcomes from Alice. These classical measurement outcomes must take a certain amount of time to be transmitted. And this time is lower bounded by the speed of light.

### Topological Quantum Computing

A topological quantum computer is a theoretical quantum computer that employs two-dimensional quasiparticles called anyons, whose world lines pass around one another to form braids in a three-dimensional spacetime (i.e., one temporal plus two spatial dimensions). These braids form the logic gates that make up the computer. The advantage of a quantum computer based on quantum braids over using trapped quantum particles is that the former is much more stable. Small, cumulative perturbations can cause quantum states to decohere and introduce errors in the computation, but such small perturbations do not change the braids’ topological properties. This is like the effort required to cut a string and reattach the ends to form a different braid, as opposed to a ball (representing an ordinary quantum particle in four-dimensional spacetime) bumping into a wall. Alexei Kitaev proposed topological quantum computation in 1997.

### Uncertainty principle

In quantum physics, we cannot simultaneously know two non-commuting variables (like the position and momentum of a particle). This implies that a quantum system in a perfectly definite state can be certain under one measurement and completely random under another. Moreover, if a quantum system starts out in an arbitrary unknown state, no measurement can reveal complete information about that state; the more information the measurement reveals, the more the state is disturbed. This is a underlying principle of quantum cryptography.

### Universal fault-tolerant quantum computer

A universal fault-tolerant quantum computer is the grand challenge of quantum computing. It is a device that can properly perform universal quantum operations using unreliable components. See also universal quantum computer.

### Universal Quantum Computer

A Quantum Turing machine (QTM), also a universal quantum computer, is an abstract machine used to model the effect of a quantum computer. It provides a very simple model which captures all of the power of quantum computation. Any quantum algorithm can be expressed formally as a particular quantum Turing machine. Such Turing machines were first proposed in a 1985 article written by Oxford University physicist David Deutsch suggesting quantum gates could function in a similar fashion to traditional digital computing binary logic gates. Quantum Turing machines are not always used for analyzing quantum computation; the quantum circuit is a more common model. These models are computationally equivalent.

## Q&A

#### Why a Digital Annealer?

Digital circuit design inspired by quantum phenomena 8192-bit full connectivity, allowing all bits to freely exchange signals, in order to solve large-scale problems Inter-bit coupling, providing 64-bit(264) gradations and extreme accuracy in comparison to all traditional quantum technology in the market today operates at room temperature versus absolute zero(-273.15°C) which is typically required for quantum computing solutions that integrates seamlessly into standard data center operating environments without the need for specific expertise or complex infrastructure.

#### Combinatorial Optimization Problems?

Combinatorial optimization refers to finding the optimal solution from a finite set of options. However, as the finite set of options increases, the computational power and the time needed to find the solution increases exponentially. For example, in the case of the ‘traveling salesman problem’ if the salesman must travel to 30 cities, then it will take the most powerful classical computer on the market today approximately 800 million years to find the shortest possible route. Using Digital Annealer, these types of problems can now be solved in less than a second. It is an extraordinary opportunity to optimize and innovate within your business environment.

#### Do business leaders believe the Digital Annealer has the potential to accelerate their journey to a Q-future?

#### When will Quantum Computing become a reality?

Technology companies and academia have spent the last decade laying the groundwork through research initiatives, which are now resulting in successful lab demonstrations of systems and simulations involving multiple Qubits. However, there is still some way to go before these evolve into commercially ready solutions.

#### When do business executives expect Quantum Computing to be ready for business use?

The majority of participants in the study believe that quantum computing won’t become a force in the business world for several years or even decades. A quarter expect it to come into play between five to 10 years, with 50% looking at a window of opportunity of between 10 and 20 years. It is executives in the transport sector who are most optimistic about a shorter-term impact, with 22% of business leaders anticipating qauantum to be business ready within five years. The study also explored how quickly business leaders expected to be actively using Quantum Computing. As we saw earlier, a relatively small proportion is currently considering whether Quantum can add value for them, and an even smaller group (17%) believes it will have live engagements running by 2025

#### How many business leaders expect to be using Quantum Computing in their business within five years?

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