# Quantum bus

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A quantum bus is a device which can be used to store or transfer information between independent qubits in a quantum computer, or combine two qubits into a superposition. It is the quantum analog of a classical bus.

The superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. So that if input A produces response X and input B produces response Y then input produces response.

Quantum mechanics, including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.

In computer architecture, a bus is a communication system that transfers data between components inside a computer, or between computers. This expression covers all related hardware components and software, including communication protocols.

## History

The concept was first demonstrated by researchers at Yale University and the National Institute of Standards and Technology (NIST) in 2007. [1] [2] [3] Prior to this experimental demonstration, the quantum bus had been described by scientists at NIST as one of the possible cornerstone building blocks in quantum computing architectures. [4]

Yale University is a private Ivy League research university in New Haven, Connecticut. Founded in 1701, it is the third-oldest institution of higher education in the United States and one of the nine Colonial Colleges chartered before the American Revolution. Yale consistently ranks among the top universities in the world.

The National Institute of Standards and Technology (NIST) is a physical sciences laboratory, and a non-regulatory agency of the United States Department of Commerce. Its mission is to promote innovation and industrial competitiveness. NIST's activities are organized into laboratory programs that include nanoscale science and technology, engineering, information technology, neutron research, material measurement, and physical measurement.

Quantum computing is the use of quantum-mechanical phenomena such as superposition and entanglement to perform computation. A quantum computer is used to perform such computation, which can be implemented theoretically or physically.

## Mathematical Description

A quantum bus for superconducting qubits can be built with a resonance cavity. The hamiltonian for a system with qubit A, qubit B, and the resonance cavity or quantum bus connecting the two is ${\displaystyle {\hat {H}}={\hat {H}}_{r}+\sum \limits _{j=A,B}{\hat {H}}_{j}+\sum \limits _{j=A,B}hg_{i}\left({\hat {a}}^{\dagger }{\hat {\sigma }}_{-}^{j}+{\hat {a}}{\hat {\sigma }}_{\text{+}}^{j}\right)}$ where ${\displaystyle {\hat {H}}={\frac {1}{2}}\hbar \omega _{j}{\hat {\sigma }}_{+}^{j}{\hat {\sigma }}_{-}^{j}}$ is the single qubit hamiltonian, ${\displaystyle {\hat {\sigma }}_{+}^{j}{\hat {\sigma }}_{-}^{j}}$ is the raising or lowering operator for creating or destroying excitations in the ${\displaystyle j}$th qubit, and ${\displaystyle \hbar \omega _{j}}$ is controlled by the amplitude of the D.C. and radio frequency flux bias. [5]

Superconducting quantum computing is an implementation of a quantum computer in superconducting electronic circuits. Research in superconducting quantum computing is conducted by Google, IBM, BBN Technologies, Rigetti, and Intel. as of May 2016, up to nine fully controllable qubits are demonstrated in a 1D array, up to sixteen in a 2D architecture.

In quantum mechanics, a Hamiltonian is an operator corresponding to the sum of the kinetic energies plus the potential energies for all the particles in the system. It is usually denoted by , but also or to highlight its function as an operator. Its spectrum is the set of possible outcomes when one measures the total energy of a system. Because of its close relation to the time-evolution of a system, it is of fundamental importance in most formulations of quantum theory.

Direct current (DC) is the unidirectional flow of an electric charge. A battery is a prime example of DC power. Direct current may flow through a conductor such as a wire, but can also flow through semiconductors, insulators, or even through a vacuum as in electron or ion beams. The electric current flows in a constant direction, distinguishing it from alternating current (AC). A term formerly used for this type of current was galvanic current.

## Related Research Articles

Quantum teleportation is a process in which quantum information can be transmitted from one location to another, with the help of classical communication and previously shared quantum entanglement between the sending and receiving location. Because it depends on classical communication, which can proceed no faster than the speed of light, it cannot be used for faster-than-light transport or communication of classical bits. While it has proven possible to teleport one or more qubits of information between two (entangled) quanta, this has not yet been achieved between anything larger than molecules.

In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables or canonically conjugate variables such as position x and momentum p, can be known or, depending on interpretation, to what extent such conjugate properties maintain their approximate meaning, as the mathematical framework of quantum physics does not support the notion of simultaneously well-defined conjugate properties expressed by a single value.

The Unruh effect is the prediction that an accelerating observer will observe blackbody radiation where an inertial observer would observe none. In other words, the background appears to be warm from an accelerating reference frame; in layman's terms, a thermometer waved around in empty space, subtracting any other contribution to its temperature, will record a non-zero temperature. For a uniformly accelerating observer, the ground state of an inertial observer is seen as in thermodynamic equilibrium with a non-zero temperature.

Quantum error correction (QEC) is used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is essential if one is to achieve fault-tolerant quantum computation that can deal not only with noise on stored quantum information, but also with faulty quantum gates, faulty quantum preparation, and faulty measurements.

In quantum mechanics, a two-state system is a quantum system that can exist in any quantum superposition of two independent quantum states. The Hilbert space describing such a system is two-dimensional. Therefore, a complete basis spanning the space will consist of two independent states. Any two-state system can also be seen as a qubit.

A trapped ion quantum computer is one proposed approach to a large-scale quantum computer. Ions, or charged atomic particles, can be confined and suspended in free space using electromagnetic fields. Qubits are stored in stable electronic states of each ion, and quantum information can be transferred through the collective quantized motion of the ions in a shared trap. Lasers are applied to induce coupling between the qubit states or coupling between the internal qubit states and the external motional states.

Quantum networks form an important element of quantum computing and quantum communication systems. Quantum networks facilitate the transmission of information in the form of quantum bits, also called qubits, between physically separated quantum processors. A quantum processor is a small quantum computer being able to perform quantum logic gates on a certain number of qubits. Quantum networks work in a similar way to classical networks. The main difference, as will be detailed more in later paragraphs, is that quantum networking like quantum computing is better at solving certain problems, such as modeling quantum systems.

The Jaynes–Cummings model is a theoretical model in quantum optics. It describes the system of a two-level atom interacting with a quantized mode of an optical cavity, with or without the presence of light. It was originally developed to study the interaction of atoms with the quantized electromagnetic field in order to investigate the phenomena of spontaneous emission and absorption of photons in a cavity.

The one-way or measurement based quantum computer (MBQC) is a method of quantum computing that first prepares an entangled resource state, usually a cluster state or graph state, then performs single qubit measurements on it. It is "one-way" because the resource state is destroyed by the measurements.

In quantum information and quantum computing, a cluster state is a type of highly entangled state of multiple qubits. Cluster states are generated in lattices of qubits with Ising type interactions. A cluster C is a connected subset of a d-dimensional lattice, and a cluster state is a pure state of the qubits located on C. They are different from other types of entangled states such as GHZ states or W states in that it is more difficult to eliminate quantum entanglement in the case of cluster states. Another way of thinking of cluster states is as a particular instance of graph states, where the underlying graph is a connected subset of a d-dimensional lattice. Cluster states are especially useful in the context of the one-way quantum computer. For a comprehensible introduction to the topic see.

Adiabatic quantum computation (AQC) is a form of quantum computing which relies on the adiabatic theorem to do calculations and is closely related to, and may be regarded as a subclass of, quantum annealing.

In quantum information science, the concurrence is a state invariant involving qubits.

Circuit quantum electrodynamics provides a means of studying the fundamental interaction between light and matter. As in the field of cavity quantum electrodynamics, a single photon within a single mode cavity coherently couples to a quantum object (atom). In contrast to cavity QED, the photon is stored in a one-dimensional on-chip resonator and the quantum object is no natural atom but an artificial one. These artificial atoms usually are mesoscopic devices which exhibit an atom-like energy spectrum. The field of circuit QED is a prominent example for quantum information processing and a promising candidate for future quantum computation.

The Jaynes-Cummings-Hubbard (JCH) model is a many-body quantum system modeling the quantum phase transition of light. As the name suggests, the Jayne-Cummings-Hubbard model is a variant on the Jaynes–Cummings model; a one-dimensional JCH model consists of a chain of N coupled single-mode cavities, each with a two-level atom. Unlike in the competing Bose-Hubbard model, Jayne-Cummings-Hubbard dynamics depend on photonic and atomic degrees of freedom and hence require strong-coupling theory for treatment. One method for realizing an experimental model of the system uses circularly-linked superconducting qubits.

In quantum optics, a superradiant phase transition is a phase transition that occurs in a collection of fluorescent emitters, between a state containing few electromagnetic excitations and a superradiant state with many electromagnetic excitations trapped inside the emitters. The superradiant state is made thermodynamically favorable by having strong, coherent interactions between the emitters.

Coplanar waveguide is a type of electrical planar transmission line which can be fabricated using printed circuit board technology, and is used to convey microwave-frequency signals. On a smaller scale, coplanar waveguide transmission lines are also built into monolithic microwave integrated circuits. Conventional coplanar waveguide (CPW) consists of a single conducting track printed onto a dielectric substrate, together with a pair of return conductors, one to either side of the track. All three conductors are on the same side of the substrate, and hence are coplanar. The return conductors are separated from the central track by a small gap, which has an unvarying width along the length of the line. Away from the central conductor, the return conductors usually extend to an indefinite but large distance, so that each is notionally a semi-infinite plane.

Linear Optical Quantum Computing or Linear Optics Quantum Computation (LOQC) is a paradigm of quantum computation, allowing universal quantum computation. LOQC uses photons as information carriers, mainly uses linear optical elements to process quantum information, and uses photon detectors and quantum memories to detect and store quantum information.

The KLM scheme or KLM protocol is an implementation of linear optical quantum computing (LOQC), developed in 2000 by Knill, Laflamme and Milburn. This protocol makes it possible to create universal quantum computers solely with linear optical tools. The KLM protocol uses linear optical elements, single photon sources and photon detectors as resources to construct a quantum computation scheme involving only ancilla resources, quantum teleportations and error corrections.

## References

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