Quantum Computing Key Concepts

Pi Pulse

An electromagnetic pulse that rotates the state of a qubit, usually represented on a bloch sphere

Oracles

In complexity theory, this term refers to an abstract or unknown machine used to study decision problems. It originated with the idea of the Turing machine.

Bloch Sphere

In quantum mechanics, this is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit)

Quantum Circuit Model

Initialize input bits, compute logical operations, output results of computation, measure output User interface -> program instructions -> superposition state -> collapse state to answer amplitude -> output binary data back to user

Classical Circuit Model

Initialize input bits, compute logical operations, output results of computation, measure output. User interface -> program instructions -> controller -> computer -> output data back to user

Dirac Notation

The ubiquitous style of notation used in quantum mechanics, also known as braket notation

Randomized Benchmarking

This QCVV (quantum characterization, verification, and validation) technique helps show us gate fidelity and other quantum performance KPIs. It consists of a long sequence of repeated target gates interspersed with random other gates (used to randomize error seen in target gate), in order to mitigate imperfect state preparation.

Gate Set Tomography

This QCVV (quantum characterization, verification, and validation) technique helps show us gate fidelity and other quantum performance KPIs. It provides 'process maps' (operator descriptions of both gate and error) descriptions of quantum gates.

Q#

This is a Quantum programming language developed by Microsoft; often used for Simulation

QASM

This is a Quantum programming language with a visual interface, best known for its use by IBM

Euclidean space

This is a name for the fundamental space of classical geometry

Superconducting Qubits

This qubit modality is made of artificial electrical circuits that behave like atoms. They have very fast gate times, but less than ideal coherence times. "QISKIT" is a common control software language for these qubits.

Josephson junction

A device consisting of two pieces of superconductor separated by a very thin layer of insulator. The current through this device can be controlled to provide very fast low-power switching.

Universal Gate Set

A finite set of logical operation gates that can approximate any unitary matrix arbitrarily well.

Shor's Algorithm

A polynomial time quantum algorithm for integer factorization. "Given an integer, find its prime factors". This algorithm famously (theoretically) can break RSA encryption in polynomial time; as opposed to the exponential time it would take on a classical computer

Grover's algorithm

A quantum algorithm that finds with high probability the unique input of an unknown function that produces a particular output value. This algorithm achieves a Quadratic speedup; i.e. it can do in n^64 iterations what a classical computer would need n^128 iterations to do.

Quantum Simulation

A quantum algorithm that mimics the behavior of a complex physical, chemical, or biological process. This class of algorithm has proven quantum speedup, in many cases.

Quantum Annealing

A qubit system specifically designed to find the lowest possible energy state, in order to solve an optimization problem

Gate Fidelity

A rigorous measure of how closely our actual gate operation matches the theoretically ideal version of that operation

Quantum Key Distribution

A secure communication method that implements a cryptographic protocol involving quantum objects. It enables two parties to produce a shared random secret code known only by them to decrypt and encrypt information.

Deutsch-Jozsa Algorithm

A simple algorithm that proofs exponential speedup over a classical algorithm. By utilizing an H gate that sets a "Data" and "Helper" qubit in a superposition state of all possible outcomes; this algorithm can do in one step what a classical algorithm would need N (# of data bits) to do.

Quantum Emulation

A system in which qubits are designed to mimic a system's behavior in the way that they connect to one another, and the strengths of those connections. This type of qubit system is done using neutral atoms and is best for mimicing condensed matter.

Quantum Error Correction

A system that mitigates the effects of decoherence and quantum noise by creating highly entangled 'spreads' of information (not exact copies, due to no-cloning theorem) to multiple other qubits

Quantum Machine Learning

A way to improve computational speed and data storage in conjunction with algorithms processing large amounts of data

NP-Hard

An algorithm in this time complexity class can only be solved if there is an NP-complete algorithm that can check the NP-hard problem for correctness in polynomial time (unlikely as this would mean P=NP). Problems of this class are "at least as hard as the hardest problems in NP".

Polynomial Time (P)

An algorithm in this time complexity class has a solution solve time bounded by a polynomial function, like n^2

NP-Complete

An algorithm in this time complexity class has a solution solve time bounded by an exponential function, but the solution can be checked for correctness by an algorithm that is polynomial in input size

Nondeterministic Polynomial Time (NP)

An algorithm in this time complexity class has a solution solve time bounded by an exponential function, like 2^N

Schrodinger's Cat

An easy way to understand "superposition". An arbitrary animal being considered (according to quantum mechanics) to be simultaneously both dead and alive until the box it sits in is opened and observed

DiVincenzo Criteria (Communication)

For quantum communication: 1. The ability to interconvert stationary and flying qubits 2. The ability to faithfully transmit flying qubits between specified locations

Quantum Dot

Human-made nanoparticles that have semiconductor properties

Stationary & Flying Qubits

In quantum communication, one of these is used for storing information and performing calculations while the other is used for propagating information between longer distances

Quantum Teleportation

The instantaneous transfer of information (quantum state) from one quantum system to another across a distance without physical contact; because the particles are entangled.

Qubit Coherence

The mean time to failure for a bit; in other words, a metric that quantifies the robustness of a qubit, or, 'the amount of time, on average, that a qubit's state is maintained, before the quantum state is lost.

Gate Time

The quantum version of 'clock speed'. This metric tells us the number of gate operations that can be implemented on a qubit, before an error occurs.

DiVincenzo Criteria (Computing)

The seven conditions necessary to achieve quantum computation For quantum computing: 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

Decoherence

There are two ways for this "loss of information" to occur; one being environmental noise (a bloch vector shifting away from its intended position), the other being 'dephasing', or loss of energy until the qubit falls back into its ground state (the north pole)

Monte Carlo Method

This broad class of algorithms rely on repeated random sampling to obtain results. Randomness is used to solve problems that MIGHT be deterministic in principle.

Quantum Communication

This is a field of applied quantum physics closely related to quantum information processing and quantum teleportation. Its most interesting application is protecting information channels against eavesdropping by means of quantum cryptography. The most well known and developed application of quantum cryptography is quantum key distribution (QKD). QKD describes the use of quantum mechanical effects to perform cryptographic tasks or to break cryptographic systems. The principle of operation of a QKD system is quite straightforward: two parties (Alice and Bob) use single photons that are randomly polarized to states representing ones and zeroes to transmit a series of random number sequences that are used as keys in cryptographic communications.

Hilbert Space

This is a name for a vector space with an 'inner product', or an operation that allows for definitive lengths and angles.

Qiskit

This is an open source software development kit (SDK) developed by IBM; often used for collaborative Quantum Algorithm development and education

Superposition

This is when a quantum object exists in two states at the same time. The 'probability' of a state manifesting upon observation is called an amplitude. They can be complex numbers.

AFRL (Air Force Research Lab)

This military lab recently designed a quantum integrated photonics processor

Superdense Coding

This occurs in quantum communication when two classical bits of information (00, 01, 10, or 11) are transmitted from a sender to a receiver; under the assumption that both parties pre-shared an entangled state.

Quantum Advantage

This occurs when a quantum computer can definitively compute something at a faster rate than a classical computer as complexity scales up

Quantum Enhancement

This occurs when quantum computing is used to speed up a specific operation or operations within a hybrid classical algorithm or set of operations

Quantum Parallelism

This phenomena is multiple possible combinations of probability amplitudes exist in a superposition all at the same time; and when pulses (gates) are applied, amplitudes in all these states change simultaneously . In other words, a quantum "memory register" (information) can exist in a superposition of multiple base states at once.

Quantum interference

This phenomenon results from the superposition of multiple possible quantum states, and allows us to bias the measurement of a qubit towards a desired set of states.

Electron Spins

This qubit modality can be trapped in a 'quantum dot', which can be made out of existing silicon fabrication materials

Nuclear Spins

This qubit modality can be trapped within the nitrogen vacancy center of a daimond, and has long coherence times but slow gate times.

Photonics

This qubit modality is also known as linear optics, where the presence or absence of a photon constitutes a qubit and beam splitters, phase shifters, and mirrors are used as gates.

Trapped Ions

This qubit modality is similar to an atomic clock, and has very high gate fidelity. This modality satisfies 4 of the 5 QC DiVincenzo criteria; its only major challenge is scalable physical systems (3D integration). "ARTIQ" is a common control software language for these qubits.

No Cloning Theorem

This rule in physics states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state.

probability amplitude

a complex number used to describe the behavior of a quantum system; in the case of QC, this is the likelihood of the quantum object landing in a certain state once observed. the square of this amplitude is the probability.

Vector

a quantity that has magnitude and direction

Scalar

a quantity that has magnitude but no direction

Matrix

a rectangular arrangement of numbers in rows and columns, to which operations like addition and multiplication can be applied

Turing machine

a very simple model of computation that is used in theoretical computer science to explore computability of problems

Qubit

any quantum object (atom, ion, photon, electron, etc) that can exist as a two-state quantum-mechanical system capable of superposition, interference, parallelism, and entanglement

Heisenberg's uncertainty principle

it is impossible to know exactly both the velocity and the position of a particle at the same time

Fault Tolerance

the ability for a system to respond to unexpected failures or system crashes as the backup system immediately and automatically takes over with no loss of accuracy

quantum entanglement

the unusual behavior of elementary particles where they become linked so that when something happens to one, something happens to the other; no matter how far apart they are.