# What Are Quantum Effects and How Do They Enable Quantum Information Science?

The *quantum effects* of physics are at the atomic and subatomic level, brought to us courtesy of *quantum mechanics*, and hold the key to major advances — *quantum* leaps — in computing, communication, measurement, and sensing, known collectively as *quantum information science*. This informal paper is not intended for physicists, but for computer scientists, software developers, and other non-physicists who wish to become involved with quantum information science, particularly *quantum computing*, and have a need (or desire) to know *something* about the underlying physics, particularly enough to understand what makes quantum information science tick, but nowhere near as much as a physicist or hard-core quantum engineer might need.

We need a lot more computing power to tackle much larger and much more complex computing challenges in the decades ahead. Ditto for communication, measurement, and sensing. That’s where *quantum effects* come in. *Quantum information science* is the broad umbrella for the theory, science, engineering, technology, infrastructure, and applications related to exploiting quantum effects (quantum mechanics) in the areas of computing, communication, and measurement and sensing.

*Quantum information science* is based on any aspect of *quantum effects* which can be observed, measured, controlled, stored, or communicated in some manner.

This informal paper will focus primarily on quantum effects alone and how they enable quantum information science, but won’t delve deeply into the various areas of quantum information science itself, such as quantum computing and quantum communication. For a broad summary of quantum information science overall, see:

This informal paper was created from material which was originally in that paper but extracted to become a standalone paper and expanded somewhat.

Here’s are the topics covered in the remainder of this paper:

- What’s so special about quantum information science?
- What is quantum?
- Quantum mechanics
- Quantum physics
- Quantum chemistry
- Quantum computational chemistry
- Quantum biology
- Quantum field theory
- Quantum theory
- Quantum system
- Isolated quantum system
- Quantum effects
- Quantum resource
- Quantum state
- Wave function
- Linear algebra
- Quantum information
- Quantum bit — qubit
- Stationary, flying, and shuttling qubits
- Measurement / observation
- Observable
- Quantum phenomena
- Macroscopic quantum phenomena

Here are the quantum effects that will be described by this paper — not in any great detail, but simply to give the more casual reader a flavor of what quantum effects are all about:

- Discrete
- Quanta
- Particle and wave duality
- Probabilistic
- Uncertainty
- Superposition
- Schrödinger’s cat
- Cat state
- Entanglement
- Spooky action at a distance
- Bell’s theorem and Bell’s inequality
- Bell states
- Phase
- Interference
- Wave function
- Density matrix or density operator
- Probability amplitude
- Unitarity principle
- Basis state
- Computational basis state
- Quantum state
- State vector
- Collapse of wave function on measurement
- Measurement
- No-cloning theorem
- Hamiltonian
- Schrödinger’s equation
- Time evolution
- Fermi-Dirac statistics
- Bose-Einstein statistics
- Fermions
- Bosons
- Pauli exclusion principle
- Spin
- Integer spin
- Half-spin or half-integer spin or spin 1/2
- Spin up and spin down
- Cooper pairs
- Superconductivity and superfluidity
- Tunneling
- Josephson effect
- Quantum hall effect
- Macroscopic quantum effects
- Zero-point energy and vacuum fluctuations

**What’s so special about quantum information science?**

There are three **key advantages** of quantum information science over classical methods:

*Quantum computing*offers**much greater performance**than classical computing through*quantum parallelism*which offers an**exponential speedup**— evaluating many (all) possibilities in parallel, in a single calculation.*Quantum communication*offers**inherent security**through*quantum entanglement*— also known as*spooky action at a distance*, in contrast to security as a problematic afterthought for classical communication and networking.*Quantum metrology and quantum sensing*offer**much greater accuracy and precision**for measurements of physical quantities and detection of objects.

All of these advantages are made possible by the magic of *quantum effects* enabled by *quantum mechanics*.

**What is quantum?**

*Quantum* is essentially a reference to *quantum mechanics*, which concerns itself with atomic and subatomic particles, their energy, their motion, and their interaction.

Larger accumulations of atoms and molecules behave in more of a *statistical* or *aggregate* manner, where the quantum mechanical properties (*quantum effects*) get averaged away. Quantum information science and its subfields focus at the quantum mechanical level where the special features of quantum mechanics (*quantum effects*) are visible and can be exploited and manipulated.

**Quantum mechanics**

*Quantum mechanics* is the field of *physics* which is the theoretical foundation of *quantum information science*. This paper won’t delve deeply into the concepts of quantum mechanics — see the Wikipedia ** Quantum mechanics** article for more detail.

The key elements of quantum mechanics are what are known as *quantum effects*, summarized below.

**Quantum physics**

*Quantum physics* is sometimes used merely as a synonym for *quantum mechanics*, but technically *quantum physics* is the application to the principles of *quantum mechanics* to the many areas of *physics* at the subatomic, atomic, and molecular level, including the behavior of particles and waves in magnetic and electrical fields.

**Quantum chemistry**

*Quantum chemistry* is the application of *quantum mechanics* to *chemistry*, particularly for the behavior of *electrons*, including excited atoms, molecules, and chemical reactions.

Applying *classical computing to *quantum chemistry is referred to as *computational chemistry*.

**Quantum computational chemistry**

Applying *quantum computing* to *quantum chemistry* is referred to as quantum computational chemistry (and here).

**Quantum biology**

*Quantum biology* is the application of *quantum mechanics* to *biology*, particularly for the behavior of *electrons* in complex, organic molecules, such as how organic molecules form, how they can change, how they can decompose, and even how they can fold.

**Quantum field theory**

*Quantum field theory* is the part of *quantum mechanics* concerned with subatomic particles and their interactions, but it is not necessary to dive down to that level of detail to comprehend *quantum information science*. For more information, see the Wikipedia ** Quantum field theory** article.

**Quantum theory**

*Quantum theory* is not technically a proper term. Used loosely, it commonly refers to *quantum mechanics* or possibly simply to *quantum effects*.

**Quantum system**

A *quantum system*, or more properly an *isolated quantum system*, is a particle or wave, or collection of particles and waves, which can be analyzed for its *quantum effects* as if it were a *single, discrete object*.

**Isolated quantum system**

Technically, any *quantum system* is an *isolated quantum system*. The emphasis is on the fact that the particles and waves within the system can be analyzed and modeled in isolation, without concern for particles and waves outside of the system. That’s the theory. In practice, no system is truly isolated (except maybe the entire universe as a whole), but the *assumption* of *isolation* dramatically simplifies understanding, modeling, and computation of the system. Without the concept of an isolated quantum system, the modeling and mathematics would be too complex to be tractable (workable.)

Each *qubit* of a *quantum computer* or a *quantum communication network* is an *isolated quantum system*, except when it is *entangled* with other qubits, in which case the entangled qubits collectively constitute a larger *isolated quantum system*.

**Quantum effects**

*Quantum mechanics* — and hence all of *quantum information science* and its subfields — is based on *quantum effects*.

A *quantum effect* is any phenomenon which cannot be fully explained by *classical mechanics* — quantum mechanics is required.

Quantum information science is based on any aspect of quantum effects which can be observed, measured, controlled, stored, or communicated in some manner.

Some quantum effects cannot be directly observed or measured, but can sometimes be indirectly inferred or at least have some ultimate effect on the results of manipulating a *quantum system*.

Quantum effects and their properties include:

**Discrete**rather than continuous values for physical quantities.**Quanta**for discrete values. The unit for discrete values. Technically,*quantum*is a singular unit and*quanta*is the plural of quantum (just as with*data*and*datum*.)**Particle and wave duality.**Particles have wave properties and behavior, and waves have particle properties and behavior. For example, a photon can act as a particle as well as a wave, and an electron can act as a wave as well as a particle.**Probabilistic**rather than strictly deterministic behavior.**Uncertainty**of exact value or measurement. More than just uncertainty of any measurement, there is uncertainty in the actual value of any property, as a fundamental principle of quantum mechanics. A given property of a given quantum system may have a range of values, even before the property is measured. For example, a particle or wave can be at two — or more — positions at the same moment of time.**Superposition**of states — a quantum system can be in two quantum states at the same time. See*spin up and spin down*.**Schrödinger’s cat**— a thought experiment which demonstrates*superposition*— the cat can be both alive and dead at the same time.**Cat state**— alternate name for*superposition*of two*quantum states*. A tribute to*Schrödinger’s cat*.**Entanglement**— the same quantum state can exist at two physically separated locations at the same time.**Spooky action at a distance**— popular reference to*entanglement*.**Bell’s theorem and Bell’s inequality**— quantum mechanics cannot be explained simply by adding “hidden variables” to classical mechanics.**Bell states**— the various combinations of quantum states for two entangled particles. The quantum states of the two particles are*correlated*— they may be identical quantum states, but they don’t have to be identical. Measuring the state of one particle will allow the observer to infer the state of the other particle. This is useful for both quantum computing and quantum communication.**Phase**— the complex or imaginary part of the*probability amplitude*of a*quantum state*. The notion of cyclical or periodic behavior or a fraction of a single cycle of a wave or circle. Measured either in*radians*(two pi radians in a circle or cycle) or a fraction between 0.0 and 1.0, where 1.0 corresponds to a full, single cycle or circle (two pi radians.)**Interference**— cancellation or reinforcement of the complex or imaginary part of the*probability amplitude*of two*quantum states*(*phases*). Useful for*quantum computing*— it enables*quantum parallelism*. Not to be confused with*environmental interference*which disrupts the operation of a quantum system.**Wave function**is used to fully describe the state of a particle or wave (technically, an*isolated quantum system*) based on the probabilities of*superposed*and*entangled*states. The sum of the*basis states*of the*quantum system*, each weighted by its*probability amplitude*.*Linear algebra*is the notation used to express a*wave function*.**Density matrix or density operator**— an alternative to the wave function for describing the*quantum state*of a*quantum system*.**Probability amplitude**— a*complex number*with both*real*and*imaginary*parts which represents the likelihood of the quantum system being in a particular state, a*basis state*. Square it and then take the square root to get the*probability*for a particular*basis state*. The imaginary part of the probability amplitude is also referred to as its*phase*.**Unitarity principle**— the*probabilities*(square root of the square of the*probability amplitude*) of all possible states of a quantum system must sum to 1.0 by definition.**Basis state**— the actual numeric value of a single*quantum state*, comparable to a binary 0 or 1.**Computational basis state**— the combined*basis states*of a collection of*qubits*. A collection of strings of 0’s and 1’s, each string having a*probability amplitude*as its weight in the*wave function*. Essentially each string is an n-bit binary value.**Quantum state**— the state of an*isolated quantum system*described by its*wave function*. Alternatively, a single*basis state*.**State vector**— a single-column matrix describing the state of a*quantum system*, where each row represents a*computational basis state*and the value in the row represents the*probability amplitude*for that*computational basis state*. For a single qubit there would be two rows, for two qubits there would be four rows, and for k qubits there would be 2^k rows. Commonly referred to as a*ket*, the right hand side of*bra-ket notation*.**Collapse of wave function on measurement**— the probabilities of superposed states will influence but not completely determine the observed value. Measurement*always*causes the wave function of a quantum system to*collapse*— permanently.**Measurement**— the process of*observing*a quantum system. By definition, measurement causes*collapse of the wave function*, and will always produce a single*basis state*(0 or 1) or*computational basis state*(string of 0’s and 1’s) regardless of any*superposition*or*entanglement*which may be defined by the*wave function*of the quantum system.**No-cloning theorem**— quantum information (quantum state) cannot be copied — attempting to read (measure or observe) quantum state causes it (its*wave function*) to collapse to a discrete, non-quantum state.**Hamiltonian**— an equation which expresses the energy of a quantum system.**Schrödinger’s equation**— describes the evolution of the quantum state of a quantum system over time in terms of its*Hamiltonian*and*wave function*.**Time evolution**— how the quantum state of a quantum system incrementally evolves over time based on its*Hamiltonian*and*wave function*. See Schrödinger’s equation.**Fermi-Dirac statistics**— rules for*fermions*which require them to obey or follow the*Pauli exclusion principle*.**Bose-Einstein statistics**— rules for*bosons*which allow them to violate (not follow) the*Pauli exclusion principle*. Sometimes referred to as*BES*.**Fermions**— elementary particles, such as electrons, and atoms which obey*Fermi-Dirac statistics*, including the*Pauli exclusion principle*. Fermions have*half-spin*(*half-integer spin*or*spin 1/2*) by definition. Fermions can collide, bounce apart, or form composite particles, even molecules.**Bosons**— elementary particles, such as photons, and some atoms under special circumstances, which obey or follow*Bose-Einstein statistics*, which permits them to violate (not follow) the*Pauli exclusion principle*. Bosons have*integer-spin*by definition. Bosons can pass right through each other, or even occupy the same position, without interacting.**Pauli exclusion principle**— no two fermions, particles with half-spin, such as electrons and most atoms, can occupy the same quantum state (e.g., position) at the same time. In contrast, bosons, such as photons and pairs of fermions in special circumstances, can occupy the same quantum state (e.g., position) at the same time.**Spin**— the angular momentum, much like a spinning gyroscope, of an elementary particle or an atom.**Integer spin**— the form of angular momentum of bosons which allows them to violate the*Pauli exclusion principle*. Bosons obey or follow*Bose-Einstein statistics*, which allow them to occupy the same quantum state (e.g., position.)**Half-spin**or**half-integer spin**or**spin 1/2**— the form of angular momentum of fermions which requires them to obey or follow the*Pauli exclusion principle*, preventing them from occupying the same quantum state (e.g., position.)**Spin up**and**spin down**—*spin*of a particle can have a*direction of spin*, which is the direction of the*vector*representing the angular momentum, and up and down are the direction of the axis of rotation, based on using the*right-hand rule*, where curled fingers represent the direction of spin and the pointing thumb represents the axis of rotation, pointing either up or down as the thumb points. Spin up and spin down can be used to represent two*basis states*for both quantum computing and quantum communication. Spin up and down for a particle can in fact be*superposed*, so that a particle (e.g., qubit) is in a*linear combination*of both spin up and spin down, corresponding to a linear combination of a 0 and a 1.**Cooper pairs**— electrons can pair up at ultracold temperatures (near*absolute zero*), so that the pair acts as a single*boson*rather than as a pair of fermions since the*half-spin*of each of the two fermions add up to be the*integer spin*of a boson. This allows the pair to violate the*Pauli exclusion principle*, enabling*superconductivity*.**Superconductivity****and****superfluidity**— the phenomenon of*zero resistance*, for electrical conduction and mechanical flow respectively, which occurs at ultracold temperatures (near*absolute zero*), allowing pairs of fermions, such as electrons and helium atoms, to pair up, which transforms the half-spin of each fermion into integral spin for the pair, allowing the pair to act as a boson, which no longer must obey the Pauli exclusion principle, so that the pairs can now occupy the same position, which is permitted for bosons which obey*Bose-Einstein statistics*, but is not possible for fermions alone, which must obey*Fermi-Dirac statistics*.**Tunneling**— the ability of a subatomic particle or wave such as an electron to appear to be able to move through a solid barrier as if it weren’t there. In actuality, quantum mechanics dictates that a particle or wave has a*probability*to be at any given location, so that a particle or wave can have a probability of being at either side of the barrier at a given moment, allowing the particle or wave to appear to skip over or through the barrier in the next moment. An example would be electrons and a*Josephson junction*used in a*superconducting transmon qubit*.**Josephson effect**—*tunneling*of*Cooper pairs*of electrons through an insulating barrier. Used to implement*Josephson junctions*, such as for*superconducting transmon qubits*. Also has applications for quantum sensing and quantum measurement.**Quantum hall effect**— quantized conductance (flow of current or electrons) induced by a magnetic field at very low temperatures. Useful for precise measurements.**Macroscopic quantum effects**— quantum effects which can be observed at the macroscopic scale — above the level of the atomic, subatomic, and molecular scale, such as*superconductivity*,*superfluidity*, and the*quantum hall effect*.**Zero-point energy and vacuum fluctuations**— uncertainty means that even a vacuum is not at absolutely zero energy. A vacuum fluctuates within the range of minimum uncertainty. Although an application to quantum information science is not clear at present, specialized hardware can be used to allow a classical computer to measure the fluctuating zero-point energy of a vacuum to generate true random numbers — which cannot be calculated by a strict Turing machine alone.**Creation and annihilation operators**— primarily to facilitate quantum mechanical modeling of many-particle systems.

**Quantum resource**

A *quantum resource* is any *quantum effect* which has some utility in *quantum information science*, such as for computation in *quantum computing* or representing *quantum information* in *quantum communication*.

It’s an odd term, but sometimes you see it used. Oddly, a *qubit* would not technically be considered a *quantum resource*, but *superposition*, *entanglement*, and *interference* would. See the list of *quantum effects* above.

**Quantum state**

*Quantum state* is the *unit* of *quantum information*.

A particle or wave — referred to as an *isolated quantum system* — has a *quantum state* for each physical quality which can be observed.

- The quantum state is described by a
*wave function*. - The individual possible states are known as
*basis states*. Such as a 0 and a 1. - Each basis state in a wave function occurs with some
*probability*. - A basis state can also have a
*complex*or*imaginary*component, known as a*phase*, which is periodic or cyclical. This is exploited in*quantum computing*to enable*quantum parallelism*using*interference*of the phase of a potentially large number of quantum states. - The probability and phase are combined into a single, complex value, called the
*probability amplitude*, where the probability is the square root of the absolute value (or*modulus*) of the complex number. - The
*basis states*and their*probability amplitudes*are combined to form the*wave function*. - If the probability of a basis state is other than 0.0 or 1.0, the two basis states are
*superposed*. - The quantum states of two separate particles or waves — two isolated quantum systems — can be shared or
*entangled*.

The concept of quantum state applies across all subfields of quantum information science, not just quantum computing and quantum communication.

See the preceding section on *quantum effects* for more detail.

**Wave function**

Each *qubit* or *collection of entangled qubits* has a *quantum state* which is described by a *wave function* using *linear algebra* to detail each of the *basis states* and its *probability amplitude*.

**Linear algebra**

*Linear algebra* is the notation used to express a *wave function* in terms of *basis states* and *probability amplitudes*. It’s complex math (figuratively and literally), and not for the faint of heart.

**Quantum information**

*Classical information (*a sequence or collection of *bits)* is represented as *quantum information* in the form of a *quantum state*, one *quantum state* for each *classical bit*.

*Quantum state* is the *unit* of *quantum information*.

To be clear, quantum information can represent more than just a 0 or 1 classical bit. Since it is a *quantum state*, it may include a superposition of both a 0 and a 1. The probabilities of 0 and 1 may differ (but they have to add up to 1.0). The probability can include a phase component, and a quantum state may be entangled or shared between two or more separate, otherwise-isolated quantum systems (particles or waves.)

The concept of quantum information applies across all subfields of quantum information science, not just quantum computing and quantum communication.

**Quantum bit — qubit**

A *quantum bit* or *qubit* is the *unit* of *storage* and *manipulation* of *quantum information* (*quantum states*).

Qubits are used for both quantum computing and quantum communication.

Despite popular misconceptions, a qubit is not the quantum equivalent of classical information or the classical bit. Rather, a qubit is a *device* for *storing and manipulating quantum information*, not the quantum information itself, which is represented as the quantum state of the device. In classical computing and classical communication a bit is the abstract information, not the physical representation.

A bit is either a 0 or a 1, regardless of whether that 0 or 1 is represented as a voltage level, a magnetic field, a photon, or a punched hole.

Quantum information is a 0 or a 1 or a linear combination of a 0 and a 1, regardless of the technology used to implement the qubit device which holds and manipulates that quantum information (quantum state.)

**Stationary, flying, and shuttling qubits**

For quantum computing, generally a qubit is a *stationary qubit*, which is a hardware device which stores and manipulates *quantum information*. It is stationary, meaning that the device does not move.

For quantum communication, a qubit is a *flying qubit*, typically a photon which gains its utility or ability to communicate by being moveable to a remote location while it is in an *entangled state* with another qubit at a different and possibly very distant location.

A *trapped-ion quantum computer* may use *shuttling* to move a qubit — an ion or atom with a net charge — a short distance so that it is easier to manipulate and measure the quantum state of the qubit, and to store more qubits than can be directly controlled or measured directly.

**Measurement / observation**

*Quantum state* is not directly observable or directly measurable using normal, non-quantum methods, devices, or instruments. We can indeed measure any *quantum information* we want, but measuring a quantum state has the effect of *collapsing the wave function* of that quantum state, eliminating the truly quantum-ness of the state (e.g., superposition, entanglement, and interference or phase), leaving the quantum information in a purely classical state, such as the 0 and 1 of classical information.

These aspects of measurement apply across all of the subfields of quantum information science — quantum computing, quantum communication, and quantum metrology and sensing.

**Observable**

Any *quantum effect* which can be *observed* or *measured* is referred to as an *observable*.

Generally, the *quantum state* is the quantum effect which is the observable.

**Quantum phenomena**

*Quantum phenomenon* is a vague term which is loosely a synonym for *quantum effect*, or any phenomenon in which a quantum effect is observable in some way, including *macroscopic quantum phenomena*.

**Macroscopic quantum phenomena**

A *macroscopic quantum phenomenon* is any phenomenon above the level of the atomic, subatomic, and molecular level in which a *quantum effect* is observable in some way.

Prime examples are *superconductivity*, *superfluidity*, and the *quantum hall effect*.

# Additional phenomena to consider

I need to dive deeper into these phenomena to figure out how they might be integrated here, especially with regard to quantum information science:

- The quantum hypothesis — in general. Historical role in transitioning from the classical world to the quantum world.
- Momentum, angular momentum, orbital momentum.
- Pure state, mixed state, density matrix, density operator.
- Wave packets.
- Nuclear magnetic resonance (NMR). Some early efforts in quantum computing relied on NMR.
- Nuclear electric resonance.
- Gravity. Nominally lies in the realm of General Relativity rather than quantum mechanics, but… who knows for sure. Can a quantum computer be used to accurately simulate or model gravity and gravitational effects, including effects on time and space?

# Conclusion

*Quantum information science* is based on any aspect of *quantum effects* which can be observed, measured, controlled, stored, or communicated in some manner.

Quantum effects enable the capabilities of quantum computing, quantum communication, and quantum sensing and measurement.

For more information about those capabilities and a broad summary of quantum information science overall, see:

# Alternative titles

I had difficulty deciding on a good title for this informal paper. These alternatives would have been equally good titles:

- Quantum effects
- Quantum effects for quantum computing
- Quantum effects for quantum information science
- What are quantum effects?
- Superficial introduction to quantum effects for non-physicists
- What are quantum effects and how do they relate to quantum computing?
- What are quantum effects and how do they relate to quantum information science?
- Quantum effects — The magic sauce which enables quantum information science
- Quantum effects — The magic sauce which enables quantum computing
- What are Quantum effects and how do they enable quantum information science?

For more of my writing: ** List of My Papers on Quantum Computing**.