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:

  1. What’s so special about quantum information science?
  2. What is quantum?
  3. Quantum mechanics
  4. Quantum physics
  5. Quantum chemistry
  6. Quantum computational chemistry
  7. Quantum biology
  8. Quantum field theory
  9. Quantum theory
  10. Quantum system
  11. Isolated quantum system
  12. Quantum effects
  13. Quantum resource
  14. Quantum state
  15. Wave function
  16. Linear algebra
  17. Quantum information
  18. Quantum bit — qubit
  19. Stationary, flying, and shuttling qubits
  20. Measurement / observation
  21. Observable
  22. Quantum phenomena
  23. 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:

  1. Discrete
  2. Quanta
  3. Particle and wave duality
  4. Probabilistic
  5. Uncertainty
  6. Superposition
  7. Schrödinger’s cat
  8. Cat state
  9. Entanglement
  10. Spooky action at a distance
  11. Bell’s theorem and Bell’s inequality
  12. Bell states
  13. Phase
  14. Interference
  15. Wave function
  16. Density matrix or density operator
  17. Probability amplitude
  18. Unitarity principle
  19. Basis state
  20. Computational basis state
  21. Quantum state
  22. State vector
  23. Collapse of wave function on measurement
  24. Measurement
  25. No-cloning theorem
  26. Hamiltonian
  27. Schrödinger’s equation
  28. Time evolution
  29. Fermi-Dirac statistics
  30. Bose-Einstein statistics
  31. Fermions
  32. Bosons
  33. Pauli exclusion principle
  34. Spin
  35. Integer spin
  36. Half-spin or half-integer spin or spin 1/2
  37. Spin up and spin down
  38. Cooper pairs
  39. Superconductivity and superfluidity
  40. Tunneling
  41. Josephson effect
  42. Quantum hall effect
  43. Macroscopic quantum effects
  44. 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:

  1. 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.
  2. 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.
  3. 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:

  1. Discrete rather than continuous values for physical quantities.
  2. 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.)
  3. 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.
  4. Probabilistic rather than strictly deterministic behavior.
  5. 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.
  6. Superposition of states — a quantum system can be in two quantum states at the same time. See spin up and spin down.
  7. Schrödinger’s cat — a thought experiment which demonstrates superposition — the cat can be both alive and dead at the same time.
  8. Cat state — alternate name for superposition of two quantum states. A tribute to Schrödinger’s cat.
  9. Entanglement — the same quantum state can exist at two physically separated locations at the same time.
  10. Spooky action at a distance — popular reference to entanglement.
  11. Bell’s theorem and Bell’s inequality — quantum mechanics cannot be explained simply by adding “hidden variables” to classical mechanics.
  12. 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.
  13. 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.)
  14. 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.
  15. 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.
  16. Density matrix or density operator — an alternative to the wave function for describing the quantum state of a quantum system.
  17. 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.
  18. 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.
  19. Basis state — the actual numeric value of a single quantum state, comparable to a binary 0 or 1.
  20. 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.
  21. Quantum state — the state of an isolated quantum system described by its wave function. Alternatively, a single basis state.
  22. 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.
  23. 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.
  24. 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.
  25. 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.
  26. Hamiltonian — an equation which expresses the energy of a quantum system.
  27. Schrödinger’s equation — describes the evolution of the quantum state of a quantum system over time in terms of its Hamiltonian and wave function.
  28. 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.
  29. Fermi-Dirac statistics — rules for fermions which require them to obey or follow the Pauli exclusion principle.
  30. Bose-Einstein statistics — rules for bosons which allow them to violate (not follow) the Pauli exclusion principle. Sometimes referred to as BES.
  31. 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.
  32. 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.
  33. 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.
  34. Spin — the angular momentum, much like a spinning gyroscope, of an elementary particle or an atom.
  35. 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.)
  36. 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.)
  37. Spin up and spin downspin 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.
  38. 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.
  39. 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.
  40. 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.
  41. Josephson effecttunneling 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.
  42. Quantum hall effect — quantized conductance (flow of current or electrons) induced by a magnetic field at very low temperatures. Useful for precise measurements.
  43. 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.
  44. 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.

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.

  1. The quantum state is described by a wave function.
  2. The individual possible states are known as basis states. Such as a 0 and a 1.
  3. Each basis state in a wave function occurs with some probability.
  4. 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.
  5. 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.
  6. The basis states and their probability amplitudes are combined to form the wave function.
  7. If the probability of a basis state is other than 0.0 or 1.0, the two basis states are superposed.
  8. 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.

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:

  1. Quantum effects
  2. Quantum effects for quantum computing
  3. Quantum effects for quantum information science
  4. What are quantum effects?
  5. Superficial introduction to quantum effects for non-physicists
  6. What are quantum effects and how do they relate to quantum computing?
  7. What are quantum effects and how do they relate to quantum information science?
  8. Quantum effects — The magic sauce which enables quantum information science
  9. Quantum effects — The magic sauce which enables quantum computing
  10. What are Quantum effects and how do they enable quantum information science?

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