# Measurement

## Measurement in Quantum Computing

In quantum computing, measurement is acritical process that significantly differs from its classical counterpart. It does not merely read a value but plays a pivotal role in determining the states of qubits, the fundamental units of quantum information. Qubits can exist in a state of superposition, embodying probabilities of being 0 or 1, unlike classical bits which are strictly one or the other.

When a qubit is measured, its wavefunction—which encodes the probabilities of its possible states—collapses to a definite state of either 0 or 1, influenced by the probabilities established prior to measurement. This collapse is both fundamental and irreversible; once a measurement is made, the superposed state and the information it held are lost. The outcomes of measurements are inherently probabilistic, with repeated measurements of the same qubit yielding results consistent with those probabilities.

Quantum measurements can be categorized as:

- Full system measurements, in which all qubits are measured at once to capture the final output.
- Mid-circuit measurements, during computational processes, which enhance algorithmic capabilities by enabling operations conditional to these measurements.
- Partial measurements, which measure specific qubits, typically ancilla qubits used for error correction, which helps identify errors without disrupting the data qubits.

Measurements, therefore, can be a consideration in algorithm design. There is also **measurement-based quantum computation**, which is a different paradigm, involving the manipulation of entangled quantum states and performing measurements on these states. Either way, measurements bridge the gap between quantum mechanics and classical output.

For more information, read Physics World Quantum Research Update “Quantum measurement splits information three ways” by Maria Violaris, as well as The Quantum Atlas article “Quantum Measurement” and our own “Feed-Forward Error Correction And Mid-Circuit Measurements.” For books, preview the Science Direct book chapters on their “Quantum Measurement” page.

#### What is Measurement in Quantum Computing

Measurement in quantum computing is acritical operation that extracts classical information from quantum information. The fundamental points are:

- Qubits exist in a superposition of 0 and 1, a state described by a wave function.
- Measurement collapses the wavefunction, forcing the qubit into a definite state, either 0 or 1.
- The result of a measurement is inherently probabilistic, determined by the wave function.
- Measuring one qubit in a system of multiple qubits affects the entire quantum system.
- The purpose of measuring is to extract classical information from quantum states.
- Advanced techniques such as mid-circuit measurements are crucial for tasks such as error correction and dynamic algorithms.
- Partial measurements allow classical information to be extracted and processed while preserving the quantum information on the qubits that have not been measured.
- Measurements can disturb the qubits and introduce errors.
- Measurements are irreversible; the original superposed states are unrecoverable.

The measurement process is indispensable in quantum computing, as this is how the results of computations are obtained. The measurement results are returned as classical information, which can then be further processed through classical algorithms executed on classical computers.

#### The Measurement Problem and Quantum Paradoxes

The quantum measurement problem highlights a fundamental relationship between quantum systems and the act of measuring them. Quantum systems exist in superpositions of states, represented by a wavefunction. This means that a quantum entity like an atom can exist with probabilities of being in multiple states until it is observed. However, upon measurement, this superposition collapses into a single definite state. The process of this wave function collapse—precipitated by measurement—is not well understood and raises several questions: What constitutes a measurement? How does measurement collapse the wave function? Is the collapse a physical phenomenon or merely a change in our knowledge?

This ambiguity feeds into several quantum paradoxes, illustrating the conflict between quantum mechanics and classical intuition. For instance, Schrödinger's Cat, a thought experiment, presents a scenario where a cat in a sealed box is simultaneously alive and dead until the box is opened, reflecting superposition. The paradoxes underscore profound questions about the nature of reality and the role of observers in quantum theory. These issues remain unresolved and are central topics of debate among physicists, challenging our understanding of the physical world.

#### Measurement Techniques and Technologies

Quantum computing measurement techniques are vital for interpreting and manipulating the information stored in qubits, the basic units of quantum information. These techniques vary from basic measurements, which ascertain the binary state of a qubit (either 0 or 1,analogous to classical bits), to more complex strategies that interact with the system during and after computations.

Mid-circuit measurements are applied to specific qubits during the operation of the quantum circuit. This approach can direct the computation’s progress based on the outcomes of these measurements. Mid-circuit measurements are also referred to as Multi-Qubit Readout (MCR). Conversely, full-system measurements are conducted at the conclusion of all computations, involving all qubits within the system. This is essential for obtaining the final state and outcome of the quantum algorithm.

Partial measurements target only a subset of qubits. This selective approach is crucial for quantum error correction, as it helps maintain the overall quantum state while identifying and correcting errors in specific parts of the system. While mid-circuit measurements, therefore, are typically partial measurements, the final measurements may also be partial measurements, not measuring, for example, the ancillary qubits that facilitated error correction.

Another measurement strategy includes Bell state measurements, which are used for pairs of entangled qubits, and are fundamental for tasks like quantum teleportation and entanglement swapping.

To avoid confusion, the term “external quantum efficiency measurement” applies to photovoltaics and optoelectronics, not quantum computing.

#### Quantum Measurement in Computing and Cryptography

Quantum measurement is critical and complex, profoundly affecting the systems it observes. Unlike classical measurements, which passively read a system's state, quantum measurements actively influence the state of a quantum system, such as a qubit. This interaction causes the qubit's wavefunction to collapse from a superposition of multiple states into one definitive state, either 0 or 1, based on inherent probabilities. This probabilistic collapse underscores the uncertainty and the fundamental limitations in predicting quantum measurement outcomes.

This uncertainty not only has algorithmic applications, but also cryptographic applications. Random numbers are of no use in cryptography if they can be predicted. While there are probabilities for a wave function’s collapse, the measurement outcome cannot be predicted with certainty. This guaranteed unpredictability is what has value in cryptography.