Quantum computers
Quantum superposition and interference can be understood using waves. 7 This makes sense as quantum amplitudes are described by the mathematical wave function. 8 The classical law of wave superposition states: ‘ The resultant displacement at each point [along the wave formed from two or more overlapping waves] is the vector sum of the displacements that each wave passing through the point would produce by itself. ’ 9 Wave interference results. Now take ‘ phase ’ to be how far a wave is through a cycle, measured as an angle. Two otherwise identical waves will always reinforce their amplitudes (here meaning maximum displacement from the equilibrium) when in phase but will fully cancel in anti-phase (180 ° or 𝜋 radians apart). 10 In this way, the states of the two waves affect the amplitude of the resultant wave. Similarly, quantum interference results from the quantum superposition of two or more particles, such as qubits, affecting the measured state of a quantum system. 11
Slightly classical superposition, a system in quantum superposition is in a combination of all possible states at once. 12 If the system’s state is measured externally, the superposition collapses into a single state. The probability of measuring the system in a particular state is given by squaring the absolute value of the state’s amplitude. The sum of the differently to
probabilities of all possible states adds up to 1, which explains why only a single state is observed. This rule is based on the ‘ Euclidean norm ’ which is the ‘ square root of the sumof the squares of the entries ’ . 13 For a single qubit, there is one probability of measuring it in the 1 state and another of measuring it as 0. These probabilities essentially represent the qubit’s va lue, allowing it to encode more than just 1 or 0 whilst in superposition. A qubit’s particular probabilities depend on the operations performed. Whilst not in superposition, it behaves like a classical bit. When particles in superposition are entangled, their quantum states cannot be described independently. 14 Measuring the state of one causes the other(s) to collapse into a state that directly correlates with the first’s. This occurs regardless of the physical distance between the particles so could transfer information across large distances 15 or between the parts of a quantum computer, which may be important for a speedup.
7 What is quantum computing? (2019). 8 Definition of Wave function (2017). 9 Kelly and Wood (2015): 131. 10 Kelly and Wood (2015): 126, 131-132. 11 What is quantum computing? (2019). 12 Helwer (2018). 13 Aarson (2006). 14 Understanding quantum computers (2020). 15 Helwer (2018).
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