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# Interference in Quantum Computing

2
August
,
2022

When discussing quantum computing, interference does not always earn a mention. Top billing goes to quantum mechanical effects such as quantum superposition, entanglement, and tunneling. Perhaps this is because interference is also a classical phenomenon that can be observed macroscopically. It is observable when two stones are dropped into a body of water, for example, and the crests cancel each other out or when someone dons an active noise-canceling headset. Nonetheless, for any quantum computer, interference is a fundamental property of computation.

## What is meant by quantum interference?

There are two kinds of quantum interference: constructive interference and destructive interference. Two in-phase waves, which is to say they peak at the same time, constructively interfere, and the resulting wave peaks twice as high. Two waves that are out-of-phase, on the other hand, peak at opposite times and destructively interfere; the resulting wave is completely flat. All other phase differences will have results somewhere in between, with either a higher peak for constructive interference or a lower peak for destructive interference.

## What causes quantum interference?

The root cause of quantum interference is wave-particle duality. At the subatomic scale, particles have wavelike properties. These wavelike properties are often attributed to location, for example, where around a nucleus an electron might be. This is why electron orbitals are depicted as clouds of probability instead of as orbits like planets around the sun. However, this uncertainty of locations also applies to energy levels and to which orbital an electron might be.

## What is quantum interference in quantum computing?

In quantum computing, interference is used to affect probability amplitudes. In other words, every possible outcome has some probability of occurring. When using only one qubit for computation, the possible outcomes are only 0 and 1. When using two qubits, the number of possible outcomes doubles; these possible outcomes are 00, 01, 10, and 11. And, when using three qubits, the number of possible outcomes doubles again to 000, 001, 010, 011, 100, 101, 110, and 111. This exponential growth is one of the factors contributing to the ability of quantum computers to perform certain computations that are believed to be impossible for even the world’s most powerful supercomputers.

For each possible outcome, the respective probability may be as low as 0 and as high as 1. Mathematically, all the probabilities of all the possible outcomes must sum precisely to 1, representing 100% of all possible outcomes. And going back to what causes quantum interference, each outcome measures the energy levels of the qubits. Is each qubit at its ground state energy level, represented numerically by 0, or is it at its first energy level, represented numerically by 1? Because that resultant binary string is the sought-after solution, for example, 101, quantum computing uses interference to arrive at that solution.

## How is interference used in quantum computing?

The most famous example of how interference is used in quantum computing is Grover’s Algorithm, used to search for values or items that meet certain criteria. This textbook algorithm has several components, including state preparation, an oracle, a diffusion operator, and measurement. Concerning quantum interference, however, a discussion of the diffusion operator is most relevant.

The Grover diffusion operator works in conjunction with the problem-defining oracle. It uses both types of quantum interference, constructive interference and destructive interference. It uses constructive interference to amplify the correct solution(s) to the problem, and it uses destructive interference to minimize all other possible outcomes. Grover’s algorithm usually requires multiple iterations of the oracle and the diffusion operator. With each iteration, up to an optimal number, the correct solution (or solutions) is amplified while incorrect solutions are minimized. By the time the quantum circuit is measured, the correct solution (or solutions) is hopefully obvious.

Algorithms created by the Classiq software platforms use quantum interference extensively. Contact us to see how they might be helpful to your quantum journey.  When discussing quantum computing, interference does not always earn a mention. Top billing goes to quantum mechanical effects such as quantum superposition, entanglement, and tunneling. Perhaps this is because interference is also a classical phenomenon that can be observed macroscopically. It is observable when two stones are dropped into a body of water, for example, and the crests cancel each other out or when someone dons an active noise-canceling headset. Nonetheless, for any quantum computer, interference is a fundamental property of computation.

## What is meant by quantum interference?

There are two kinds of quantum interference: constructive interference and destructive interference. Two in-phase waves, which is to say they peak at the same time, constructively interfere, and the resulting wave peaks twice as high. Two waves that are out-of-phase, on the other hand, peak at opposite times and destructively interfere; the resulting wave is completely flat. All other phase differences will have results somewhere in between, with either a higher peak for constructive interference or a lower peak for destructive interference.

## What causes quantum interference?

The root cause of quantum interference is wave-particle duality. At the subatomic scale, particles have wavelike properties. These wavelike properties are often attributed to location, for example, where around a nucleus an electron might be. This is why electron orbitals are depicted as clouds of probability instead of as orbits like planets around the sun. However, this uncertainty of locations also applies to energy levels and to which orbital an electron might be.

## What is quantum interference in quantum computing?

In quantum computing, interference is used to affect probability amplitudes. In other words, every possible outcome has some probability of occurring. When using only one qubit for computation, the possible outcomes are only 0 and 1. When using two qubits, the number of possible outcomes doubles; these possible outcomes are 00, 01, 10, and 11. And, when using three qubits, the number of possible outcomes doubles again to 000, 001, 010, 011, 100, 101, 110, and 111. This exponential growth is one of the factors contributing to the ability of quantum computers to perform certain computations that are believed to be impossible for even the world’s most powerful supercomputers.

For each possible outcome, the respective probability may be as low as 0 and as high as 1. Mathematically, all the probabilities of all the possible outcomes must sum precisely to 1, representing 100% of all possible outcomes. And going back to what causes quantum interference, each outcome measures the energy levels of the qubits. Is each qubit at its ground state energy level, represented numerically by 0, or is it at its first energy level, represented numerically by 1? Because that resultant binary string is the sought-after solution, for example, 101, quantum computing uses interference to arrive at that solution.

## How is interference used in quantum computing?

The most famous example of how interference is used in quantum computing is Grover’s Algorithm, used to search for values or items that meet certain criteria. This textbook algorithm has several components, including state preparation, an oracle, a diffusion operator, and measurement. Concerning quantum interference, however, a discussion of the diffusion operator is most relevant.

The Grover diffusion operator works in conjunction with the problem-defining oracle. It uses both types of quantum interference, constructive interference and destructive interference. It uses constructive interference to amplify the correct solution(s) to the problem, and it uses destructive interference to minimize all other possible outcomes. Grover’s algorithm usually requires multiple iterations of the oracle and the diffusion operator. With each iteration, up to an optimal number, the correct solution (or solutions) is amplified while incorrect solutions are minimized. By the time the quantum circuit is measured, the correct solution (or solutions) is hopefully obvious.

Algorithms created by the Classiq software platforms use quantum interference extensively. Contact us to see how they might be helpful to your quantum journey.

## About "The Qubit Guy's Podcast"

Hosted by The Qubit Guy (Yuval Boger, our Chief Marketing Officer), the podcast hosts thought leaders in quantum computing to discuss business and technical questions that impact the quantum computing ecosystem. Our guests provide interesting insights about quantum computer software and algorithm, quantum computer hardware, key applications for quantum computing, market studies of the quantum industry and more.    