Quantum: Basics to Practical Applications Quantum Superposition (2)
Welcome to Part 2 of our series on the basics and practical applications of quantum computing. Today's discussion will focus on the key concept of quantum superposition.
Quantum superposition is a fundamental principle in quantum mechanics stating that a quantum system can exist in multiple states simultaneously. This means a quantum system can be in a combination of different states, rather than being in just one state at a time.
This principle has no analogue in classical physics or the "real world." It is counterintuitive and often difficult to grasp. It is not a play on words. It literally means that the system, let's use a single photon as an example, is in multiple states at the same time. It does not mean we simply don't know what state it is in. It actually means the photon, with respect to whichever of its characteristics we might be considering, is in more than one state simultaneously. (1)
If you read the last piece in this series on quantum entanglement, you'll remember we mentioned two characteristics of photons: "spin" and "polarization." We called any single characteristic a "basis," and multiple characteristics, "bases." We said that when a basis is measured, the measurement output is called an "outcome." We also touched on the fact that before a basis is measured, the outcome is predictable; it's probabilistic and the current state is undefined, not because we don't or can't know it, but because it is not in any actual single state. It is in a superposition of states.
So, the photon exists in a superposition, meaning it's in multiple states at once, but only as long as it remains unmeasured—scientists like to say "unobserved." The act of measurement (or observation) forces the system to "choose" a single state, a process called "wave function collapse." This is true for all quantum systems.
Wave Functions
In quantum mechanics, a wave function is a mathematical description of a system's state. It encodes all the possible states and their probabilities. When a measurement occurs, the wave function instantly changes. It "collapses" from a superposition of possibilities to a single, definite state. This is a discontinuous, non-deterministic process. We can't predict which state the system will collapse into, only the probabilities of each outcome. (2)
Wave function collapse is a topic of much debate in quantum theory. There is no good explanation for the "why," only a reasonable prediction of the resulting behavior as a set of probabilistic outcomes.
However, wave function collapse is an important aspect of quantum computation. Here is why: all matter and energy can be thought of as waves. Quantum systems are no different. If a quantum system is in multiple states at the same time, that means it's also in multiple wave states at the same time. Waves can be coherent, that is, additive, or destructive, that is, canceling. Just think about how your noise-canceling headphones work. Hold that thought!
As we said, superposition can be used in quantum computers to execute parallel computations. In quantum computers, qubits (quantum bits made up of systems in superposition) are combined with quantum gates (operational gates like NAND and NOR gates in classical CPUs) that can operate on all the states of a superpositioned system "passing through" it. Here, the qubits are the data, and the gates make up the operations or algorithm. Because the gates operate on all states simultaneously, in effect, for a combinatorial problem like the knapsack algorithm, every possible combination is being checked at the same time, as if there were a classical, fully independent CPU core for every one of those possible combinations.
Quantum Computation
Quantum computers use quantum gates (the instructions or algorithm) to manipulate superpositioned waves. By carefully designing the gates, they can make certain outcomes interfere constructively and others interfere destructively. This is called constructive and destructive interference. If the instructions are sequenced correctly, they'll cancel out the incorrect solutions and amplify the correct one.
Quantum computers can find specific numbers in a list using superposition and quantum gates. First, qubits are put into a superposition representing all the numbers simultaneously. Then, quantum gates are applied to cause constructive interference for the target value and destructive interference for other numbers. When measured, the wave functions collapse, and the computer is more likely to get the target value due to its amplified probability from constructive interference. Effectively, in classical terms, the entire list was searched with a single comparison.
A Practical Example: Portfolio Optimization
Imagine you're a financial institution managing a massive investment portfolio. You have a wide range of assets (stocks, bonds, real estate, etc.), each with its own risk and return profile. Your goal is to find the optimal mix of these assets to maximize returns while minimizing the overall risk.
This is a classic combinatorial optimization problem. The number of possible combinations of assets grows exponentially as the number of assets increases, making it incredibly difficult for classical computers to find the optimal solution. Most classical algorithms, even those using massive parallelism, use shortcuts (hints, designers would call them) and do not generate the ultimate solution or even a good approximation of it. Brute force would yield the correct solution but might take weeks to run.
Quantum computers can represent various potential portfolio allocations as quantum states (a combination of qubits). The quantum computer leverages superposition to simultaneously explore numerous potential portfolios.
Specific quantum algorithms, such as quantum annealing and variational quantum eigensolvers, can then be used to find the optimal portfolio. These algorithms utilize superposition and interference to efficiently search for solutions. (3)(4)
By carefully designing the quantum operations, the probability of superior portfolios can be amplified through constructive interference, and the probability of less optimal portfolios can be reduced through destructive interference. When the qubits are measured, the quantum computer has a better chance of finding a near-perfect portfolio.
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Next Time
Next time we'll look at some more practical applications, talk about D-Wave hardware, and Quantum Annealing.
Disclaimers:
All opinions are my own!
No cats were injured writing this article.
I am long quantum, specifically but not limited to, D-WAVE, IonQ, Rigetti, Quantum Computing Inc, and Microsoft. Additionally, my partner is the founder and CEO of a fully funded quantum computing startup in the defense space as it relates to signal processing where I am a board advisor.
More Information and Sources
(1) Superposition
Explore Quantum, Superposition, Microsoft Azure Quantum
(2) Wave Function Collapse
Experiments Spell Doom for Decades-Old Explanation of Quantum Weirdness, Quanta Magazine https://www.quantamagazine.org/physics-experiments-spell-doom-for-quantum-collapse-theory-20221020/
(3) Quantum Annealing
Quantum Annealing, Science Direct, https://www.sciencedirect.com/topics/mathematics/quantum-annealing
What is Quantum Annealing, D-Wave Systems, https://docs.dwavesys.com/docs/latest/c_gs_2.html
(4) Variational Quantum Eigensolver
Variational Quantum Eigensolver, IBM, Beginner
Defense | Quantum Computing | Investor | CrossFitter
4 周I like how you keep these simple and directed and always have a practical example you could solve now. It's here now!
Accelerate the Business Value of Your Data & Make it an Organizational Priority | ex-CDO advising CDOs at Data4Real | Keynote Speaker & Bestselling Author | Drove Data at Citi, Deutsche Bank, Voya and FINRA
4 周Thank you, Salvatore Magnone , this is incredibly helpful! I am starting to see where your excitement about quantum computing is coming from. Look forward to the next article in the series.