As computers continue to become more efficient, the well-known and universal use of the Turing machine in all computations is paving the way for newer, smaller, more advanced quantum computers. These computation systems are very different, even if they can perform the same processes.
Turing machines follow the basic principles of practical computation. Quantum computers use exponential and infinite computational approaches, while Turing machines use finite rules and states to compute data.
This article will cover the most notable differences between Turing machines and quantum computers, putting the complexities of these computational models in the simplest terms possible. It will also discuss Turing’s completeness and how it applies to quantum computers.
Quantum Computers vs. Turing Machines
Despite the controversy on this subject, no computer has ever passed the Turing test, despite significant advances in computing and artificial intelligence. Quantum computation, once fully realized, would be a major front-runner in the race to pass the turing test.
While most computer scientists, engineers, and philosophers disagree about whether a quantum computer is a Turing machine, all computers perform the same processes slightly differently.
Both systems compute encoded information using classical logic, finding relationships between statements translated into 1’s and 0’s. However, that’s where their similarities end.
Table 1
Comparison of the fundamental differences between Turing machines and quantum computers.
| Features | Turing Machines | Quantum Computers |
| Units | Bits | Qubits |
| How values change | Each value can only change via finite rules defined by the internal state table | Values can be superposed, meaning each qubit can be in two states at once |
| Amount of data | Finite data possibilities | Exponentially increasing data possibilities |
| Speed | Slower | Faster |
| Relations between states | Values are separate and independent | Values can become entangled and share a state |
| Determinant of the state | Transistor | Rotation angle |
| Reliability | 100% reliable | External factors and entanglement may alter the solution |
How Turing Machines Work
According to the Church-Turing Thesis, a computational rule that still holds today, “every effective computation can be carried out by a Turing machine.” Operations performed in a quantum computer can be done by a Turing machine.
However, infinite or unsolvable problems will not find a solution using a Turing machine, which fully illustrates the limits of computers.
Bits
Turing machines, invented by Alan Turing in 1936, predate quantum computers. They are the simplest form of any computational device.
Turing machines employ bits, or “binary digits,” to create a numerical representation of a more complicated mathematical equation. They are programmable, meaning they use a finite data set of ones and zeros to solve a problem.
Computation Methods
In a simple Turing machine model, a scanner with an internal set of instructions feeds in a long, thin piece of ticker tape with small cells of binary code written on it.
The machine then uses an internal state table or state transition diagram to run an operation, moving from one number to the next. Depending on the state transition diagram, the machine will alter the value in each cell, leave it as it is, return to the beginning of the tape, or move to the end.
As the machine carries out these operations, electricity moves through transistors, or logic gates, which can create “and,” “or,” “xor,” “nand,” “xnor,” and “not” relationships between each state.
Any algorithm or program that a computer can execute, whether a calculator, PC, laptop, smartphone, or MP3 player, usually runs using the principles of a Turing machine.
How Quantum Computers Work
Quantum computers are an evolved form of Turing machines. While these computational devices do the same things a Turing machine does, they use different units and systems to identify, alter, and define relationships between states.
Although today’s Quantum computer machines are large by definition, quantum computer inner workings are tiny and function at the sub-atomic level in their computation.
Qubits
To maximize the space in a quantum computer, the computer can read each “state” or qubit three-dimensionally. This 3D scan will alter or record the qubit’s state and the logic gate’s definition.
Instead of using bits to create a long stream of 1s and 0s, quantum computers use qubits. These systems can represent both 1’s and 0s simultaneously.
They may also become entangled, allowing the computer to interpret the probability of two outcomes simultaneously and create logic gates between two states. This ability is the most significant benefit of quantum computing.
Computation Methods
As a quantum computer computes, the qubit itself moves throughout a closed system that does not require electrical transistors to work. The qubit passes vertically or horizontally in this secure system through superconductors and small filters.
Depending on the rotation angle of each qubit, the computer will interpret it as a 1 or 0, completing each step of an algorithm.
The versatility and size of this system, which, in its final form, will not require the flow of electricity to define relationships using logic gates, make it far more advanced than a Turing machine.
The logic gates in a quantum computer are also reversible, minimizing the amount of space it takes for a quantum computer to perform complex calculations.
Since quantum computers move at the speed of light and don’t rely on electrical currents and transistors to perform logic operations, they can complete functions much more quickly than Turing machines.
While a Turing machine could perform these operations, the specific characteristics of a quantum computer make quantum computation faster, more efficient, and more compact.
Are Quantum Computers Turing-Complete?
Quantum computers capable of simulating Turing machines are Turing-complete. However, quantum computers are not yet stable enough to reliably complete Turing machine operations in most environments.
Studies such as Quantum Complexity Theory by Ethan Bernstein and Umesh Vazirani have proven that quantum computers can simulate Turing machines with higher speeds and less electrical usage.
Thus, Quantum computers, when functioning correctly, are Turing-complete. In addition, Turing machines are capable of running any program that you can run on a quantum computer.
However, Quantum computers are not yet reliable. Since they record and alter data based on microscopic movements, errors are common when using quantum computers–only an isolated environment will yield reliable results.
The Benefits and Disadvantages of Quantum Computers
So, if quantum computers and Turing machines perform the same operations, what are the benefits of quantum computation?
The Pros
Quantum computers, when fully realized, will have many advantages that make them far superior to traditional computers that run on Turing machine processes:
- Quantum computers are more energy-efficient, smaller, faster, and more versatile than Turing machines.
- Since each qubit in a Turing machine can fluctuate between values of 1 and 0, and since each logic gate in this system is reversible, quantum computers can calculate endless probabilities simultaneously and find the best solution to any given equation in record time.
- Quantum computers do not require much electricity to run. Quantum computers can encrypt data rapidly.
The Cons
Although these computers have many benefits, they have not become well-developed enough to have fewer cons than pros:
- Quantum computers are not as stable as Turing machines. Since they function at the sub-atomic level, any subatomic change in pressure, temperature, or conductivity can render them faulty or damage the system.
- It takes a lot of electricity to insulate and cool quantum computers. Much of the required power currently goes toward running the refrigeration that keeps the quantum processors cool, but that is also changing.
- They are too volatile to use in a personal setting.
- They are costly to produce.
- They are significantly faster at decrypting data, and in the wrong hands, people could easily hack into almost anything that does not run on quantum computation.
Interested in learning more? We recommend reading our article on artificial intelligence, where we discuss whether an AI can create another AI. The answer can be more complicated than you think. Can an AI Create Another AI?
Key Takeaways
Quantum computers can perform any classical logic operation that a Turing machine can, but they do so in a unique, subatomic way.
Thus, quantum computers may be considered Turing machines, but their unique structure makes them far more efficient than traditional computers.
Quantum computers capable of simulating Turing machines are Turing-complete. However, quantum computers are not yet stable enough to reliably complete Turing machine operations in most environments.
Quantum computers are still in their infancy and have much to be realized in their continued creation.
References:
- Stanford Encyclopedia Of Philosophy: The Church-Turing Thesis
- Physics World: Quantum computers take on quarks
- Princeton University: Turing Machines
- University of Illinois: Lecture 36: Turing Machines [Fa’14]
- Tech Target: What is a logic gate (AND, OR, XOR, NOT, NAND, NOR and XNOR)
- IEEE Spectrum: How Much Power Will Quantum Computing Need?
- Stanford Encyclopedia Of Philosophy: Turing Machines
- SIAM Journal on Computing: Quantum Complexity Theory