Chapter 6 – Entanglement

Quantum computers

We have all seen headlines about quantum computers solving problems amazingly fast but what are quantum computers and how do they work?

A traditional computer uses bits (binary digits) that have value 0 or 1.

Quantum computers use qubits that have superposition of values 0 and 1. A qubit can exist in a superposition
of 0 and 1 so it has a combination of these states.

This might suggest that the state of a qubit is somewhere on a line between 0 and 1 but qubits are more complex than that.

A qubit’s proportion of 0 and 1 uses complex numbers so the value of a qubit is actually a point on a sphere with 1 at the bottom and 0 at the top.

Despite this complexity, a qubit always returns the value 0 or 1 when measured. The probability of the result depends on where its state is on the sphere compared to the 0 value at the top and the 1 value at the bottom.

Entangled qubits

Qubits can be entangled to represent an exponential number of states:

• 2 entangled qubits can represent 4 basis states simultaneously
• 3 entangled qubits can represent 8 basis states simultaneously
• 10 entangled qubits can represent a thousand basis states simultaneously
• 30 entangled qubits can represent a billion basis states simultaneously

A single operation on entangled qubits operates on all states at once. The state of entangled qubits can be represented as a point on a multidimensional sphere. The operations transform the point

Quantum gates

A traditional computer solves problems by passing bits through logic gates AND, OR, NOT, test, etc. to run a program.

Quantum computer programs pass qubits through quantum gates which rotate or mirror qubit states around the sphere. Some common quantum gates are:

• Hadamard gate: rotates state of one qubit about a diagonal axis
• NOT gate: flips a qubit
• Controlled-NOT: flips a qubit based on state of a target
• SWAP gate: swaps two qubits

Programming quantum computers

Quantum computer programs manipulate qubits by passing them through a sequence of quantum gates. These gates rotate individual qubit states and create entanglement between qubits. By using superposition, entanglement, and interference, the program increases the probability of measuring the correct answer. At the end of the computation, the qubits are measured, and each one returns either a 0 or a 1.

Quantum computers use software on classical computers to interpret a program. The classical computer drives the interaction of the gates on the quantum computer. The gates are driven by carefully controlled microwave or laser pulses

Quantum computers can rapidly solve certain types of problems like:

• Advanced drug design
• Solve complex optimization problems
• Break older encryption keys

It is important to recognize that there are only certain types of problems that are optimized with quantum computers. Most of the work done on classical computers will not run faster on quantum computers.