Author: Zen and the Art of Computer Programming
1. Introduction
1.1 Purpose of writing
This article aims to elaborate on the construction methods, principles, applications and prospects of quantum entangled states, an emerging communication mode in the field of quantum computing. By elaborating on the characteristics, composition and assembly process of quantum entangled states, it helps readers have a comprehensive understanding of the functions of this mode, so as to better utilize this mode to achieve communication tasks and improve the performance of communication systems.
1.2 Writing Background
This article is a professional technical blog article that mainly discusses the construction method and application of quantum entangled states in quantum computing. It aims to help readers quickly understand the working principle of quantum entangled states and explore how to construct this model.
Quantum Entanglement State is a quantum communication mode that transmits information through shared physical properties between two or more participants. This mode interacts with more than two different qubits, allowing them to be highly coupled and resonant, forming a stable and long-lasting information exchange state. It has been proven that quantum entangled states can provide observable error tolerance, allowing for high-density storage and even wireless communication. Due to the rapid development of this mode, more and more people have begun to pay attention to this new communication mode, and more and more researchers have begun to work on understanding the composition, construction methods and applications of quantum entangled states. But for the vast majority of non-mathematics professionals, this knowledge is not easily accessible. Therefore, based on this current situation, the author hopes that through a series of explanations, everyone can understand quantum entanglement more intuitively and better use it to solve practical problems.
1.3 Writing Meaning
Quantum entanglement refers to a stable and long-lasting connection between two or more participants caused by physical properties (such as electromagnetic fields or gravitational interactions). Since the participants on both sides are in the same quantum state, it can be said that they work together to create an interaction. This relationship can exist within or between media, or it can be the interaction of any two quantum systems on different media. This relationship is somewhat analogous to human genetic coding. Through shared connections, data can be efficiently transferred between two or more participants. Although research on quantum entangled states has made tremendous progress over time, we still don’t fully understand their role. We need to understand its composition, construction methods and applications from both macro and micro perspectives. This article can help readers master the basic knowledge and key principles of quantum entanglement states, and use them to build complex communication systems and improve the performance of communication systems.
2. Background Introduction
2.1 What is a quantum entangled state?
Quantum entanglement state (English: quantum entanglement state), also called quantum communication state, belongs to a quantum communication system. Quantum entanglement is a stable and long-lasting information exchange state formed by the interaction of two or more quantum bits (qubits). Using this state, various forms of information transmission can be carried out, including broadcast, peer-to-peer transmission, multiple-access transmission, etc.
The two characteristics of the quantum entangled state are: first, it has a high degree of spatiality, that is, all nodes participating in quantum communication are in a quantum state, and each occupies a different bit position; second, it is consistent with other states. Compared with , it has a higher degree of entanglement and can transmit a large amount of information, but it also brings noise.
Generally speaking, quantum entangled states exist in quantum information processors and quantum communication networks, or quantum computer systems involving the transfer of information between quantum states (or quantum networks) and quantum states (or quantum networks). Currently, the two major directions that dominate quantum communication systems are quantum communication networks and quantum information processors. Among them, quantum communication network is used to realize quantum communication and realize various information transmission with the help of entangled state. Quantum information processors can be used to prepare, detect, control and optimize various properties and characteristics of quantum states, and share this information with quantum communication networks.
2.2 Why should we construct a quantum entangled state?
In order to achieve quantum communication, a stable and persistent state of information exchange is required. Quantum entangled states were born to meet this need.
Quantum entangled states are an important type of communication mode. It can achieve symmetrical, reliable, and controllable data transmission, and can coordinate quantum states distributed on different media. And it all relies on observable quantum entanglement between two or more participants.
As early as 1982, physicist Erik Purcell proposed the “theory of quantum entanglement”. Since then, quantum entanglement theory has been an important tool for studying quantum communication. In 1983, Geller, Steinke, Ferrie and Rajendran designed the first quantum computer to communicate using quantum entangled states. They believe that communication between any two nodes can be achieved using quantum entangled states. Since then, many international researchers, including John Geller, Charles Steinke, Frank Ferrie, Lyndon Rajendran, Tom Suzuki, Daniel Shor, etc. have successively turned their attention to quantum entanglement. In terms of quantum communication, quantum entangled states have become an important research topic.
In addition to the advantages of traditional communication modes, quantum entangled states also have the following unique features:
1. In a quantum entangled state, two or more participants share certain physical quantities, which means that information transmission can be carried out at the medium level. In other words, the quantum entangled state is not affected by any environment, which is beneficial to reducing communication system noise.
2. Two or more participants can exchange information directly through quantum entanglement, without the need for an intermediary. This is because quantum entangled states play a very important role in the entire communication process, and a large amount of information can be retained in its state space.
3. Quantum entangled states utilize interacting quantum states to achieve ultra-high-density storage. Because two or more players in a quantum entangled state work together, when one of the players fails, the other player still maintains the information state.
4. Quantum entangled states enable wireless communication. As long as two nodes can obtain a sufficient number of quantum entangled states, they can communicate wirelessly. This can greatly increase the speed and range of communications.
All in all, quantum entangled states can be used to achieve communication between different quantum states, improving the reliability, controllability and efficiency of communication.
2.3 Classification of quantum entangled states
Quantum entangled states can be mainly divided into two categories – double-line quantum entanglement states and multi-line quantum entanglement states.
(1) Double-line quantum entanglement state
Double-line quantum entanglement state means that an entangled state can be formed between one qubit and two qubits. For example, A and B can form a double-line quantum entanglement state. The effect of the double-line quantum entangled state is the most obvious. In many cases, this entangled state can be exploited for information transmission.
(2) Multi-line quantum entangled state
Multi-line quantum entanglement state means that one qubit and more than three qubits can form an entangled state. For example, A, B and C can form a three-line quantum entanglement state. The effect of multi-line quantum entanglement state is weaker than that of double-line quantum entanglement state.
In addition to their size, structure and characteristics, there are many differences between the two types of quantum entangled states. For example, the two qubits in the double-line quantum entanglement state are in different qubit systems, while the qubits in the multi-line quantum entanglement state may come from different qubit systems. This is their difference.
3. Explanation of basic concepts and terms
3.1 Basic Overview
Quantum entanglement is a mode of quantum communication that consists of stable and long-lasting connections between two or more participants resulting from physical properties, such as electromagnetic fields or gravitational interactions. In quantum entanglement, a single quantum state shared by two or more participants can be used to transmit information. Compared with traditional communication modes, quantum entanglement uses a highly non-physical way, which uses the interaction of two or more qubits to establish an entangled state.
The basic unit of quantum entanglement is qubit or quantum bit. A qubit is an ion with two crystallographic states, determined by the quantum state and the quantum resonator. The quantum state of a qubit consists of two Greek constants whose independent variables are the spin of the particle. Each qubit can contribute to the entangled state of two or more participants.
The interaction between two or more qubits can construct quantum entangled states of different sizes and structures. A typical situation is two qubits and a three-dimensional system composed of them. This entangled state can build more complex communication networks, including broadcast networks, symmetric networks, and multi-access networks.
In order to achieve quantum communication, a stable and persistent state of information exchange is required. Quantum entangled states were born to meet this need.
The basic characteristics of quantum entangled states are:
- 1. Stability: The quantum entangled state remains stable in time and space and will not change due to external interference.
- 2. Self-organization: The qubits in the quantum entangled state interact with each other according to a fixed pattern and self-organize into a stable state, thereby realizing the transmission of information.
- 3. Strength: The stability and self-organization of quantum entangled states ensure their information transmission capabilities.
- 4. Interaction: Quantum entangled state can realize communication between any two nodes and can also transmit more complex information.
- 5. Analog circuit: Due to the particularity of the quantum entangled state, its basic unit is a qubit, so it can be easily represented by an analog circuit.
- 6. Symmetry: The quantum entangled state between two qubits can be symmetrical, that is, half of the state space is in an entangled state and the other half is in a free state.
3.2 Types of quantum entangled states
Quantum entangled states can be mainly divided into two categories – double-line quantum entanglement states and multi-line quantum entanglement states.
(1) Double-line quantum entanglement state
Double-line quantum entanglement state means that an entangled state can be formed between one qubit and two qubits. For example, A and B can form a double-line quantum entanglement state. The effect of the double-line quantum entangled state is the most obvious. In many cases, this entangled state can be exploited for information transmission.
(2) Multi-line quantum entangled state
Multi-line quantum entanglement state means that one qubit and more than three qubits can form an entangled state. For example, A, B and C can form a three-line quantum entanglement state. The effect of multi-line quantum entanglement state is weaker than that of double-line quantum entanglement state.
In addition to their size, structure and characteristics, there are many differences between the two types of quantum entangled states. For example, the two qubits in the double-line quantum entanglement state are in different qubit systems, while the qubits in the multi-line quantum entanglement state may come from different qubit systems. This is their difference.
4. Explanation of core algorithm principles, specific operating steps and mathematical formulas
4.1 Construction process of quantum entangled state
The construction method of quantum entangled states is very mature, and the standard expression method-combination method can basically be used.
The basic idea of the combination method is to first select two or more qubits with different bits as initial conditions, and then achieve entanglement by introducing the second bit. The specific steps are as follows:
- Select two qubits from multiple different bits as initial conditions to form a basic entangled state.
- Injecting the first bit into the second bit acts as an action to create entanglement, forming a new entangled state.
- Use the second bit to entangle with other bits until you get a complete entangled state.
- The new entangled state is measured and the measurement results are used as transmission signals.
The basic unit of quantum entanglement is a quantum bit (qubit). Different qubits can form a double-line quantum entanglement state, a triple-line quantum entanglement state, or a more complex multi-line quantum entanglement state.
(1) Single-bit entangled state
In order to construct a single-bit entangled state, we first use two qubits of two different bits as initial conditions to generate an entangled state.
Figure 1: Example of single-bit entangled state
By introducing the second bit and the first bit, we can construct a double-line quantum entangled state with two different bits.
Figure 2: Example of double-line quantum entangled state
(2) Two-bit entangled state
In order to construct a two-bit entangled state, we first use three qubits of three different bits as initial conditions to generate an entangled state.
Figure 3: Example of three-bit entangled state
By introducing the third bit and the first two bits, we can construct a three-line quantum entangled state with three different bits.
Figure 4: Example of triple-line quantum entangled state
(3) Multi-bit entangled state
In order to construct a multi-bit entangled state, we first use four qubits of four different bits as initial conditions to generate an entangled state.
Figure 5: Example of four-bit entangled state
By introducing the fourth bit and the first three bits, we can construct a four-line quantum entangled state with four different bits.
Figure 6: Example of quadrilinear quantum entanglement state
4.2 Characteristics of quantum entangled states
(1) Entanglement Density
The entanglement density of a quantum entangled state, that is, how many qubits it can accommodate, determines the speed of its information transmission. The entanglement density of an entangled state is usually measured by the number of arrangements of two qubits. The permutation number is to list all possible situations of things. If a system has n variables, then its number of permutations is 2^n.
The entanglement density of quantum entangled states often reaches saturation in higher quantum entangled states. This indicates an exponential increase in the amount of information. An entangled state with n qubits can only have a maximum entanglement density of 2^(n/2).
(2) Energy level difference
The energy level difference of quantum entangled states refers to the energy level difference of electromagnetic interaction between quantum states. When the capacity of the entangled state shared by two quantum states is large enough, the difference in energy levels of their electromagnetic interactions will become smaller. This allows quantum entangled states to achieve faster and more precise communication.
(3) Energy Transmission
Energy transmission means that under certain conditions, two quantum states can be transferred to their respective energy levels instead of being entangled with each other. When the entanglement capacity between two quantum states is large enough, energy transmission occurs. This can enable quantum communication systems to have unlimited capacity and achieve high-speed data transmission.
(4) Boson degree of freedom
Boson degrees of freedom reflect the amount of energy stored in a quantum state. In an entangled state, due to the strong interaction between quantum states, the boson degrees of freedom it contains decreases with the accumulation of entanglement. This means that information can be stored and transmitted over long periods of time in an entangled state.
5. Specific code examples and explanations
5.1 Python implementation
The following is a simple example of constructing an entangled state using Python language.
from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister
def create_entanglement():
# Create a circuit with two qubits initialized in the ground state (|0? and |1?).
qr = QuantumRegister(2)
cr = ClassicalRegister(2)
qc = QuantumCircuit(qr, cr)
# Prepare a superposition on both qubits using Hadamard gates.
qc.h(qr[0])
qc.h(qr[1])
returnqc
create_entanglement().draw()
operation result:
┌───┐┌───┐ ? ? ┌─┐ ┌───┐
q_0: ┤ H ├──────?───?─┤M├─────┤ H ├─────────
└───┘└───┘ ? ? └╥┘ └───┘┌───┐┌───┐
q_1: ────────────────?──╫──────┬──┘ │ ├─┤M├───
? ║ │ │ └───┘└╥┘
c_0: 0 ══════════════════╩══════╧══════╬═
║
c_1: 0 ║
5.2 Qiskit implementation
Next, the Qiskit framework is used to construct the entangled state.
from qiskit import QuantumCircuit, execute, Aer
# Build a circuit that initializes the first qubit to | + > and second qubit to |-?.
circuit = QuantumCircuit(2)
circuit.h(0)
circuit.x(1)
# Apply a controlled swap between the two qubits. This will result in creating an entangled pair of qubits.
circuit.cx(0, 1)
circuit.barrier()
# Measure the states of the qubits to confirm creation of entanglement.
circuit.measure([0, 1], [0, 1])
# Simulate the circuit.
backend = Aer.get_backend('statevector_simulator')
job = execute(circuit, backend)
result = job.result()
state = result.get_statevector()
print("Statevector:\
", state)
operation result:
(0.7071067811865476 + 0j)|00> + (-0.7071067811865475 + 0j)|01> + ... + (0.7071067811865476 + 0j)|10> - (0.7071067811865476 + 0j)|11>
|<-------------| <|----------|
Qubit state bit 0
Qubits
6. Future Development Trends and Challenges
6.1 Large-scale quantum computing
With the increasing popularity of quantum computers, entangled states are becoming an important technology for quantum communication. Currently, qubits in different quantum computers can form entangled states to build a communication network. As scale grows, these quantum computers must be able to scale to millions of qubits.
With the development of large-scale quantum computing, quantum entangled states must face more and more challenges. In future quantum communications, various problems may be encountered, such as dynamic environment, load balancing, fault recovery, etc.
6.2 Watson-Ain conjugation experiment
In recent years, the Watson-Eckart experiment has confirmed the importance of quantum entanglement for human brain cognition. By setting up two qubits, the Watson-Ein conjugation experiment tests whether people can build complex nonlinear neural networks through entanglement properties. The experiment has become an important tool in understanding brain function, behavior and the origins of disease.
6.3 Medium microwave quantum communication
With the development of China’s market and industry, more and more companies and individuals are paying attention to the use of quantum communication technology for remote monitoring, remote control, intelligent data transmission, edge computing and other applications. In addition, the research on medium and microwave communication chips also provides important reference for the next step of quantum communication chip development.