Anyone into quantum computing

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Hi All, Is there anyone here that has been experimenting with quantum computers or use them in their profession. Would be interested in discussing the math and applications

I am a computer scientist. I don’t use quantum computers in my work or at home. I have read that Google made a “time crystal” using a quantum computer.

I also have a book summarizing Dick Feynman's thoughts on the physics limitations of computing (someplace). Magz might be able to comment on the math involved.
I took physics in college to cover most of my electives and avoid writing, including relativity. Never did quantum.

● Feynman Lectures On Computation by Richard P. Feynman

● Stanford physicists help create time crystals with quantum computers

Me:
how does a quantum computer work?

ChatGPT:
A quantum computer operates on the principles of quantum mechanics,
taking advantage of unique quantum properties to perform computations.
Unlike classical computers, which use bits as the basic unit of information
(either 0 or 1), quantum computers use quantum bits or qubits. Here are the
key principles of how quantum computers work:
1. Superposition: Qubits can exist in multiple states simultaneously,
thanks to the principle of superposition. This allows quantum computers
to perform parallel computations on different possibilities at the same
time.
2. Entanglement: Qubits can be entangled, meaning the state of one
qubit is directly related to the state of another, regardless of the physical
distance between them. Changes to one entangled qubit will
instantaneously affect the other, enabling faster information transfer.
3. Quantum Gates: Quantum computers use quantum gates to
manipulate qubits. These gates perform operations that exploit the
principles of superposition and entanglement to perform complex
computations efficiently.
4. Quantum Measurement: When a quantum system, such as a qubit, is
measured, it collapses from a superposition of states to a definite state.
The outcome of the measurement provides the result of the
computation.
5. Interference: Quantum computers utilize interference to enhance the
probability of obtaining the correct solution while minimizing the
probability of incorrect solutions. This is a crucial aspect of quantum
algorithms.
Quantum computers are particularly powerful for certain types of problems,
such as factoring large numbers, searching unsorted databases, and
simulating quantum systems. Algorithms like Shor's algorithm and Grover's
algorithm demonstrate the potential advantages of quantum computers in
these specific areas.
It's important to note that building and maintaining a quantum computer is a
complex challenge due to the delicate nature of quantum states and the need
to minimize decoherence, which can disrupt quantum information.
Researchers are actively working on developing practical and scalable
quantum computers for various applications.

Me:
what kind of math should I know if I really want to understand quantum
computing? tensors? imaginary numbers?

ChatGPT:
To understand quantum computing, a foundation in certain areas of
mathematics is indeed crucial. Here are some key mathematical concepts that
are particularly relevant to quantum computing:
1. Linear Algebra: This is perhaps the most fundamental mathematical
tool for understanding quantum computing. Quantum states are
represented as vectors in a complex vector space. Understanding
concepts like vectors, matrices, eigenvalues, and eigenvectors is
essential.
2. Complex Numbers: Quantum mechanics heavily relies on complex
numbers, including imaginary and complex conjugates. Complex
numbers are used to represent quantum states, quantum gates, and
various quantum operations.
3. Probability Theory: Quantum mechanics involves probabilistic
outcomes. Understanding probability and statistical concepts is
important for interpreting measurement outcomes and the inherent
randomness in quantum systems.
4. Calculus: Basic knowledge of calculus, including concepts like limits and
derivatives, can be helpful. Quantum mechanics involves differential
equations, and a familiarity with calculus aids in understanding the
continuous evolution of quantum states.
5. Boolean Algebra: Quantum computing often involves the manipulation
of quantum bits (qubits) using quantum gates. Boolean algebra
concepts are relevant for understanding how quantum gates operate
and how quantum circuits are designed.
6. Tensor Mathematics: While not strictly necessary for beginners, a
deeper understanding of quantum mechanics and quantum information
theory may involve tensors, especially when dealing with multipartite
quantum systems and more advanced topics.
7. Group Theory: In the context of quantum computing, group theory is
relevant to the study of symmetries and operations on quantum states.
It becomes particularly important when exploring quantum error
correction and fault-tolerant quantum computing.

It's worth noting that while a strong mathematical foundation is beneficial,
there are introductory resources and programming languages (such as Qiskit
for IBM Quantum computers or Cirq for Google's Quantum processors) that
allow you to start experimenting with quantum computing without an
extensive mathematical background. As you delve deeper into the subject, a
more thorough understanding of the mathematical concepts will enhance
your ability to grasp the intricacies of quantum algorithms and quantum
information theory.