What is Quantum computing: Definition and 255 Discussions
Quantum computing is the exploitation of collective properties of quantum states, such as superposition and entanglement, to perform computation. The devices that perform quantum computations are known as quantum computers. They are believed to be able to solve certain computational problems, such as integer factorization (which underlies RSA encryption), substantially faster than classical computers. The study of quantum computing is a subfield of quantum information science. Expansion is expected in the next few years as the field shifts toward real-world use in pharmaceutical, data security and other applications.Quantum computing began in 1980 when physicist Paul Benioff proposed a quantum mechanical model of the Turing machine. Richard Feynman and Yuri Manin later suggested that a quantum computer had the potential to simulate things a classical computer could not feasibly do. In 1994, Peter Shor developed a quantum algorithm for factoring integers with the potential to decrypt RSA-encrypted communications. Despite ongoing experimental progress since the late 1990s, most researchers believe that "fault-tolerant quantum computing [is] still a rather distant dream." In recent years, investment in quantum computing research has increased in the public and private sectors. On 23 October 2019, Google AI, in partnership with the U.S. National Aeronautics and Space Administration (NASA), claimed to have performed a quantum computation that was infeasible on any classical computer.There are several types of quantum computers (also known as quantum computing systems), including the quantum circuit model, quantum Turing machine, adiabatic quantum computer, one-way quantum computer, and various quantum cellular automata. The most widely used model is the quantum circuit, based on the quantum bit, or "qubit", which is somewhat analogous to the bit in classical computation. A qubit can be in a 1 or 0 quantum state, or in a superposition of the 1 and 0 states. When it is measured, however, it is always 0 or 1; the probability of either outcome depends on the qubit's quantum state immediately prior to measurement.
Efforts towards building a physical quantum computer focus on technologies such as transmons, ion traps and topological quantum computers, which aim to create high-quality qubits. These qubits may be designed differently, depending on the full quantum computer's computing model, whether quantum logic gates, quantum annealing, or adiabatic quantum computation. There are currently a number of significant obstacles to constructing useful quantum computers. It is particularly difficult to maintain qubits' quantum states, as they suffer from quantum decoherence and state fidelity. Quantum computers therefore require error correction.Any computational problem that can be solved by a classical computer can also be solved by a quantum computer. Conversely, any problem that can be solved by a quantum computer can also be solved by a classical computer, at least in principle given enough time. In other words, quantum computers obey the Church–Turing thesis. This means that while quantum computers provide no additional advantages over classical computers in terms of computability, quantum algorithms for certain problems have significantly lower time complexities than corresponding known classical algorithms. Notably, quantum computers are believed to be able to quickly solve certain problems that no classical computer could solve in any feasible amount of time—a feat known as "quantum supremacy." The study of the computational complexity of problems with respect to quantum computers is known as quantum complexity theory.
A CBS 60 Minutes article described the state of Quantum Computing and specifically cited a protein-modelling system the IBM plans on supplying to Cleveland Clinic.
Of particular interest was the claim by a couple of the interviewees that there are currently no obvious barriers to scaling up...
Hi,
if I wanted to show ##(Z \otimes Y)^{\dagger} = Z \otimes Y##, then I could simply multiply out the matrices belonging to the operators of quantum gates ##Z## and ##Y##.
But my question is whether this is also solvable via the properties of the tensor product and the properties of the...
Hi.
This is Annwoy Roy Choudhury. I have just completed my first-year undergraduate studies in Physics. I am new to Quantum Mechanics. There are certain confusions I have regarding Quantum Measurements. It would be really kind of you to help me out.
Postulate 3 states,
An example is,
Let's...
IBM is offering their Quantum Explorers program. It runs from Jul 06, 2023 to Feb 01, 2024.
Registration here: https://challenges.quantum-computing.ibm.com/quantum-explorers-23
More information: Quantum Explorers: A Game-Based Approach to Quantum Education
From the registration website:
Hello to everyone,
I would like to ask you to brief questions.
The first one is whether you could recommend any pedagogical books on Quantum Information and Computation. I tried Nielsen and Chuang but I found it too dense for a beginner in the field.
The second question is the following: to...
When I observe a qubit's state, decoherence happens such that I find the qubit in a particular state. After I cease observing a qubit's state, what physical process causes a fresh superposition of states to develop? Is zero-point energy at least a contributor?
Hi, this is my first time using the Physics Forums so please let me know if this question belongs somewhere else.
I'm a senior undergraduate at a mid-size institution in the United States seeking to purse a PhD in High Energy Theoretical physics or Quantum Information/Computing. I'm aware these...
Hello.
I need to code a project (solution of a typical problem or approaches to new one) of quantum computation and I want to study any solved project in order to understand the algorithms and how to run the script in a real quantum computer or simulator.
Where can I found some repositories of...
I want to do a masters related to quantum computing from a physics background and my criteria for the place is:
1. A quantum computing group with experimental realizations and
industrial ties.
2. A strong theoretical physics department with research in fundamental physics
3. A good chance of...
I want to learn about Quantum Computing (QC). I am familiar with Quantum Mechanics. So far I have found two types of literature: (1.) Introductions to QC for the layman, and (2) Literature for people who are already knowledgeable about the field. Can someone recommend a mid-level source along...
A while ago I started writing a quantum computer simulator in order to learn more about quantum computing. It certainly has helped me.
The simulator is written in Python and the development was done on a Raspberry Pi 4. It has also been tested on a pc.
In order to see it do something useful I...
I have some questions to this Ansatz and I would really appreciate it if I can get some insight:
1. What is the current status of gate fidelity and what are the current struggles to improve it?
2. Same question but with coherence times.
3. What are the current issues with scalability?
4. Could...
In Nielsen and Chuang p.223 we have the following situation:
$$\frac{1}{2^t} \sum\limits_{k,l=0}^{2^t-1} e^{\frac{-2\pi i k l}{2^t}} e^{2 \pi i \varphi k} |l\rangle$$
Which results from applying the inverse quantum Fourier transform to state ##\frac{1}{2^{t/2}} \sum\limits_{k=0}^{2^t-1}...
Is advanced quantum computing the key to achieving the world's first true artificial general intelligence? The astronomical amount of computing power required for an AGI is currently not possible with classical computing.
Please note: I am really a beginner in this field. If I write nonsense just let me know, I just gather information.
As far as I understood Quantum Computing is super fast but (this is basically my question) not suited to all kinds of engineering questions. As far as I know it should work best...
Is it likely that this year's Nobel prize could be awarded to the field of quantum cryptography with Charles H Bennet, Gilles Brassard and Artur Ekert as possible nobel laureate candidates?
Hi, I'm going through Nielsen and Chuang's Quantum Computation and Quantum Information textbook and I don't really understand this part about quantum parallelism:
Shouldn't the resulting state be (1/sqrt(2^4)) * (|0, f(0)> + |0, f(1)> + |1, f(1)> + |1, f(0)>), since the resulting state would...
I have written and rewritten a lot of times but I need some fresh eyes on my sop.
It would be great if someone can help me out. I have less than a week to readjust it and send.
My motivation to apply for the Masters Degree in quantum engineering at University of Wurzburg is to...
Existence of an universal problem solver, a polynomial-time NP-complete algorithm is a $1000000 prize question.
But suppose that we were able to know something "simple", e.g. an electron state or electron wave function exactly.
Would we be able to solve complex mathematical problems (like...
Hello,
I was watching a video lecture from MIT 8.04 (Allan Adams)– lecture #24 (around the 38 minute mark give or take)
The topic is quantum computing, Dr. Adams is deriving / explaining how to get various computing operations. For the “NOT” operation he explains that the operator
$$ U_{Not}...
To elaborate a little on what I think I do understand / accept:
1. I don't think I have a problem accepting the "weirdness" of quantum concepts. So, for example, I am willing to accept the concept that a quantum system can "exist" in a large number of different states simultaneously.
2. I...
Hello I am trying to choose a school and am interested in quantum computing theory in the physics department. I haven't decided whether or not I want to stay in academia so I would like the option to go into industry maybe at Google, IBM or a startup. Ideally I'd like the reputation/research to...
Here's what I think I understand:
First off, the GHZ state ##|GHZ \rangle = \frac {|000\rangle+|111\rangle} {\sqrt 2}##, and ##\sigma_x## and ##\sigma_y## are the usual Pauli matrices, so the four operators are easy to calculate in Matlab.
I'm thinking the expectation values of each operator...
I know |GHZ>=(1/sqrt(2))[1; 0; 0; 0; 0; 0; 0; 1], and |000>= the tensor product |0> x |0> x |0> = [1; 0; 0; 0; 0; 0; 0; 0].
Can I apply single qubit gates (i.e. 2x2 matrices) and CNOT (a 4x4 matrix) to 8x1 column vectors? If so, does anyone know a good starting point or a hint to get me moving...
I have numerous points of confusion: what does it mean that the matrices are within the exponential? How do I go about doing the matrix multiplication to prove the given form of CZ matches the common form, the 4x4 matrix?
Update: using the fact that exp(At)=∑ ((t^n)/n!)*A^n, where A is a...
Am I correct in thinking that the system measures the probability |<f|1>|^2 for some state <f|? Then the probabilities for each of the six states would be:
|<0|1>|^2= 0
|<1|1>|^2= 1
|<+x|1>|^2= |(1/√2)|^2 = 1/2
|<-x|1>|^2= |(-1/√2)|^2 = 1/2
|<+y|1>|^2= |(-i/√2)|^2 = 1/2
|<-y|1>|^2= |(i/√2)|^2...
Part a:
Gate
H
X
Y
Z
S
T
R_x
R_y
Theta
pi
pi
pi
pi
pi/2
pi/4
pi/2
pi/2
n_alpha
(1/sqrt(2))*(1,0,1)
(1,0,0)
(0,1,0)
(0,0,1)
(0,0,1)
(0,0,1)
(1,0,0)
(0,1,0)
Using the info from the table and equation 1, I find:
U_H=(i/sqrt(2))*[1,1;1,-1]
U_X=i*[0,1;1,0]
U_Y=i*[0,-i;i,0]
U_Z=i*[1,0;0,-1]...
Hi guys, I am an absolute beginner in quantum computing. I am really curious about its mechanics but my lack of knowledge in mathematics makes me struggle. I cannot entirely understand why numbers |1> cancel each other out while double Hadamard gates are applied. If the rule is to cancel out the...
The arrival of quantum computing reminds me of "the manhattan project" and "the sputnik alert" when physicists are highly demanded.
And this makes me wonder if the age of quantum computing means the better future for physicists since the development of quantum computers needs at least...
Hello, I am calculating the krauss operators to find the new density matrix after the interaction between environment and the qubit.
My question is: Is there an operational order between matrix multiplication and tensor product? Because apparently author is first applying I on |0> and X on |0>...
I am an undergraduate doing research on QC/QI. My current topic to learn is continuous-time quantum walks, but first I must learn the random quantum walk. That being said, I was wondering if someone could simply explain what a random quantum walk is and then explain how they could be useful with...
Assume ##P_1## and ##P_2## are two projection operators. I want to show that if their commutator ##[P_1,P_2]=0##, then their product ##P_1P_2## is also a projection operator.
My first idea was:
$$P_1=|u_1\rangle\langle u_1|, P_2=|u_2\rangle\langle u_2|$$
$$P_1P_2= |u_1\rangle\langle...
This is an exercise from "Quantum search as a quantum simulation " in Chapter "Quantum search algorithms".
The circuit is shown as the following picture.
For small time interval, the effect of the operation in the problem statement could be written as ## exp \left ( -i \left | \psi \right >...
I am confused about the vector notation of quantum states when I have a 2 qubit system.
For 1 qubit, I just write l1> = (0 ;1 ) for representing 1,
and l0> = (1;0) for representing 0.
Dirac notation is straightforward
However when it comes to representing two qubits in linear algebra I...
Hi everyone,
I'm a computer scientist (not a physicist), so I will ask a computer scientist's question.
In all the descriptions I found of Grover's algorithm, there is an element that is puzzling the computer scientist in me: it seems that you need to tell the Oracle about the position of the...
I am fascinated by Einstein’s quote that the most unbelievable aspect of the universe was that it was intelligible. So my question is does anyone know whether it is so unlikely as to be absurd to suppose that random unguided processes could produce a rational brain in man in as little as 3...
Hello,
I was wondering if any of you know about good books on various qubit approaches for making quantum computers. There are a lot of road maps on the internet covering the pros and cons of each approach (for example: https://qt.eu/app/uploads/2018/04/QT-Roadmap-2016.pdf ) but I was hoping...
Hi everyone! Sorry for the bad English!
I'm trying to read the "entanglement between photons that never coexisted " from 2012. Avaliable at: https://arxiv.org/abs/1209.4191
And there's this equation:
##
|φ± \rangle = \frac 1{√2}(|HaHb ± |VaVb\rangle)
##
##
|ψ± \rangle = \frac 1{√2}(|HaVb ±...
I was wondering how to measure the first or even the second qubit in a quantum computing system after for example a Hadamard Gate is applied to the system of these qubits: A|00>+B|01>+C|10>+D|11>?
A mathematical and intuitive explanation would be nice, I am a undergraduate sophomore student...
Hello, I am looking for a good textbook to learn quantum computing. My background is that I am a double major in math and computer science, and I pretty much don't know anything about quantum mechanics. I prefer something that is more computer science oriented, like quantum algorithms, rather...
Following these links:
https://people.cs.umass.edu/~strubell/doc/quantum_tutorial.pdf
https://www.codeproject.com/Articles/1131573/Grovers-Search-Algorithm-explained
I have these questions:
The Oracle "knows" the correct bits in the first invocation itself. So why do sqrt(N) invocations where...
In a 2 level quantum system, should I consider the states
|0>
and
|1|>
to be qubits by themselves?
Or is only the SUPERPOSITION of these two states,
\alpha |0> + \beta |1>
considered to be a qubit?
I'm watching a lecture on the intro to quantum computing.
See the attached image which will be useful as I describe my question.
So the professor says that we have this single photon and it's in this state, ## | 0 > ##.
He states that when we send this photon through a beam splitter that it...