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Why do quantum gates have to be reversible?

One possible reason I have come up with is that we are modeling quantum gates by unitary matrices. And since unitary operations are reversible we have to be able reverse the operation in the physical ...
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3answers
80 views

Transforming Qubits Into Bits

From what I understand, a qubit exists in a superposition of states and once it has been measured, it must fall into one of the two possible states. Now, I have been told that once a qubit is measured,...
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2answers
54 views

Quantum Logic Gates

In classical computation, a bit can have the value of either 1 or 0 and one can apply a logic gate to this bit. As far as I understand, in classical computation, no matter what gate is used, the value ...
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2answers
83 views

Is it possible to reverse engineer quantum computer?

Case: I give you a "live" box with quantum signals going through it (while performing calculations) and which contains quantum logic gates. You don't know exact internal structure of box, but you're ...
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1answer
43 views

Something about non BCS pairing

When I have read about literatures, the non-BCS type superconductor always involve some kind of pairing which the energy gap $\Delta$ is not a constant but a function of momentum $k$: $\Delta=\Delta(k)...
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1answer
55 views

How to prove that quantum computers can't solve problems outside PSPACE quickly?

What are general methods to prove that certain complexity class is not proper superset of PSPACE class, and how to apply them in quantum case (for BQP class, for example).
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69 views

Quantum computer able to compute non-computable elements? [closed]

I just recently read the journal article (below) about the Orchestrated Objective Reduction theory put forth by Roger Penrose and Stuart Hammeroff. According to this theory, the phenomenon of '...
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0answers
17 views

Interactions preserving separability

Consider the interaction (described by a unitary matrix U) of two qubits initially in a separable state |ab⟩ = |a⟩ ⊗ |b⟩, such that after interaction the composite system is in state U|ab⟩. Are there ...
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1answer
45 views

Can quantum computer provide random or just pseudo-random number, or none of both? [closed]

Can quantum computer provide random or just pseudo-random number, or none of both? It's a bit confusing me, since collapse of wave function once measured.
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3answers
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Two qubits system in polar co-ordinates

I know that I can write a single qubit state in terms of polar co-ordinates $(r,\theta,\phi)$ on a Bloch sphere. \begin{equation} \rho = \begin{pmatrix} \frac{1+r \cos\theta}{2} &\frac{r \exp(-i\...
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1answer
61 views

How to choose proper measurement operator?

Let's assume I have two states inside the Bloch sphere, at radial vectors $r_1$ and $r_2$ respectively $(r_1<r_2<1)$. Their angular location is same. These are like: \begin{equation} \rho = \...
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1answer
56 views

Intuition for defining basis for Hamiltonian in momentum representation

I am going through Quantum information approach to the Ising model: Entanglement in chains of qubits by Stelmachovic et al. In Section A.4, the authors determines the eigenvalues and eigenstates of ...
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1answer
60 views

rotation of a state in Bell basis

Suppose I have a state in Bell basis. For example \begin{equation} \rho = \begin{pmatrix} \rho_{11} &0 & 0 & \rho_{14} \\ 0 &\rho_{22} & \rho_{23} & 0 \\ 0 &\rho_{32} &...
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0answers
45 views

Toric code vs Shor's code

I study computer science and wanted to get into the field of quantum computing. Right now, I'm trying to tackle the subject of quantum error correcting codes. As is the usual, I've started with Shor's ...
2
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1answer
71 views

Are the 'clock' and 'shift' operators used in Qudit codes physically realizable?

I've recently started doing some reading on the subject of qudit codes. In particular, i'm interested in the frequently used clock and shift operators. Can these operators be physically realized? Or,...
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0answers
40 views

Why does the Quantum Approximate Optimization Algorithm work?

I am trying to understand the structure of the QAOA algorithm (see here) which is seen as one of the candidates to demonstrate early quantum supremacy. Yet Farhi, Goldstone and Gutmann only describe ...
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0answers
33 views

Questions on the Lechner-Hauke-Zoller quantum annealing architecture

The Lechner-Hauke-Zoller quantum annealing architecture was first introduced in A quantum annealing architecture with all-to-all connectivity from local interactions. While going through the paper, I ...
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0answers
41 views

Probability of measuring a pure qubit state after some unitary rotation [closed]

Suppose I have the prepared state $$|+\rangle = \frac{|0\rangle + |1\rangle}{\sqrt{2}}$$ and the unitary $Z_{\pi/2}$ which rotates a state in the Bloch sphere by $+\pi/2$ about the $z$-axis. As I ...
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1answer
31 views

Can we perform matrix operations of CNOT on 2 qubit systems? [closed]

I am trying to get started on quantum computing. I find that 2x2 matrices like Pauli X,Y,Z,or gates like H,S can be used to perform operations on single qubits as direct matrix multiplication. For e.g ...
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2answers
79 views

Variation of schrodinger cat replaced by quantum computer

In the "classical" imaginary Schrodinger's cat experiment, which seems to be no longer serious, or at least irrelevant, by many (some?) people, everything is explained away by decoherence. Now, let ...
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2answers
65 views

What's Bob's state after this quantum circuit? [closed]

As shown in the picture, we know Alice's state will be intact after this circuit, but what about Bob's state, will it be $|0\rangle$ or $(|0\rangle+|1\rangle)/\sqrt{2}$ and why? I think it will be $(|...
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1answer
27 views

Heisenberg Representation of Quantum Computers explain observable transformations

The Heisenberg Representation of Quantum Computers (Daniel Gottesman) http://arxiv.org/abs/quant-ph/9807006 Suppose we have a quantum computer in the state $|\psi\rangle$, and we apply the ...
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0answers
35 views

Can anyone recommend some recent journal articles on the limitations of Quantum Computing

More specifically, I would like some reading material on what the issue is with quantum computers, why can we not yet create them? Are there any journal articles that comprehensively list the reasons ...
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2answers
103 views

How do we know WHEN to get the result from quantum computers?

So I always hear that you can't disturb quantum computers because this will ruin the particles superstate. Well, how do we know WHEN to retrieve the result from the calculation? How can we determine ...
2
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2answers
321 views

Quantum Grover's algorithm: constructing the black box gate

Grover's Algorithm uses a black box gate that can recognize an x such that $f(x) = 1$ for a certain function f. It inverts this x and leaves all other inputs unchanged. My question is about the ...
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1answer
34 views

How can a quantum dot be used as a qubit?

Many people say that quantum dot is a potential physical representation of qubit. A qubit should have two distinguishable states which may carry quantum information. What are the two states of a ...
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0answers
22 views

Is there a quantum computing model accounting for uncertainty of a qubit state?

Any physical quantum computer would have a limit on the fidelity with which it can create qubit superposition states. If we're trying to create $|\Psi\rangle = c_0|0\rangle + c_1|1\rangle$, the ...
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2answers
79 views

What do operations on single Qubits of Unfactorable Superpositions Do?

So suppose I have the following Quantum Circuit: A ---- |Control| -----|Hadamard|---- B ---- |xxxxxxx|------------------------ Which is a 2 input Controlled Gate (applying some gate of two choices ...
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3answers
102 views

Quantum computing entanglement dimensions question

While trying to understand the basics of how quantum computers work, I recently read this statement. "...consider that single-qubit states can be represented by a point inside a sphere in 3-...
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2answers
67 views

Can a non-entangled qubit be teleported by entangling it?

Let's say I have a qubit that is not entangled in state $\psi$. I want to teleport this qubit by entangling it with another qubit but still getting $\psi$ back in the end. Is this possible, or would ...
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2answers
125 views

What exactly does No cloning mean, in the context of Quantum Computing?

I am trying to get an intuitive idea of how the No-Cloning theorem affects Quantum computation. My understanding is that given a qubit $Q$ in superposition $Q_0 \left| 0 \right> + Q_1 \left| 1 \...
3
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1answer
53 views

Is QC with Superpositioned Quantum Gates any different than normal Quantum Computation?

This might be more appropriate for theoretical CS stackexchange, but it feels sufficiently low level to be relevant here. Consider the following thought experiment: I have a Quantum FPGA, it is a ...
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0answers
58 views

Approximate cloning of a quantum state, informed by past measurements

Suppose I give you a state $|\psi\rangle$, and tell you a sequence of measurements that have been performed on it. The measurements are not guaranteed to be orthogonal to each other, or to cover the ...
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21 views

When will a useable universal quantum computer first be realised? [closed]

Ideally with the reference to the type of technology, when do experts predict a small universal quantum computer of a couple hundred qubits will be developed? From my reading the leading techology is ...
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5answers
160 views

How Are Quantum Computers Able to Store Any Data at all?

So if qubits can have more than two states, and according to this video, https://www.youtube.com/watch?v=T2DXrs0OpHU you don't know what you get until you actually "open the box", if its all ...
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1answer
86 views

Can a system be PERFECTLY simulated by a quantum (and classical) computer? [closed]

This is a thought experiment, and as such will assume some crazy things. Let's say I decide to perfectly simulate my university as it is right now. I use a magic machine to instantly scan the entire ...
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1answer
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C2(U) Unitary Matrix Representation

Above is my work for the unitary matrix representation of a C2(U) gate. However, this does not agree with a link I found online for what it should look like. Below my work, I have written the ...
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1answer
93 views

Unitarity of quantum evolution

In this paper by Charles Bennett, he says on page 25, I understand why U(XOR) gives the result it does but why is that a consequence of its unitary property? Thanks
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0answers
36 views

How many states does a qubit have? [closed]

There is something I am trying to understand about qubits. If a qubit can exist in an infinite (is that even correct?) number of states prior to the measurement, then why can it only be measured in ...
2
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1answer
143 views

How do Quantum Computers work? [closed]

I have a decent knowledge of quantum mechanics, undergraduate level, but would like a description of how a quantum computer works and why it is important that superpositions of states, ie coherence, ...
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3answers
221 views

What's so confusing about quantum physics? [closed]

Okay, just right off the bat, I want to make it clear that this is a stupid question. Check out this graph, from SMBC: Ignore the 'political discourse' part and replace it with 'talking about ...
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1answer
62 views

What are some of the differences between (the fields of) quantum computation and quantum information theory? [closed]

I have just started self-learning quantum information theory, and have a sub-trivial question: what is the difference between that field of study and quantum computation? I have some understanding ...
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0answers
50 views

Electron jump into a transistor to read qubit state

Prof. Andrea Morello, a quantum physicist, in one of its quantum computer models uses the spin of the outermost electron in a phosphorus atom to represent a qubit. This atom is embedded to a transitor....
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2answers
39 views

Looking for an example of an operator that will not converge on maximally mixed state

Based on my former questions and the kind help from the answers (especially Norbert Schuch), it seems that the maximally mixed state is not that special as I thought. But still I have to admit that it ...
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1answer
61 views

Holonomic and Topological Quantum Computing [closed]

In topological quantum computation, anyons are braided in spacetime, performing non-trivial evolutions of some degenerate groundstate. In holonomic quantum computation, the system is braided in ...
1
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1answer
74 views

How to solve such a maximal entropy oriented optimization problem?

I am considering such a problem: (1) Given a finite dimensional composite system AB whose initial state is a product state of A and B so that $\rho_{AB}=\rho_A\otimes \rho_B$. (2) Assuming AB ...
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0answers
42 views

Finding the dependence of dephasing time on flux noise in Transmon Qubits

Before introducing some relevant concepts I'll begin by stating my question. What I am looking for is the connection between the noise the flux through the SQUID in my transmon qubit (related to the ...
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0answers
28 views

Probability of obtaining the desired state in quantum linear regression

I was reading today the paper "Pattern classification with linear regression on a quantum computer" where the authors calculate in a final step the probability of success to measure the last qubit in ...
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Adiabatic turning on of coupling constant in simulation of $\phi^4$ theories in the JLP algorithm

In the Quantum Algorithms for Quantum Field Theories by Jordan, Lee and Preskill they have devised an efficient algorithm to simulate $\phi^4$ theories. Given by the Lagrangian density $$\mathcal{L}(\...
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67 views

A question about ultimate computation capability

If we consider the physical limit of computational capability of a system with average energy $E$, then (1) According to Margolus and Levitin, a quantum system with average energy $E$ takes time at ...