2
votes
1answer
50 views

Bell State vs. Bell Measurement

What is the difference between a Bell state and a Bell measurement? I am studying quantum computation, and Bell states have been introduced. I understand that Bell states can be prepared using the ...
0
votes
1answer
39 views

What is a good book for quantum mechanics and quantum computation? [duplicate]

I am looking for a book in quantum computers for self-learning.The kind of book that teaches quantum-mechanics + quantum-computation. I have basic understanding in calculus , linear-algebra (like ...
4
votes
2answers
71 views

Tensors of rotations about an arbitrary vector in C^2

I'm trying to solve the following equation: $$e^{-i\theta/2 \sigma_{\vec{i}}^A} \otimes e^{-i\theta/2 \sigma_{\vec{i}}^B} |\Psi\rangle_{AB} = e^{i\phi} |\Psi\rangle_{AB} $$ where $e^{i\phi}$ should ...
1
vote
3answers
128 views

A question on quantum computing and de Broglie's pilot wave theory

I don't know much about quantum computing except what I have read about on wiki and popsci. I have been reading about the de Broglie-Bohm pilot wave theory and how they describe quantum mechanics in ...
0
votes
0answers
19 views

A question on quantum computing? [duplicate]

I dont know much about quantum computing except what i have read about on wiki and popsci. I have been reading about the de broglie-bohm pilot wave theory and how they describe quantum mechanics in ...
4
votes
0answers
115 views

Eigenvalue of the adiabatic Hamiltonian of Farhi's three qubit 2-SAT problem

I was trying to reproduce example 3.3 of Quantum Computation by Adiabatic Evolution by Edward Farhi et. al. This is an adiabatic algorithm to solve an instance of three qubits 2-SAT problem. I think ...
0
votes
0answers
61 views

What math do I want to focus on for 1) quantum computing and 2) quantum physics? [closed]

What math do I want to focus on for 1) quantum computing and 2) quantum physics? I am interested in studying quantum computing and the Higgs Boson (quantum physics?) and ultimately working in some ...
1
vote
2answers
67 views

Quantum computing and ambiguity

I do a bit of hobby programming and I often search the internet for little oddities that are fun to ponder over. I have read a few passages that try to explain quantum computing to the layman like ...
6
votes
1answer
51 views

Is the subadditivity of quantum entropy valid in the infinite-dimensional case?

Does the subadditivity (and strong subadditivity) of quantum entropy hold for infinite dimensional quantum systems as well? Unfortunately the books in my hand give proof for finite dimensional cases ...
4
votes
0answers
81 views

Output of a beamsplitter with photon number (Fock) state inputs

Given a beamsplitter drawn below, where $\hat{a}$ and $\hat{b}$ are input modal annihilation operators, transmissivity is $\tau\in[0,1]$, and output modal annihilation operators are ...
4
votes
0answers
104 views

Is it possible to construct a quantum “computer” using laser light similar to the double-slit experiment?

Is it possible to construct an arrangement of optical devices (lasers, mirrors, slits, splitters) such that the construction could carry out a single quantum "computation"? I understand that such a ...
1
vote
3answers
145 views

Does processing for a quantum computer take place in other universes?

Apologies in advance if my question seems misinformed. I am a software developer, and neither quantum mechanics nor physics are my specialties. From ...
1
vote
0answers
58 views

Can the new results (about photonic time travel) make quantum computers feasible?

New results published about photonic time travel, reference here make quantum computers a reality in the near future? These results seem to indicate that there can be qubits that can exhibit nonlinear ...
1
vote
1answer
84 views

How to derive quantum Fourier transform from discrete Fourier transform (DFT)?

I am interested in Shor's algorithm, and I am reading several papers that related to the quantum Fourier transform (QFT). I know the there is a difference between the output of QFT and DFT (DFT). ...
0
votes
2answers
79 views

Understanding of measurement in quantum mechanics?

I have a computer science background with basically zero physics background. I am trying to gain a 'high-level' understanding of quantum mechanics to aid me in some computer science work. Is my ...
3
votes
3answers
159 views

Advantage of taking qutrits in place of qubits

In general, all the quantum algorithms which I have read so far use qubits (so the space is $\mathbb{C}^2$) and the tensor products of the qubit spaces (space is ${\mathbb{C}^2}^{\otimes n}$). So my ...
0
votes
1answer
115 views

Design a quantum circuit from a matrix

I have unitary matrix and I would find the quantum circuit associated. There are 3 qubits input so it's a 8x8 matrix but it's not a simple operation. The number of gates is not specified. Is there a ...
3
votes
0answers
54 views

Physical consequences of non-trivial quantum states homology

The set of quantum states of a finite dimensional system is a complex projective space, whose homology groups are non-trivial http://en.wikipedia.org/wiki/Complex_projective_space#Homology. Has this ...
4
votes
1answer
246 views

Trace of an operator matrix (Quantum computation and quantum information)

I'm reading the book Quantum computation and quantum information by Mike & Ike and I'm stuck at 2.60/2.61. There, the author says that, given the operator $A|ψ⟩⟨ψ|$, its trace is: $${\rm ...
2
votes
0answers
22 views

Quantum computing records (storage times)

Long storage times for qubits will be integral in the construction of a scalable quantum computer. This leads me to ask the current state of affairs in our ability to store qubits. Namely, what is the ...
1
vote
1answer
68 views

Info request on studying QIT/QIS or QM with a Computer Science background [closed]

I've been considering a career change for a long time and recently discovered the Two-Slit Experiment, which, to put it frankly, blew my mind. I then started some hefty reading and investigation into ...
9
votes
0answers
242 views

Quantum computing records (entangled qubits)

What is the current record number of entagled qubits and how has this number been increased? The latest result on stack exchange, which is 3 years old, reports 14 via this post: How many stabilised ...
3
votes
1answer
226 views

Bra-ket notation, Bits, & Superposition

I am a quantum computing enthusiast, and recently I stumbled upon this the following two propositions: $$ \alpha|1\rangle + \beta|0\rangle$$ What does this mean? My understanding of this is that: ...
4
votes
0answers
152 views

Finding the ground state of the toric code Hamiltonian

How do I write by proof, the ground state of the toric code (by Kitaev) Hamiltonian $ H=-\sum_{v}A(v)-\sum_{p}B(p) $ where $A(v)=\sigma_{v,1}^{x}\sigma_{v,2}^{x}\sigma_{v,3}^{x}\sigma_{v,4}^{x}$ and ...
0
votes
2answers
203 views

Can you read and write a quantum state to a particle without collapsing its probability field?

I know the main problem with a quantum computer is that you can't read and write data from it until after it has run though all of its calculations. But would reading and writing quantum data to ...
0
votes
0answers
73 views

Double-slit experiment formulated in a quantum circuit

What would the double-slit experiment or something analogous to it look like implemented as a quantum circuit/program? Also, what about the delayed choice quantum eraser, how would that look in a ...
1
vote
1answer
117 views

CNOT gate broken in 2 different quantum simulators? Or am I wrong?

My understanding is that the control qubit in a controlled-not gate remains unchanged after the controlled-not operation is performed on a target-qubit (so the Pauli-X gate is performed only on the ...
4
votes
2answers
114 views

Approaches to Fault tolerant quantum computation

What are the various approaches to fault tolerant quantum computation ? Two examples are 1. topological quantum computation which uses topological phases in quantum states (2-Dimensional for ...
5
votes
1answer
300 views

Explanation for the power of quantum computers

I have seen various explanations for the power of quantum computers: Quantum computers perform operations in parallel universes Quantum computers can use quantum tunneling to reach a global extremum ...
2
votes
1answer
126 views

What does $\left|x\right\rangle \left|0\right\rangle$ actually mean in bra-ket notation?

Initialize the registers to $Q^{-1/2} \sum_{x=0}^{Q-1} \left|x\right\rangle \left|0\right\rangle$ where ''x'' runs from 0 to ''Q'' − 1. This initial state is a superposition of ''Q'' ...
3
votes
1answer
107 views

Understanding operations of quantum computing advantages

For example, let us examine the case of quantum (discrete) fourier transform. There are $2^N$ samples. How do we initialize these $2^N$ samples into $N$ qubits? I have a hard time understanding this. ...
1
vote
0answers
62 views

Usage example of stabilizer codes QEC

This question directly follows the previous one about $X$ stabilizers and phase-flip errors: Practical example of stabilizer codes Let's now consider a second part of the quantum circuit that is ...
1
vote
0answers
52 views

Adiabatic evolution for initial Hamiltonian on Hadamard basis and problem Hamiltonian as diagonal

This is spawned from a comment at the answer to one of my previous questions. Someone suggested to me that claiming the following statement might be NP-hard. Could anyone please help me to figure out ...
1
vote
1answer
93 views

Practical example of stabilizer codes

Given the Steane code $$ \left|0\right\rangle_L \equiv \frac{1}{\sqrt{8}}(\left|0000000\right\rangle + \left|1010101\right\rangle + \left|0110011\right\rangle + \left|1100110\right\rangle + ...
1
vote
1answer
64 views

Confusion about a lemma on the time constraint of an adiabatic evolution (arXiv:quant-ph/0604077)

I am going through the paper Quantum adiabatic evolutions that can't be used to design efficient algorithms by Zhaohui Wei and Mingsheng Ying. On the second page they prove a lemma. The statement goes ...
2
votes
1answer
49 views

Purposes of QEC stabilizers

I am going through the idea of stabilizer formalism. Defined what is a Pauli group $P_n$ and its properties, we describe a stabilizer set $S$ as: $$S\subset P_n$$ The stabilizer set establishes ...
2
votes
0answers
61 views

How to obtain stabilizer's generators of a QEC code

The theory of QEC with stabilizer codes defines an alternative way to represent a quantum state in terms of operators. To understand better what I am concerning about, let's consider the 7-qubit ...
2
votes
0answers
104 views

Can we “safely” assume that quantum computing systems will be finite-dimensional?

This is a common assumption in the study of quantum computation to assume that the quantum systems involved are finite-dimensional, since qubits lives in the two-dimensional Hilbert space. According ...
4
votes
1answer
157 views

Entropy inequality

Assume that you have two bipartite systems $\rho_1^{AB},\rho_2^{AB}$ then I would like to prove the following: $$S(\frac{1}{2}( ...
2
votes
1answer
92 views

Coefficients of the vectors in a tensor product

The postulate says that if we want to build the compound state of two sub-systems, we just take the tensor product $\otimes$ of the respective state vectors. This means that if one of the vectors has ...
3
votes
0answers
119 views

Optimality of product input state in quantum channel

Let $\mathcal N^{A_1\rightarrow B_1}_1,..,\mathcal N^{A_1\rightarrow B_1}_k$ be a set of valid quantum evolutions with equal input and output dimensions. And let the effect of a channel on a system ...
4
votes
2answers
130 views

Quantum circuit equivalent of quantum pseudo-telepathy game

I'm trying to understand the wikipedia article on quantum pseudotelepathy. I've been trying to figure out the quantum circuits the players can use to win the game from the wiki article. (Level of ...
4
votes
2answers
219 views

Is entanglement necessary for quantum computation?

Is entanglement necessary for quantum computation? If there was no error in the computation,superposition of states would be sufficient for quantum computation to be carried out.Is this right?
14
votes
2answers
704 views

Why doesn't the no-cloning theorem make lasers impossible?

As I understand lasers, you start off with a few photons that are in an identical state, and other photons that are created later tend to have the same quantum numbers due to Einstein-Bose statistics. ...
2
votes
0answers
93 views

Second quantization with qubits

Is "second quantization" means system wich can contain variable, unknown, superposed and otherwise uncertain number of qubits? Can "second quantized" system contain 0.5% of 1 qubit and 95% of 2 ...
5
votes
2answers
215 views

Classically efficient universal quantum computation (P=BQP) with magic and bound states

$\text P$ vs $\text {BQP}$ is an open question. That is, "can systems which require a polynomial number of qubits in the size of an input be described with only a polynomial number of bits?" If the ...
2
votes
2answers
156 views

Why does the classical equivalent to a quantum computer take so many bits?

A quantum computer with 10 qubits is classically equivalent to $2^{10}$ bits. How is this equivalence worked out? I understand that a single qubit is a vector in a 2-dimensional hilbert space, whose ...
2
votes
1answer
389 views

Help on applying a Hadamard gate and CNOT to two single q-bits

I am stuck on a few issues in this video. (Note: It is at the frame concerning this question.) In it, from what I understand (which could be wrong) we first apply the Hadamard gate to a qbit in the ...
1
vote
2answers
223 views

Quantum XOR: How do you generalize it?

Consider the classical XOR Gate: Given a 2 bit system: $G = [u_1, u_2]$ $$XOR(G) = (u_1 + u_2) \ mod \ 2$$ Is the following a good generalizaiton of a Quantum XOR Gate: Given a 2-qubit system: ...
2
votes
0answers
119 views

Quantum annealing computing

What is Quantum Annealing and quantum annealing computing and what are its advantages and disadvantages with respect to quantum circuit quantum computing/computers?