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4
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7answers
458 views

Quantum computers: are they possible or impossible?

I know quantum computers are very complicated and my question is is there any way in "Principle" to create one? Are there already quantum computers being created?
15
votes
5answers
382 views

direct sum of anyons?

In the topological phase of a fractional quantum Hall fluid, the excitations of the ground state (quasiparticles) are anyons, at least conjecturally. There is then supposed to be a braided fusion ...
3
votes
3answers
116 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
2answers
169 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
2answers
65 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 ...
11
votes
3answers
787 views

How much is quantum computation changing the interpretation of quantum theory, and, if at all, how?

At the beginning of quantum computation, David Deutsch made a strong claim that the Many Worlds interpretation of quantum theory was at the foundation of his ability to do what he did. There was a lot ...
6
votes
1answer
82 views

Correspondence principle and quantum computers

I just read this article at https://medium.com/the-physics-arxiv-blog/7ef5eea6fd7a about the work of a physicist called Bolotin, that states that P!=NP (from computer science) implies that large ...
1
vote
1answer
195 views

Hamiltonian reduction having constant of the motion

I have this $2^n*2^n$ matrix that represent the evolution of a system of $n$ spin. I know that I can have only one excited spin in my configuration a time. (eg: 0110 nor 0101 ar not permitted, but ...
0
votes
1answer
61 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
3answers
216 views

If quantum computing requires hundreds of digits of accuracy, how will it be possible?

Leonid Levin said, "Exponential summations used in QC require hundreds if not millions of decimal places accuracy. I wonder who would expect any physical theory to make sense in this realm." See ...
2
votes
0answers
43 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 ...
6
votes
1answer
446 views

Why do we want to entangle qubits?

The title is pretty much all I want to ask. Why are qubits entangled? To my knowledge (which isn't that deep) a quantum register can be realized without entangling the qubits.
1
vote
0answers
27 views

Different implementation of Feynman's clock

In equation 7 of the paper, Feynman's clock, a new variational principle, and parallel-in-time quantum dynamics, the clock register is different from Feynman's original proposal. According to this ...
4
votes
1answer
124 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 ...
9
votes
0answers
178 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 ...
2
votes
0answers
16 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
48 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 ...
4
votes
6answers
766 views

Why do some physicists believe that scalable quantum computing is possible? [closed]

If you drop a glass cup on the ground, it will break and shatter into pieces. This happens all the time and is consistent with quantum mechanics. But it never happens that a shattered glass cup ...
3
votes
1answer
177 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: ...
3
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0answers
66 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 ...
5
votes
1answer
74 views

When is an operator subspace the span of Kraus operators?

Let $A$ and $B$ be finite dimensional Hilbert spaces, and let $\mathcal{L}(A \to B)$ be the space of linear operators from $A$ to $B$. Say that a subspace $K \subseteq \mathcal{L}(A \to B)$ is a span ...
4
votes
2answers
173 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?
0
votes
0answers
55 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
83 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 ...
3
votes
2answers
90 views

Smallest number of quantum gates to simulate other gates?

What is the smallest number of Fredkin gates needed to simulate a Toffoli gate? What is the smallest number of Toffoli gates needed to simulate a Fredkin gate? Where the Toffoli's gate is the CCNOT ...
1
vote
1answer
193 views

CNOT gate output with both inputs in superposition

What is the output of a CNOT gate if both inputs are in superposition? For example, what happens if: $\left|x\right>=\alpha_x\left|0\right>+\beta_x\left|1\right>$ and ...
4
votes
2answers
97 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 ...
1
vote
2answers
106 views

Quantum Computation

Is there any rule or technique so that one can design quantum gate operator from matrix operator? Suppose, what will be the quantum gate operator for this matrix operator : $$ \left( \begin{array}{c ...
0
votes
0answers
39 views

How can a qubit superposition state be written to a quantum register?

If a 3 qubit register can simultaneously store all 8 possible values in superposition, then how it is achieved to write 8 values in to the register? And How these 8 values can be processed parallel to ...
10
votes
3answers
2k views

How are physics and computer science getting united?

How is theoretical computer science getting united with physics? Phenomena like Quantum Computing uses Quantum Mechanics to be able to compute things, how are computers helping not just to model our ...
1
vote
2answers
105 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 ...
5
votes
1answer
262 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 ...
4
votes
2answers
113 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 ...
2
votes
1answer
116 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
96 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. ...
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vote
0answers
36 views

Which model of computation can be viewed as being extended by the currently most relevant models of quantum computation?

Which model of quantum computation resembles most closely the attempts of implementation currently being made? And which non-quantum model of computation is the conceptually closest one to the above ...
2
votes
0answers
168 views

How does Landauer's Principle apply in quantum (and generally reversible) computing

I understand that a reversible computer does not dissipate heat through the Landauer's principle whilst running - the memory state at all times is a bijective function of the state at any other time. ...
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0answers
39 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
1answer
82 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
0answers
45 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
57 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
48 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 ...
3
votes
3answers
360 views

What is the next step beyond quantum computation?

Assuming we develop quantum computers one day, what would be theoretically the next step? Would it be string-theory based computers? How would these computers differ performance-wise (ie what can they ...
0
votes
2answers
84 views

Question on quantum computation, entanglement and speed of information propagation

Imagine a following thought experiment. Suppose we have a large amount of entangled particle pairs, several million or billion. Now suppose there are two observers, each carrying one member of ...
5
votes
2answers
190 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
0answers
48 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
93 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 ...
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0answers
74 views

Beginner projects in NMR quantum computing [closed]

I have applied for a summer project in NMR quantum computing as I want to learn this field, but my professor wants me to tell him the project title. I have no idea about the field and what projects ...
4
votes
1answer
150 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}( ...
3
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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 ...