Most Popular
1500 questions
8
votes
1 answer
How to calculate the average fidelity of an amplitude damping channel
An answer to this question shows how to calculate the average fidelity of a depolarizing channel. How would one go about calculating this for an amplitude dampening channel? I tried working out the math myself but had no luck. The tricks used in the…
Quantum Guy 123
- 1,499
- 6
- 20
8
votes
1 answer
How do we find the stabilizer generators for the three-qubit bit-flip code spanned by $|000\rangle$ and $|111\rangle$?
In Nielsen & Chuang's book "Quantum Computation and Quantum Information" section 10.5.6, page 467 there is the following statement
Consider the familiar three-qubit bit-flip code spanned by the states $|000\rangle$ and $|111\rangle$,…
user27286
- 1,015
- 6
- 17
8
votes
1 answer
What are the fundamental differences between trapped ion quantum computers and other architectures?
There are many different ways to build quantum computers, such as superconducting qubits, quantum dots, and ion traps.
What I would like to understand is why some universities and research organizations have chosen to study trapped ion quantum…
Riz-waan
- 203
- 1
- 9
8
votes
2 answers
What's the 'physical consistency' in the partial trace scenario?
I'm reading 'Why the partial trace' section on page 107 in Nielsen and Chuang textbook. Here's part of their explanations that I don't quite understand:
Physical consistency requires that any prescription for associating a ‘state’, $\rho^A$, to…
ZR-
- 2,408
- 9
- 24
8
votes
1 answer
List of practical quantum computing algorithms that have speed-up higher than quadratic speed-up?
From this link (provided by @KAJ226's comment in this question), it appears as though current error correction methods are not enough to get practical speedup out of algorithms that have quadratic speedups (before taking error correction into…
Steven Sagona
- 1,149
- 7
- 17
8
votes
3 answers
Square root of Pauli operators: is there a common convention to define them uniquely?
There exists many different matrices square root. For instance I can define either of the two for square root of $X$:
$$\sqrt{X}^{(1)} \equiv \frac{1}{\sqrt{2 i}} \begin{pmatrix} 1 & i \\ i & 1 \end{pmatrix}$$
Or as suggested on…
Marco Fellous-Asiani
- 2,220
- 2
- 15
- 42
8
votes
1 answer
Necessary and sufficient condition to define logical operation (stabilizer code)
My question is highly related to this topic
It is about defining logical operation on a Stabilizer code.
I call $S$ the stabilizer group of a code space $C$, and I assumed it is generated by a family $S=\langle s_1,...,s_p \rangle$. I call $G_n$ the…
Marco Fellous-Asiani
- 2,220
- 2
- 15
- 42
8
votes
5 answers
Why isn't output of Deutsch–Jozsa Algorithm simply $|0\rangle$?
If I look at the circuit diagram of the Deutsch–Jozsa Algorithm:
Now given the fact that Hadamard matrix or gate is its own inverse (see here), shouldn't the output (top wire) simply give back $|0\rangle$?
morpheus
- 391
- 1
- 7
8
votes
2 answers
What kind of boolean functions are faster to compute on qc?
Deutsch-Jozsa algorithm can compute if some function $f : \{0,1\}^n \rightarrow \{0,1\} $ is constant. This goes exponentially faster than on classical computers.
If we consider the set of all boolean functions $f : \{0,1\}^n \rightarrow \{0,1\} $…
user3680510
- 183
- 3
8
votes
1 answer
Does quantum computing provide any speedup in evaluation of transcendental functions?
With the integer factorisation problem, Shor's algorithm is known to provide a substantial (exponential?) speedup compared to classical algorithms. Are there similar results regarding more basic maths, such as evaluating transcendental…
Norrius
- 687
- 11
- 18
8
votes
1 answer
Why is HHL the popular choice to solve QLSP and not the Childs et al. (2017) algorithm?
The Childs, Kthari, and Rolando (2017) (CKS) algorithm can solve the quantum linear systems problem (QLSP) in $\operatorname{poly}(\log N, \log(1/\epsilon))$ time while the HHL algorithm solves it in $\operatorname{poly}(\log N, 1/\epsilon)$ time.…
thespaceman
- 597
- 6
- 16
8
votes
3 answers
How can we reliably know if a key size is still safe to use as new quantum computers are created?
I've heard that quantum computers pose a major threat to 1024 bit and possibly even 2048 bit RSA public-private key cryptography. In the future however, bigger size keys will probably become at risk at one point or another, as newer, faster quantum…
Alex Jone
- 633
- 7
- 8
8
votes
2 answers
Are qutrits more robust to decoherence?
A string of $n$ qutrits has a state-space spanned by the $3^n$ different states $\lvert x \rangle $ for strings $x \in \{0,1,2\}^n$ (or $x \in \{-1,0,+1\}^n$, equivalently), while $n $ qubits can only represent $2^n$ computational basis…
user609
8
votes
2 answers
How to compute the measurement probability in swap test?
The figure of a circuit and the state are as follows.
The final state before the measurement is…
karry
- 689
- 4
- 14
8
votes
2 answers
How do quantum computers prevent "quantum noise"?
On the Wikipedia page for Shor's algorithm, it is stated that Shor's algorithm is not currently feasible to use to factor RSA-sized numbers, because a quantum computer has not been built with enough qubits due to things such as quantum noise. How do…
ack
- 183
- 1
- 6