Most Popular
1500 questions
8
votes
0 answers
Empirical Algorithmics for Near-Term Quantum Computing
In Empirical Algorithmics, researchers aim to understand the performance of algorithms through analyzing their empirical performance. This is quite common in machine learning and optimization. Right now, we would like to know something about the…
hopefully coherent
- 697
- 6
- 14
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
- 1,371
- 5
- 18
8
votes
1 answer
What are tentpole topics in quantum computing?
Lots of beginners are starting to learn quantum computing. But there are also experienced people that have been working in this field for many years.
What are some topics that might be considered important for a beginner to learn thoroughly?
By…
user27286
- 955
- 4
- 14
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-
- 2,388
- 7
- 19
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
- 1,119
- 7
- 16
8
votes
1 answer
Are almost-Clifford circuits almost easy to simulate?
Circuits consisting entirely of Clifford operations in $\{X, Y, Z, H, S, \text{CNOT} \}$ are "easy" to simulate classically since there is a method that can fully compute such circuits over $n$ qubits with $O(n^2)$ complexity.
I'm curious if…
forky40
- 6,678
- 2
- 9
- 30
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
- 1,514
- 2
- 13
- 33
8
votes
4 answers
Superposition of quantum gates
In the standard model of quantum computation a gate is a unitary that acts on a subsystem. Physically, it can be implemented by some device. Now, any device is also a part of our quantum world, thus it has a quantum state. This quantum state, in…
Danylo Y
- 7,144
- 11
- 20
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
- 359
- 1
- 7
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
- 657
- 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
- 511
- 4
- 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
1 answer
What is known about quantum algorithms for graph isomorphism?
Shor's algorithm (for factoring integers) and Grover's algorithm (for searches) are the two most well-known quantum algorithms. I was wondering if there was a similar result in QC that dealt with the Graph Isomorphism problem?
I can't seem to find a…
paulinho
- 221
- 1
- 4