Most Popular
1500 questions
7
votes
2 answers
What are the pros/cons of Trapped Ion Qubits, Superconducting Qubits and Si Spin Qubits?
Among available qubit technologies for universal quantum computing these 3 come up as promising. NV centers and Majorana qubits also underway but relatively new.
I find superconducting qubits and Trapped Ion qubits very hard to scale. Also…
mando
- 355
- 3
- 11
7
votes
1 answer
What problems in chemistry or materials science could be solved with 100 fault-tolerant qubits?
Background
IBM, Infleqtion, QuEra, and other quantum hardware companies have announced roadmaps where they expect to have 100 or more fault-tolerant qubits by the end of the decade. It seems increasingly likely that at least one of them will…
taciteloquence
- 219
- 1
- 3
7
votes
3 answers
Is there something like GitHub for quantum programming?
I'm just learning about quantum computer but some of it has been available for people to research & practice so I'd like to study it myself. The only kind of quantum computing I found so far is IBM cloud service and Q# quantum simulator but the…
Dan Minh Toan
- 145
- 3
7
votes
2 answers
Does "quantum registers with $n$ qubits are able to hold $2^n$ values and therefore scale exponentially" actually hold that straightforwardly?
A lot of people claim that quantum provides exponential speedup whereas classical computers scale linearly. I have seen examples (such as Shor's algorithm and Simon's) that I believe, but the layman's explanation appears to boil down to "quantum…
Thomas Hubregtsen
- 624
- 1
- 4
- 10
7
votes
1 answer
Are qubits preferred over qumode, and if so, why?
Qubit and qumode are different forms of quantum computation. But most existing quantum computers/chips seems to be of discrete variables. I heard that a group chose qubit for a quantum optical frequency comb experiment relating to quantum computing…
raycosine
- 880
- 8
- 12
7
votes
2 answers
What are reliable references on analytical and/or numerical studies of threshold theorems under faulty quantum error correction?
By "faulty", I mean that you can have errors on the ancilla qubits, you can have faulty syndrome extraction, etc.
Sherif F.
- 171
- 3
7
votes
1 answer
Computing of the action of the amplification operator $\mathbf Q$ over $|\Psi_i\rangle$ in the quantum amplitude amplification algorithm
$\newcommand{\Q}{\mathbf{Q}}\newcommand{\S}{\mathbf{S}}\newcommand{\A}{{\mathcal A}}\newcommand{\H}{\mathcal H}$In the quantum amplitude amplification algorithm, as explained in Brassard et al. 2000 (quant-ph/0005055), the unitary performing the…
glS
- 27,510
- 7
- 37
- 125
7
votes
1 answer
What is the purpose of the TDG gate in QISKit?
The QISKIT documentation doesn't explain what a TDG gate does and I can't find it anywhere else online.
Theodore Lewitt
- 71
- 2
7
votes
2 answers
Arbitrary powers of NOT and SWAP
The square-root of not and square-root of swap gates are often singled out for discussion of gates displaying important properties relating to quantum computers.
How do I define arbitrary (non-integer) powers of the square-root of NOT or…
DaftWullie
- 62,671
- 4
- 55
- 140
7
votes
2 answers
Can we think that any multi-qubit quantum gate has a constant complexity from physics perspective?
It's known that any multi-qubit quantum gate can be represented as a product of a number of CNOT and single-qubit gates. The total number of these simple gates required is exponential (in the number of qubits) on average, and thus we can say that an…
Danylo Y
- 8,076
- 13
- 24
7
votes
1 answer
How to get smaller stabilizer codes with Gottesman's construction?
I'm following the construction from Section 3.5 of Daniel Gottesman's thesis (third paragraph), which is supposed to allow us to construct an $\left[ \hspace{-1pt} \left[ n-1, \, k + 1, \, d - 1 \right] \hspace{-1pt} \right]$ stabilizer code $C'$…
Ben Criger
- 93
- 4
7
votes
1 answer
Is it possible to derive a Schmidt decomposition for a mixed state?
It is relatively simple to derive the Schmidt decomposition of a pure state $|{\psi}\rangle \in H_A \otimes H_B$ with the SVD decomposition theorem. There are plenty of examples (lecture notes, books, videos, etc.) on the subject.
The question I…
JMark
- 195
- 6
7
votes
2 answers
Is there a no-go theorem for or an upper bound on code threshold?
My understanding of the code threshold for an $ [[n,1,3]] $ code is something roughly like the setup given in
How to compute the error threshold for the $9$-qubit Shor code?
where the error channel is a depolarizing channel in which no error occurs…
Ian Gershon Teixeira
- 5,062
- 6
- 30
7
votes
1 answer
Anything in between quadratic and exponential speedups?
Question
There exist a handful of proven quadratic quantum speedups (some examples include [1-3]) and even a few proven exponential quantum speedups (some examples include [4-6]). But there seems to be a dearth in quantum algorithms with proven…
sheesymcdeezy
- 2,021
- 8
- 27
7
votes
1 answer
Why is the orbit of a unitary t design a complex projective t design?
The paper Qubit stabilizer states are complex projective 3-designs states in the final paragraph that "any orbit of a unitary t-design is a complex projective t-design." Using this fact one can take the simple proof that the Clifford group is a…
Ian Gershon Teixeira
- 5,062
- 6
- 30