Questions tagged [quantum-computing]
Quantum computation and computational issues related to quantum mechanics
363
questions
9
votes
1answer
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What are the general direction and target question in the field of quantum error correction?
After quantum error correction was introduced in mid '90s, in subsequent years many of the classical analogues regarding the structure of code (such as singleton bound, GV bound etc) were obtained in ...
46
votes
17answers
4k views
Physics results in TCS?
It seems clear that a number of subfields of theoretical computer science have been significantly impacted by results from theoretical physics. Two examples of this are
Quantum computation
...
5
votes
1answer
67 views
Survey on Quantum error correction
Are there any standard recent survey articles on quantum error correction (and may be including fault Tolerant computing)? The most standard ones that many people refer to are this and this. Both of ...
0
votes
0answers
4 views
Direct Diffie-Hellman by Shor's algorithm
Shor's algorithm appears to be capable of finding discrete logarithm even if the modulus is composite. Does the algorithm implicitly compute the Carmichael Lambda which goes in the exponent or somehow ...
6
votes
1answer
199 views
Are all computational models of quantum computing equivalent?
So the question was inspired by a seminar which presented the following models of quantum computing:
Quantum Computing with Photons
Quantum Computing with Rydberg atoms
Quantum Computing with trapped ...
0
votes
0answers
44 views
generalizations of hidden subgroup problem
Quantum Fourier Sampling tries to solve hidden subgroup problem which is defined via a map $f$ from group $\mathrm{G}$ to some set $X$ that separates cosets of sum unknown subgroup $\mathrm{H}$.
$f(...
1
vote
0answers
50 views
Does the approximatibility of individual gates together with unitarity imply BPP=BQP
Suppose you can prove upper bounds on errors from approximating an individual quantum gate by randomly hashing the qubits of a circuit to a polylog number of qubits. (So, you prove a bound on how much ...
2
votes
0answers
90 views
Can hash functions speed up quantum simulation? (Generalizing May and Schlieper's idea) [closed]
To conform with the CS Theory SE crossposting rules, I've created a separate post for dequantizing Shor's algorithm (discussion on the Quantum Computing Stack Exchange was mostly about Shor's ...
0
votes
0answers
47 views
Gate definitions for quantum random access codes
I would like to know how the gates are defined in quantum random access codes? Consider the $2 \to 1$ code described in Lemma 3.1 of this paper.
The section defines the encoding and decoding circuits. ...
1
vote
0answers
108 views
Quantum error correction and graph codes
I was reading combinatorial approach towards quantum correction. A lot of work in this is on finding diagonal distance of a graph. Let me add definition of diagonal distance so that this remains self-...
0
votes
0answers
39 views
Hardwiring the output in a quantum circuit
In this paper, while using a diagonalization argument in Section $5$, the authors write:
Fix some enumeration over all $poly(n)$-size quantum verifiers $M_{1},
M_{2},...$ which we can do because the ...
7
votes
0answers
151 views
What is the complexity of estimating the number of paths between two vertices of a large graph?
Consider an $N\times N$ adjacency matrix $A$ of some large, $b$-sparse undirected graph $G$. The $(i,j)$ entry of $A^m$ counts the number of $m$-length paths between vertex $i$ and vertex $j$.
We let ...
21
votes
2answers
830 views
PPAD and Quantum
Today in New York and all over the world Christos Papadimitriou's birthday is celebrated. This is a good opportunity to ask about the relations between Christos' complexity class PPAD (and his other ...
-2
votes
1answer
156 views
What evidences are there that $PP$ is in $BQP$ and $PP$ is not in $BQP$?
Unlike hierarchy collapse arguments for classical complexity we have that quantum complexity is different.
What evidences are there that $PP$ is in $BQP$?
What evidences are there that $PP$ is not ...
1
vote
0answers
43 views
Non-rigid isomorphic structures
In many of the problems trying to solve hidden shift over some objects like graphs mainly the rigid classes are considered. For eg. in this and this isomorphism problem restricted over rigid graphs is ...
3
votes
2answers
816 views
Continued Fraction Algorithm in Shor's Algorithm
I am just trying to make the final link of Shor's algorithm clear. Here $r$ is the order of $x$ modulo $N$.
We have a number $\psi$, which for a rational number $\dfrac{s}{r}$ satisfies
\begin{...
22
votes
5answers
6k views
Is there any connection between the diamond norm and the distance of the associated states?
In quantum information theory, the distance between two quantum channels is often measured using the diamond norm. There are also a number of ways to measure distance between two quantum states, such ...
1
vote
1answer
102 views
On the paper “Quantum Computing Hamiltonian cycles”
The paper Quantum Computing Hamiltonian cycles claims:
An algorithm for quantum computing Hamiltonian cycles of simple,
cubic, bipartite graphs is discussed. It is shown that it is possible to
evolve ...
1
vote
1answer
100 views
Google quantum supremacy experiment data
I don't know if this is the right place to ask.
Still, I vaguely remember that there was a desire expressed by some people in this community to get access to the data of the 53 qubit Google quantum ...
5
votes
1answer
124 views
Is black box parallel quantum speedup ever nontrivial?
Grover's algorithm is not parallelizable, in that $p$ quantum processors searching over $n$ elements can't do better than $O(\sqrt{n/p})$ queries.
Are there any oracle problems where quantum ...
0
votes
0answers
34 views
Must the cryptographic test for quantumness in [BCMVV18] use post-quantum Trapdoor Claw-Free Functions?
Brakerski, Christiano, Mahadev, Vazirani, and Vidick propose a scheme for verifiable computational quantumness based on a strengthening of trap-door claw-free functions (TCFs).
In the above scheme:
...
5
votes
1answer
246 views
Witness verifiable quantum advantage
Update: A slightly different version of this question has been answered here.
As far as I can see, a major issue with Google's recent quantum supremacy claim is that it is hard to verify the results.
...
1
vote
0answers
36 views
Oracle separation between coNP and QMA implies oracle separation between NP and QMA
In [this] paper, Aaronson remarks (page 2, footnote) that:
From the BBBV lower bound for quantum search [6], one immediately
obtains an oracle $A$ such that $coNP^{A} \not\subseteq QMA^{A}$ for ...
1
vote
1answer
118 views
Diagonalization arguments for QMA type proof systems
Diagonalization is a very common technique to find oracle separations. For example, it can be used to separate $\cal{P}$ and $\cal{NP}$, with the essential idea being that of constructing an oracle in ...
5
votes
0answers
122 views
Is there an analogue of QMA where Merlin gives Arthur unitaries rather than states?
$\def\braket#1#2{\langle#1|#2\rangle}\def\bra#1{\langle#1|}\def\ket#1{|#1\rangle}$Is there an analogue to $\mathsf{QMA}$ where Merlin provides to Arthur single-use access to a unitary operator $U$? By ...
77
votes
8answers
42k views
What would a very simple quantum program look like?
In light of the announcement of the world's first programmable quantum photonic chip, I was wondering just what software for a computer that uses quantum entanglement would be like. One of the first ...
6
votes
1answer
292 views
Proof that Entanglement Cannot Increase the Capacity of a Noiseless Classical Channel
I am aware that quantum entanglement cannot increase the asymptotic capacity of a noiseless classical channel. However, can anyone provide some type of reference in the literature that contains a ...
6
votes
2answers
197 views
Quantum evasiveness conjecture?
A property of simple $n$-vertex graphs is said to be evasive if its deterministic query complexity is exactly maximal, $\binom{n}{2}$ (that is, the best algorithm must query all $\binom{n}{2}$ ...
21
votes
1answer
6k views
Oracle Construction for Grover's Algorithm
In Mike and Ike's "Quantum Computation and Quantum Information", Grover's algorithm is explained in great detail. However, in the book, and in all explanations I have found online for Grover's ...
25
votes
1answer
531 views
Approximately sampling from convex polyhedrons with quantum computers
Quantum computers are very good for sampling distributions that we don't know how to sample using classical computers. For example if $f$ is a Boolean function (from $\{-1,1\}^n$ to $\{-1,1\}$) that ...
3
votes
1answer
82 views
What is 'circuit problem' mentioned in Kempe-Kitaev-Regev's local hamiltonian problem paper
I have been going through Kempe-Kitaev-Regev's paper The Complexity of the Local Hamiltonian Problem. In the first paragraph of page 3, the authors point out that:
To the best of our knowledge, ...
2
votes
0answers
69 views
Proof: Why are MM-1QFA strictly more powerful than MO-1QFA? // Quantum automata
While dealing with quantum finite automata (QFA), I repeatedly come across the statement that measure-many QFA (MM-1QFA, KW97) are strictly more powerful than measure-once QFA (MO-1QFA, MC97). More ...
10
votes
0answers
240 views
Does MIP* = RE algebrize?
Does the MIP* = RE result algebrize? (It doesn’t relativize, as noted here.)
If it doesn’t algebrize, is there a more complicated similar notion that it does satisfy?
0
votes
3answers
248 views
What would be the next step after quantum computing? [closed]
Is their anything that would make Quantum computing obsolete in the future? I know a Matrioksha Brain is the most powerful theoretical computer; but it probably won’t ever be realized. Too large and ...
8
votes
3answers
535 views
Is the wording of Google's QC Supremacy valid?
Quantum supremacy using a programmable superconducting processor was published today. Scott Aaronson posted a few weeks ago a post about this paper and it was clear we will see a Nature or Science ...
5
votes
1answer
147 views
Complexity of finding automorphism group of code
What is the computational complexity (may be both classical or quantum) for finding automorphism group of a general linear code?
Is there better bound on complexity if structure of code is known for ...
5
votes
1answer
235 views
Are there problems that can be solved in time $2^{n-q^c}$ with $q$ qubits?
This is another attempt to formalize my former question on the topic.
I'm looking for a problem for which all known classical algorithms take exponential time, but given ANY number of few qubits (...
7
votes
1answer
412 views
Quantum Money where not even the Bank can counterfeit
The Quantum Money system proposed in "Quantum Copy-Protection and Quantum Money" has the following properties:
The bank can produce bank notes in the form of quantum states.
Anyone can verify that ...
2
votes
0answers
137 views
Quantum advantage beyond the black-box model
Question
Aaronson wrote in his thesis that
“essentially all quantum algorithms that we know today—from Shor’s algorithm, as discussed previously, to Grover’s algorithm, to the quantum adiabatic ...
5
votes
1answer
221 views
Qubit gates in google supremacy
The gates in quantum supremacy experiment are nearest-neighbor and have spatial locality. Would this additional information help bolster IBM's argument to perhaps simulate quantum supremacy experiment ...
2
votes
1answer
133 views
How exactly is solving the random circuit sampling problem a computation in the Church-Turing thesis sense? [closed]
Note: This has been cross-posted to Quantum Computing SE.
If we assume $\mathsf{BQP} \neq \mathsf{BPP}$, then we can say with reasonable certainty that Google's random sampling experiment falsifies ...
4
votes
1answer
217 views
Results comparing BQP and NEXP
Are there oracle results with $$P=NP\neq BQP=NEXP\mbox{ and }P=NP\neq BQP\neq NEXP?$$
Also is there a $PCP$ characterization of $BQP$ like $$PCP(O(poly(n)),1)=PCP(O(poly(n)),O(poly(n)))=NEXP?$$
16
votes
1answer
422 views
Oracular separations between poly- and log-depth quantum circuits
The following problem appears in Aaronson's list Ten Semi-Grand Challenges for Quantum Computing Theory.
Is $\mathsf{BQP}=\mathsf{BPP}^{\mathsf{BQNC}}$ In other words, can the "quantum" part of any ...
2
votes
0answers
83 views
Quantum security of cryptosystems
One of the main candidates for PQ cryptography is code based cryptography (other than lattice based). The Niederreiter cryptosystem based on goppa codes is shown to be resistant to hidden subgroup ...
4
votes
1answer
150 views
Given a subset of of the hypercube and an affine transform of it, find the affine map
This is a follow up to this resolved question.
Suppose we are given a set of bitvectors $A\subseteq\mathbb{F}_2^d$ and an invertible affine transformed copy of it
$$B=\{Mx + s\mid x\in A\}$$
for some ...
7
votes
2answers
328 views
Given a subset of the hypercube and a copy translated by s, find s
Problem: Suppose we are given an $n$ element subset $A\subseteq\{0,1\}^d$ of the $d$ dimensional hypercube and a translated copy $B= A+s$ by some secret $s\in\{0,1\}^d$. Find $s$ as fast as possible ...
0
votes
1answer
78 views
Grover's algorithm, M out of N, when M is large
The more general version of Grover's algorithm searches for one of $M$ entries that match a criterion, out of $N$ total entries.
I have seen it written that this takes $O(\sqrt{N/M})$ iterations, to ...
2
votes
1answer
63 views
QPIP minimal client quantum capabilities
It is conjectured that classical (BPP) client blind quantum computing is implausible according to Aaronson et al:
https://www.researchgate.net/publication/...
8
votes
1answer
306 views
Is there any quantum analog of the VP vs. VNP problem?
From Wikipedia:
$\mathsf{VP}$: The class VP is the algebraic analog of P; it is the class of polynomials $f$ of polynomial degree that have polynomial size circuits over a fixed field $K$.
$\mathsf{...
9
votes
3answers
543 views
Why exactly are complexity theorists interested in closed timelike curves?
Context:
There are several papers that study the implications of closed timelike curves (CTCs) to quantum complexity. In 2008, Aaronson and Watrous published their famous paper on this topic which ...
