Questions tagged [quantum-computing]
Quantum computation and computational issues related to quantum mechanics
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What are some “must-read” papers for someone getting into Quantum Cryptography?
I'm a graduate student that just finished a first course on quantum computation. I've also done a graduate-level course in (classical) cryptography.
I'm interested in Quantum Cryptography and would ...
1
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0answers
16 views
What is known about the stabilizer rank of this simple state?
Consider the uniform superposition of all length-$n$ bit-strings of Hammming weight $w$,
$$ |\phi_w\rangle =\sum_{x\in \{0,1\}^n,|x|=w} |x\rangle$$
What is known or conjectured about the stabilizer ...
7
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4answers
2k views
Factoring as a decision problem
I've seen in multiple places stating that factoring is in BQP and referencing Shor's algorithm, but Shor's algorithm is not solving a decision problem. How can factoring be restated in a decision ...
4
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3answers
138 views
The complexity of LH with constant gap
Kitaev's quantum equivalent of the Cook-Levin Theorem, provides a polynomial time classical reduction from a QMA verification circuit to a sum $H$ of local hamiltonians, such that the least eigenvalue ...
1
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1answer
152 views
Pursuing Theoretical Computer Science after CS major
So I am currently a sophomore majoring in Computer Science. In the Data Structures course that I am currently studying, I studied the basics of complexity of a program and big O-notation, etc. That ...
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0answers
30 views
Which algorithm for linear programming is suitable for the context of quantum computing?
There are two major types of algorithms for linear programming : extreme point based, interior point based.
Which will be suitable for quantum computing?
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1answer
96 views
Quantum complexity of TQBF with an untrusted oracle
This is a follow up to Quantum complexity of TQBF, trying to model the situation where we have good heuristics.
Let $L$ be the language of true, fully alternating totally quantified boolean formulas ...
7
votes
1answer
142 views
Quantum complexity of TQBF
There is no classical algorithm for $n$-bit TQBF with better than $O(2^n)$ complexity. Is that also the best known bound for quantum algorithms / circuits?
Edit: As pointed out by Huck Bennett, in ...
8
votes
1answer
98 views
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
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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
...
4
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1answer
82 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 ...
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0answers
14 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
213 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
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0answers
45 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(...
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0answers
51 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
95 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
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0answers
50 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. ...
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0answers
112 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
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0answers
40 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
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0answers
158 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
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2answers
864 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
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1answer
158 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 ...
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0answers
44 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
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2answers
883 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
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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
113 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
101 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
126 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
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0answers
35 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
247 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.
...
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0answers
70 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
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1answer
125 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
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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
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8answers
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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
293 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
206 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 $\binom{n}{2}$ ...
22
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
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1answer
535 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
83 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
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0answers
70 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 ...
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0answers
248 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
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3answers
251 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
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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
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1answer
163 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
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1answer
237 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
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1answer
419 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
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0answers
146 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
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1answer
225 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 ...
1
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1answer
137 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
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1answer
221 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 $$PCP(O(poly(n)),1)=PCP(O(poly(n)),O(poly(n)))=NEXP?$$
