Questions tagged [quantum-computing]
Quantum computation and computational issues related to quantum mechanics
338
questions
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An algebro-combinatorial argument that P = NP
Also asked in normal CS stack exchange.
I have long been fascinated by this question and recently wrote an article about it. The version of computation described in the article is similar to those ...
3
votes
1answer
164 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
102 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 ...
2
votes
0answers
60 views
Quantum advantage beyond the black-box model
The common quantum algorithms I know of can be all explained using black-box model (i.e., query model):
Grover's search. An $O(\sqrt{n})$-query algorithm that computes the OR of $n$ bits.
Shor's ...
8
votes
3answers
427 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 ...
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69 views
If Shore's Algorithm can solve factorization efficiently, how can it be in NP?
having a somewhat decent knowledge about classic complexity theory but not about Quantum Complexity Theory, I really struggle to understand the following:
Under the ...
4
votes
1answer
181 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 $$PCP(O(poly(n)),1)=PCP(O(poly(n)),O(poly(n)))=NEXP?$$
10
votes
2answers
455 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 ...
0
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0answers
39 views
Hidden subgroup problems in a tower of subgroups
Let $H$ be a hidden subgroup of $G_1$ that is indistinguishable from subgroup $H^{\prime}$ by quantum Fourier sampling. Now take a larger group $G_2$ such that it contains $G_1$. Now if I do quantum ...
2
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0answers
71 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 ...
3
votes
1answer
134 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
319 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
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1answer
68 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 ...
1
vote
1answer
58 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
3answers
424 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 ...
2
votes
1answer
127 views
Lower bound on alternations needed in $BQP$ versus $PH$ result?
What is the fastest $f(n)$ the relatively new result of oracle separation of $\mathsf{BQP}$ from $\mathsf{PH}$ provides such that ${\#\mathsf{SAT}}\not\subseteq\mathsf{FP}^{\mathsf{PH}[O(f(n))]}$ ...
8
votes
1answer
264 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 $K$.
$\...
3
votes
0answers
193 views
In light of Raz and Tal's results, what can we say about whether there's a BQP problem for each level of the polynomial hierarchy?
[cross-posted on QCSE a couple of weeks ago]
Every Venn diagram or Hasse diagram I see illustrating the "standard model" of computational complexity describes a universe of $\mathsf{PSPACE}$ problems,...
3
votes
0answers
119 views
What can be some bachelor thesis ideas in Quantum random walks?
Note: Cross-posted on Quantum Computing Stack Exchange.
I am an undergraduate, reading about quantum information and quantum technology. For about some time, I have been interested in the ...
3
votes
1answer
177 views
String theory based computations
I was reading Arora and Barak's book on computational complexity and in the section on 'criticism on Turing machine model and the class P' along with quantum computer it also mentions possibilities of ...
4
votes
0answers
89 views
Is there a universal gate set for classical probabilistic computing?
We know that NAND gates are universal for deterministic classical circuits, Toffoli gates are universal for reversible deterministic classical circuits, and Clifford+T is universal for quantum ...
4
votes
0answers
114 views
Dequantumizability known and unknown?
Dequantumizable problems have been taking some headlines these days (for example https://www.scottaaronson.com/blog/?p=3880 and https://www.quantamagazine.org/teenager-finds-classical-alternative-to-...
1
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0answers
21 views
whether two sets of stabilizer generators are related by a Clifford circuit
I have two stabilizer models each specified with a given set of generators. Let's call the two generating sets $S_1$ and $S_2$. By stabilizer model, I mean putting the generators on unit cells of a ...
11
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5answers
878 views
List of quantum-inspired algorithms
Advances in quantum computing have led to the development of new classical algorithms. Notable recent examples are quantum-inspired algorithms for linear algebra:
A quantum-inspired classical ...
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1answer
56 views
QMA definition of difference between probabilities intuition
I'm reading about the complexity classes related to quantum computation, currently I'm studying QMA class. A language is in QMA(c,s) if there exists a polynomial time verifier and polynomial $p(n)$ ...
1
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0answers
70 views
Complexity of enumerating over promise problems and circuits?
Given an enumeration over all Turing Machine which run with increasing length, is there a ``complexity class'' which describes the complexity of determining whether a given TM satisfies the promise ...
1
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0answers
67 views
Complexity class of approximating perfect match count
We know we can approximate perfect matching count of bipartite and approximate volume of convex bodies in randomized polynomial time.
Is there any evidence these approximations could be in Nick's ...
9
votes
0answers
168 views
Relatively low ambitious frontiers
What are some of the current "relatively" low ambitious frontiers for MA/PhD thesis in complexity theory class separations/containment or quantum computing?
For example: In the draft version of Arora ...
6
votes
0answers
96 views
Efficient quantum algorithm for CLASSICAL FFT
Is there a known improvement on the current O(n*log(n)) algorithm for CLASSICAL FFT using quantum computation? 'n' is the number of samples.
I need to find the amplitude and phase of the K dominating ...
3
votes
0answers
57 views
Hardness of ancilla free quantum circuit extraction from circuit with ancillas
Is there any known result regarding the hardness of the following problem:
Given a quantum circuit with ancillae implementing a unitary, find a quantum circuit that does not use any ancillae that ...
10
votes
1answer
222 views
Fast classical simulation of quantum algorithms
Are there examples of cases where the classical simulation of a quantum algorithm for a problem outperforms the best previously known classical algorithm for this problem? "Outperforms" doesn't have ...
1
vote
1answer
82 views
Quantum circuit simulation divergence in results
I'm learning about quantum computing in order to code a simulator. I tried the following circuit in Quirk
And ran the same circuit using OPENQASM 2.0:
Notice that the input is |11> in both cases, ...
5
votes
1answer
367 views
Can one do quantum computing without negative amplitudes?
The typical representation I see of $k$ qubits is a $2^k$ complex numbers $c_i$ for every possible combination of values of those bits, such that the sum of all the squared magnitudes of those numbers ...
1
vote
2answers
207 views
Which cryptographic protocols are secure against quantum computer attacks?
Are there any cryptosystems that we know that would be secure against an attack by a quantum computer?
Are there problems which are known or suspected to be hard for quantum computers, and can these ...
9
votes
0answers
231 views
How would proof of the Lindelöf hypothesis improve our understanding of computational complexity classes?
A recent press release from the Viterbi School of Engineering at USC discussed the proof of the Lindelöf hypothesis by Athanassios Fokas, a visiting professor from the Department of Applied ...
1
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0answers
690 views
BQNC and Abelian Hidden Subgroup Problem
We know integer factorization is in $BPP^{BQNC}$ from Cleve and Watrous.
Is Abelian Hidden Subgroup Problem also in $BPP^{BQNC}$?
In particular is Discrete Logarithm in $BQNC$ or at least in $BPP^{...
1
vote
1answer
136 views
Complement for joint POVMs?
I'm trying to relate some notions of set theory to POVMs. I firstly explain the scenario with set theory and then in the POVM setting.
For some finite $N \in \mathbb{N}$, let $A_i$ and $B_i$ for $i=1,...
1
vote
1answer
84 views
PromiseBQP and expectation values of operators
This question is regarding The Equivalence of Searching and Sampling by Aaronson. In page 4 he makes the following statement,
... a difficult and unsolved meta-question is whether PromiseBPP = ...
0
votes
1answer
183 views
What would be a complete QC circuit?
In classical computing NAND is a complete set (functionally complete) of binary operations, namely any Boolean circuit can be expressed using NAND gates.
Is there an equivalent for quantum computing ...
1
vote
1answer
123 views
Is $CAPP \in P$ known to collapse some quantum complexity classes to classical ones?
Lets define the class
$ZBQP = \{ L \mid \exists \textit{P-uniform circuit family } \{C_i\}, \forall n \in \mathbb{N}, |x| = n, |\langle 0|C_n|x \rangle - I(x \in L)| \leq 9/10 \Longleftrightarrow x \...
1
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0answers
66 views
Query complexity of quantum search with measuring oracle
Consider the following problem:
Let $x\in X$ be a uniformly random value.
Let $O$ be an oracle that measures whether the register $Q$ contains $x$. More precisely, $O$ measures $Q$ using the ...
1
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0answers
129 views
QUBO formulation of a discrete-variable optimization problem
I am facing a non-linear, discrete optimization problem, which I can formulate in this abstract manner: I have a certain non-analytic non-linear real-valued function $f:S \to \mathbb{R}$ which takes ...
1
vote
0answers
61 views
What is the average sensitivity of a quantum circuit with depth $d$ and size $s$?
We have some quantum circuit $C$ with $k$ ancillae and $n$ input bits of depth $d$ and size $s$, and we can define a function $f$ which, for any $x \in \{0, 1\}^n$, is the random variable which is the ...
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votes
1answer
143 views
Complexity class on quantum computation and classic ones
Does the complexity speedup in superpolynomial by quantum computation mean it is possible to find new algorithm on classic Turing Machine which can speedup in classic Turing Machine in ...
6
votes
1answer
207 views
Quantum polynomial hierarchy vs counting hierarchy
First of all, I'm kinda surprised that I couldn't find any paper/article defining such hierarchy.
It can be defined as follows:
$\Delta_0^{\mathsf{BQP}}=\Sigma_0^{\mathsf{BQP}}=\Pi_0^{\mathsf{BQP}}=\...
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2answers
252 views
How can I get $\sum_n e^{i a_n} |n\rangle$ from $\sum_n a_n |n\rangle$?
Suppose that I have a normalized quantum state $\sum_n a_n |n\rangle$, is there a quantum operation/circuit so that I can get $\frac{1}{N} \sum_n e^{i a_n} |n\rangle$ at output? How?
1
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0answers
96 views
Is there a way to extract the mean from a quantum superposition?
Given the superposed output of some quantum computation, suppose I want to know the mean state, i.e. the mean probability of each qubit sampled over all states.
The most obvious way to get this is ...
1
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0answers
121 views
Connection between diamond norm and output purity norm
Setting of the problem: Given a quantum channel $\mathcal{E}: \mathcal{H}_A\rightarrow \mathcal{H}_B$ (where $\mathcal{H}$ refers to a Hilbert space and subscript refers to the quantum register ...
2
votes
0answers
59 views
A random ensemble of sparse boundary operators
The following question arises from the study of quantum error correction, and high-dimensional expanders:
Is there an algorithm that for given numbers $n>0,d≤n,r≤n$ samples uniformly a linear ...
11
votes
1answer
4k 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 ...
