Questions tagged [quantum-computing]
Quantum computation and computational issues related to quantum mechanics
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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 ...
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44 views
Isometric Extension of an Erasure Channel [migrated]
Show that an isometric extension of the erasure channel is $$U^N_{A\to BE} =\sqrt{1−\epsilon}\left(|0\rangle_B \langle 0|_A +|1\rangle_B \langle 1|_A \right)\otimes|e\rangle_E+ \sqrt{\epsilon}|e\...
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60 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 ...
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140 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 ...
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91 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 ...
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43 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 ...
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1answer
197 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 ...
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1answer
72 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, ...
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1answer
321 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 ...
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2answers
197 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 ...
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203 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 ...
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120 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 $BPP^{BQNC}$? If not what is it that makes integer factorization special?
In ...
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1answer
131 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,...
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1answer
70 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 = ...
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1answer
175 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 ...
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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 \...
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0answers
64 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 ...
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95 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 ...
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53 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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1answer
134 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 ...
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1answer
181 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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3answers
236 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?
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95 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 ...
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109 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 ...
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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 ...
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0answers
158 views
Grover's for QUBO form?
My preferred formulation of the quadratic unconstrained binary optimization problem (QUBO) is the following:
Find $\min(z)=x'Qx$, where $x$ is a $n$-vector of binary variables, $x'$ is its transpose, ...
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1answer
2k 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 ...
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1answer
366 views
What would a quantum computer architecture look like? [closed]
More specifically, assuming we manage to make an efficient quantum switch, some kind of "quansistor"(quantum transistor) and manage to resolve the problem of joining a bunch of them together without ...
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0answers
216 views
Convexity argument in QMA Amplification
I'm interested in the basic amplification procedure for QMA: the prover sends $O(r)$ copies of his witness to the verifier, which decreases the error probability to $2^{-O(r)}$ (Chernoff bound). The ...
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1answer
226 views
Simulating quantum measurements by unitaries
I have seen many papers in which quantum measurements are assumed to be replaced by unitaries. See this quotation from [KW00] for instance:
Often we will describe quantum circuits in a high-level ...
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1answer
74 views
Finding a basis for quantum measurement with maximum distinguishability
I wish to find a basis state for the quantum measurement of two states which provides the maximum possible distinguishability. In this example let's say we wish to find the best basis ($|\psi\rangle$) ...
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2answers
351 views
Numerical accuracy of superpositions in quantum computers
I am new to the topic of quantum computers (though I am very familiar with both quantum and computers, and I have studied Shor's paper about his eponymous algorithm at some point). Still, I have the ...
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1answer
164 views
general statement what kinds of problems can be solved more efficiently
is there a general statement what kinds of problems can be solved more efficiently using quantum computers (quantum gate model only)? do the problems for which an algorithm is known today have a ...
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1answer
619 views
When can be used the “uncompute garbage” trick in quantum computing?
As far as I have understood, "uncomputation" in quantum computing is a way to restore the working memory to its initial state, while keeping the result of the computation in another register. This ...
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1answer
81 views
Running multiple rounds of a BQP computation, without multiple measurements? [closed]
BQP as usually defined is: the class of decision problems solvable by a quantum computer in polynomial time, with an error probability of at most 1/3 for all instances.
Just like BPP, the choice of 1/...
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1answer
145 views
Is graph automorphism Karp-reducible to graph isomorphism under hidden subgroup representation?
The classical representations of the graph automorphism problem is Karp-reducible to the classical representation of the graph isomorphism problem. The sketch of proof for this can be written as ...
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How to simulate the quantum measurement of a quantum state in Quantum Image
I'm trying to implement (simulate) the Novel Enhanced Quantum Representation (NEQR), which is one of the quantum image representation models, but i'm stuck in the measurement part. In other words i ...
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146 views
Computational Complexity of cycle double cover
Let $\mathcal{G}$ be the set of all finite simple graphs. Let graph $G\in \mathcal{G}$ and $C_G=\left <C_1,...,C_m \right >$ be a sequence of cycles of $G$ for some $m$. For every edge $e$ of $G$...
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Quantum polynomial method and L2-norm
Consider a quantum query algorithm that takes as input $x \in \{0,1\}^n$. Denote by $X_i$ the variable that evaluates to $1$ on input $x$ if the $i$-th bit of $x$ is 1, and $-1$ otherwise. Let $X_{\...
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1answer
349 views
What does a tangible Quantum-Gate look like?
I'v read published books, articles and papers about Quantum-Computing.
I found that all the materials I've seen are, instead of describing quantum gate from basic physics to abstraction, trying hard ...
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93 views
Cutting edge of quantum error correction
Often I find myself needing to know the best error correcting code for a certain quantum scenario. For example, suppose my logical systems are 3-dimensional; then what's the most efficient encoding to ...
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1answer
927 views
Is the 2016 implementation of Shor's algorithm really scalable?
In the 2016 Science paper "Realization of a scalable Shor algorithm" [1], the authors factor 15 with only 5 qubits, which is fewer than the 8 qubits "required" according to Table 1 of [2] and Table 5 ...
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1answer
121 views
Can a computer generated organism be self aware? [closed]
Imagine that a computer generating a small universe similar to our own. Same table of elements, same physics, ect. Starting from the very beginning, with the creation of all the atoms in the ...
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1answer
169 views
The factoring problem reduces to order finding or is it the other way around? [closed]
initially i was not at all equipped in theoretical computer science and knew only basics of number of theory.
I started working from scratch on the age old problem of primality testing which led me to ...
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1answer
245 views
Which areas of computer science have lots of overlap with physics?
I'm an undergrad in computer science but I've always loved physics and its ability to constantly amaze and surprise us about our world. I am wondering if there are areas in graduate level computer ...
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1answer
56 views
Iterating over all stabilizer operations on $k$ qubits
Stabilizer circuits, i.e. quantum circuit that only use the $H$, $\sqrt{Z}$, and $CNOT$ gates, can only implement a finite subset of all possible unitary operations.
I want to iterate over all these ...
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Why primitive rotation is $53.13^\circ$ in the quantum Turing machine used by Vitanyi for Quantum Kolmogrov Complexity?
Right now I am going through Quantum Kolmogorov Complexity Based on Classical Descriptions by Vitanyi.
In the introduction, the author assumed the primitive rotation $\theta = 53.13^\circ$ to have ...
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147 views
Questions about the definition of the Quantum Turing Machine
I am trying to have a better understanding of the definition of the Quantum Turing Machine.
My questions:
If the output of a quantum program is the eigenvalue of the ground state of a Hamiltonian ...
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2answers
2k views
Do any quantum algorithms improve on classical SAT?
Classical algorithms can solve 3-SAT in $1.3071^n$ time (randomized) or $1.3303^n$ time (deterministic). (Reference: Best Upper Bounds on SAT )
For comparison, using Grover's algorithm on a quantum ...
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90 views
Two definitions of $QMA$
In this question, I am trying to understand the equivalence between the following two definitions of the complexity class QMA.
In Quantum Computational Complexity, John Watrous defines the class QMA ...
