Questions tagged [quantum-computing]
Quantum computation and computational issues related to quantum mechanics
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questions with no upvoted or accepted answers
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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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123 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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80 views
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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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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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 ...
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122 views
Quantum algorithms for generalizations of determinants
There are a wide variety of determent-like constructions. Some like the permanent or immanents are variations on the ordinary determinant for matrices over fields or commutative rings. Some like ...
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142 views
Quantum computer versus Random 3-SAT?
It seems to be commonly believed that quantum computer cannot efficiently solve NP-hard problems. What about the challenging problems in average-case, such as Planted Clique and Random 3-SAT?
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First register in the hidden subgroup representations of Simon's and graph isomorphism problems
The Simon's problem involves a function which takes binary strings as inputs. One seeks to find the period of the function which acts on those inputs. In the standard method, the first register has ...
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107 views
Is Logic Done on Superpositional Bit Values Useful?
Let's say I have a way to represent $N$ bits such that those bits are in a superposition of the $2^N$ possible states those bits can have and that I can do XOR and AND on those superpositional bits to ...
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34 views
Coset state of $3$-node graph isomorphism problem
The hidden subgroup representation of a $3$-node graph isomorphism problem is defined over the symmetric group, $G = S_6$. So, any hidden subgroup algorithm that wishes to solve the problem should ...
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93 views
Non-Transversal Fault Tolerant Gate
I have always heard that transversality is a sufficient, not a necessary condition for fault-tolerance in quantum computation. However, I have never seen any examples of non-transversal fault tolerant ...
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90 views
Period of a Multivariable Function using Quantum Computing
consider a function
$$f(x_1,x_2...x_n)$$
I am told it is possible to compute the period of the function as a vector
$$<l_1,l_2...l_n>$$
where each l denotes the period of the function for ...
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173 views
Relationship between size of quantum superposition and rate of decoherence
I am new here in StackExchange and this will be my first question to ask. I have a background in Computer Science and I am interested in looking into Distributed Quantum Computing (DQC). I have read ...
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144 views
Is there a lower bound for the decisional Grover search problem?
What is known about the decisional version of the search problem? By decisional version of the search problem, I mean the problem in which you wish to determine whether there are $0$, or exactly $t$ ...
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256 views
Separating the QIP hierarchy
Background: I'm a CS grad student. I've taken a course on computational complexity.
Question:
Can you suggest an introductory book on quantum computation, especially regarding the details of ...
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40 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 ...
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149 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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97 views
What is the relationship between quantum tomography and quantum error correction?
To realize correct quantum computing it seems that both quantum error correction and quantum tomography would be necessary. Is this true? What is the relationship between these two fields?
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29 views
Hardness of finding similar (quantum) states
Consider a quantum state $\lvert \psi \rangle$, we know from the no cloning theorem, that it cannot be perfectly cloned. Also, loosely speaking, that it can be imperfectly cloned s.t. one can produce ...
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124 views
Determining if a function is constant or not using period finding
Consider an arbitrary boolean function
$$f: {\lbrace 0,1 \rbrace}^n \rightarrow \lbrace 0,1 \rbrace$$
which we write as:
$$f(x_1, x_2 ... x_n) $$
where each $x_i$ is a boolean variable
We note ...
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126 views
Computing the period of a function using a quantum computer
Consider a blackbox function
$$f(x): Z \rightarrow \lbrace 0,1 \rbrace $$
Which inputs an integer and outputs 0 or 1 with bit complexity n.
If the period P of this function satisfies
$$P \in O(2^{...
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383 views
Is it possible to add quantum physics theory to traditional machine learning algorithms to get more accurate results
Lets suppose your data set includes locations in several dimensions and the kind of entity which is the class of the data set, is there other kind of information you need to add (such as times, ...
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1answer
183 views
What would be a complete QC circuit?
In classical computing NAND is a complete set (functionally complete) of binary operations, namely any Boolean circuit can be expressed using NAND gates.
Is there an equivalent for quantum computing ...
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Conjuagate operation solution
Let A,B two matrices over binary field that are similar. So there exists a solution to equation of type
$$B=XAX^{-1} $$
Is there an algorithm to find all X's?
If not classical, may be a quantum ...
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0answers
99 views
Can the aliens hustle us with Chaitin's constant?
Premise
Suppose you are an alien and want to fool Earthlings you have extracted the value of Chaitin's Constant. Does the strategy below work? If so, any explicit(/basic ideas for) algorithm? If not, ...
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1answer
144 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 ...
