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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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 ...
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131 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 ...
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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 ...
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71 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 ...
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69 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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68 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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134 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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65 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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97 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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128 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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81 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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120 views
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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122 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 ...
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135 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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148 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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55 views
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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35 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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102 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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91 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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0answers
175 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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148 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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259 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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1answer
260 views
Quantum Computing: project ideas
I'm an undergraduate computer science student and I'm currently taking a course in the field of quantum computing requiring projects. I've read already a huge number of articles but still cannot come ...
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28 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:
...
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44 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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151 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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99 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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30 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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128 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
184 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
149 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 ...
