Questions tagged [quantum-computing]
Quantum computation and computational issues related to quantum mechanics
76
questions with no upvoted or accepted answers
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430 views
Adiabatic quantum computing with level crossings
Question.
In adiabatic evolution, to ensure that the ground state high overlap with the unique ground state of the system (i.e. to achieve arbitrarily small error) using adiabatic theorems, it is ...
19
votes
1answer
254 views
Is there a geometrical picture for adiabatic quantum computation?
In adiabatic quantum computation (AQC), one encodes the solution to an optimization problem in the ground state of a [problem] Hamiltonian $H_p$. To get to this ground state, you start in an easily ...
17
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0answers
445 views
Quantum Hardness of Finding Nash Equilibria
This question is inspired by the recent, beautiful work On the Cryptographic Hardness of Finding a Nash Equilibrium by Bitansky, Paneth, and Rosen.
Their main result is that the existence of ...
15
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0answers
64 views
Lower bounds for quantum circuits using the geodesic framework
(this question is a crosspost from cstheory. I've incorporated the one answer there into the question)
Some of us have been reading Michael Nielsen's paper on a geometric approach to using quantum ...
13
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0answers
300 views
Is there any known nontrivial result on QIP systems having a space-bounded verifier?
Is there any known nontrivial result on quantum interactive proof (QIP) systems having a space-bounded verifier?
The only paper I know is An application of quantum finite automata to interactive ...
10
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0answers
187 views
How hard it is to approximate the ground state of the (2-D) Hubbard model
The Hubbard model (see also the wikipedea article on the Bose-Hubbard model) is a basic quantum model of solid-state physics.
Question: What is the computational complexity of approximating the ...
10
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0answers
248 views
What are the most recent developments in small-depth quantum circuits?
Back in 2005, Scott Aaronson posted a list of 10 "semi-grand" challenges for quantum computing theory which contained the following challenge:
The power of small-depth quantum circuits. Is $BQP = ...
9
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0answers
169 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 ...
9
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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 ...
9
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0answers
112 views
Non-tomographical certification of projectors, using product states?
I'm interested in operational ways of demonstrating (with high probability of confidence, in an error-free setting) that a POVM operator on n-qubit states is a projector. Specifically, I'm interested ...
8
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0answers
319 views
Approximation of Quantum Channels
Background:
In quantum information theory, a wide class of processes acting on stochastic quantum states can be described using the formalism of Quantum Channels:
A quantum channel is a linear, ...
7
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0answers
59 views
Explicit error bounds on the abelian hidden subgroup problem
What are some explicit forms for the error probability in the typical quantum abelian hidden subgroup algorithm as a function of oracles queries?
Ettinger, Hoyer, and Knill give a result that the ...
7
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0answers
260 views
Implication of Bell test loopholes on Vazirani-Vidick random sequence generation scheme
I am trying to imagine what would be the implications of the loopholes on Bell test on the random sequence generation scheme proposed by Vazirani and Vidick (VV protocol) in the paper titled '...
7
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0answers
193 views
Are the minimal quantum and classical span programs the same?
A span program is a linear-algebraic way of specifying a boolean function introduced here which has found recent application in quantum query complexity.
A span program for a function $f: \{0,1\}^n \...
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 ...
6
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0answers
175 views
Local Hamiltonian and combinatorial search problems
I was going through the PhD thesis of Daniel Nagaj. At the beginning of chapter two he indicated a relation between the local Hamiltonian perspective of adiabatic quantum computation and combination ...
5
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0answers
270 views
Generating quadratic optimization problems amenable to quantum annealing
Some context: there is a current debate in adiabatic quantum computing over whether a particular machine, the D-Wave quantum annealer, can outperform a classical algorithm [*]. Earlier this year, a ...
4
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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
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0answers
117 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-...
4
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0answers
98 views
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 ...
4
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0answers
174 views
Two questions on Shor's algorithm
Does Shor's algorithm produce factors of a $n$-bit number and discrete log modulo $n$-bit prime in $O((\log n)^{2+\epsilon})$ bit operations using fast multiplication? I am trying to read from ...
4
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0answers
184 views
Do the quantum communication complexity lower bounds hold when parties can send a “duplicated” qubits?
This question continues from the previous question where I mistakenly asked a question that is too general.
In quantum communication complexity, we always assume that Alice and Bob have unlimited ...
3
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0answers
120 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
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0answers
59 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 ...
3
votes
0answers
226 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 ...
3
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0answers
99 views
Quantum annealing or adiabatic quantum optimization with continuous optimization problems
How do quantum annealing or adiabatic quantum optimization deal with continuous optimization problems such as SDP?
3
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0answers
61 views
Does simulating chiral gauge theories lie within BQP?
In theoretical physics, there is a branch of quantum field theory dealing with chiral gauge theories. It has been conjectured by Feynman [1] and others that all quantum field theories can be simulated ...
3
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0answers
159 views
Are NQP and QMA comparable?
Both definitions try to create a quantum analog for NP. NQP's definition comes from non-deterministic algorithms: it contains languages for which a Quantum Algorithm accepts with non-zero probability ...
3
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0answers
200 views
Environment-assisted quantum transport computation
The paper below and the news story based on it describe a new form of computation based on what they call environment-assisted quantum transport (ENAQT).
ENAQT involves a combination of quantum and ...
2
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0answers
120 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 ...
2
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0answers
73 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 ...
2
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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 ...
2
votes
0answers
150 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 $G$...
2
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0answers
98 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 ...
2
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0answers
40 views
Non-commutative quantum counting with aggregate constant work per increment
Classically, it's very easy to create an incrementing function that can perform up to $n$ increments with $O(n)$ work:
...
2
votes
0answers
101 views
On FFT and trigonometric matrix eigenvalues
Let $N=2^n$ for a natural number $n$ and $B$ be the $N\times N$ square matrix of $0$'s and $1$'s
$$
B=\begin{pmatrix}
0 & 1 & 0 & \ldots & 0 \\
1 & 0 & 1 & \ldots ...
2
votes
0answers
96 views
Why hidden subgroup problem is easy for very large subgroup?
I am going through QUANTUM MECHANICAL ALGORITHMS FOR THE
NONABELIAN HIDDEN SUBGROUP PROBLEM by Grigni et al. On page 2, it is said that solving the hidden subgroup problem becomes very easy when the ...
2
votes
0answers
93 views
Claw finding using quantum walk: superposition for Szegedy's framework
Within Claw Finding Algorithms Using Quantum Walk there is the subroutine $claw_{detect}$ described. As in above paper:
Let $J_f(N, l)$ and $J_G(M, m)$ be Johnson graphs. Let $F$ and $G$ be vertices ...
2
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0answers
94 views
Proofs to verify quantum states without revealing their description
Consider the following function $$f_s: k \rightarrow \lvert \psi_k \rangle$$
where $s,k$ are bit strings, and $\lvert \psi_k \rangle$ is a $n$-qubit state.
Assume the function is a one-to-one mapping....
2
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0answers
53 views
How the errors of the measured quantities of an adiabatic Hamiltonian are inversely proportional to the square root of the number of measurements?
I am going through the paper, Solving the graph-isomorphism problem with a quantum annealer, by Hen et. al. In the last line of the second paragraph of the second column of page 2, it says,
Since ...
2
votes
0answers
152 views
Why is Shor's algorithm in $BPP^{BQNC}$ when needing to uncompute subprocedure call?
Why is Shor's algorithm in $BPP^{BQNC}$? It's true the quantum Fourier transform is in $BPP^{BQNC}$, but the algorithm needs to call a number theoretic function f which has period p which is a factor ...
2
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0answers
156 views
Quantum algorithm of graphs: How to create superposition of paths?
Let us allow path to have same vertexes in it. (defining)
So suppose we have a graph of $N$ vertexes and we want to separate it into some superposition of paths that have $N$ vertexes (so if the ...
2
votes
0answers
1k views
From CHSH inequality to CHSH game
I have been going through Certifiable quantum dice: or, true random number generation secure against quantum adversaries by Umesh Vazirani and Thomas Vidick. They have used entangled particles as ...
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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 ...
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 ...
1
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0answers
742 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
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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
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0answers
62 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 ...
