Quantum computation and computational issues related to quantum mechanics

learn more… | top users | synonyms (1)

-3
votes
0answers
23 views

Proving that a state is separable [on hold]

Not sure if I have "proved" a trivial exercise: Consider the state $|\phi>=\frac{3}{5\sqrt{2}}|00>+\frac{3i}{\sqrt{5}}|01>+\frac{4}{5\sqrt{2}}|10>+\frac{4i}{5\sqrt{2}}|11>$. Prove that ...
2
votes
0answers
38 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 ...
-5
votes
0answers
79 views

Quantum computing : theoretical impossibility vs practical crookery? [on hold]

You are probably aware of the recent controversy about impossibility of Quantum computing, opposing on the theoretical side G. Kalai and A. Harrow, and on the practical side the D-Wave company and ...
-1
votes
0answers
50 views

Standard deviation of random walk vs quantum walk?

I have seen it stated in multiple places that the standard deviation of an unbiased one-dimensional random walk with $n$ steps is $\sqrt n$ and the variance of a quantum walk with $n$ steps is $n$. I ...
8
votes
0answers
179 views

How powerful is exact “quantum” computing if you suspend unitarity?

Short Question. What is the computational power of "quantum" circuits, if we allow non-unitary (but still invertible) gates, and require the output to give the correct answer with certainty? This ...
-1
votes
0answers
11 views

How to do Tensor product of two qubits using gates [migrated]

I want to do tensor product of two qubits which are passed through two Hadamard gates. I understand feeding the control bit of CN gate the output of Hadamard gate and target bit |0> gives me the Bell ...
4
votes
1answer
162 views

Applications of Quantum Walks?

Can someone explain to me what real world applications could potentially benefit from the study of quantum random walks? I have researched a fair amount on how quantum walks operate and their ...
5
votes
1answer
162 views

Grover's search algorithm for 3 coloring

According to Arora & Barak (pdf), pg. 186, for a polynomial-time computable function $f: \{0,1\}^n \to \{0,1\}$ (represented as a circuit computing $f$), Grover's algorithm finds in ...
1
vote
1answer
194 views

Running Simon's algorithm on D-wave machine

I was wondering whether Simon's algorithm could be run on a D-wave machine. The Simon's algorithm is a promise problem. On the other hand the D-wave machine can run only quadratic unconstrained ...
10
votes
0answers
111 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 ...
2
votes
0answers
75 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 ...
1
vote
1answer
80 views

Why is finding the ground state of a Hamiltonian in QMA?

Why is finding the ground stte of a Hamiltonian in QMA? It's in QMA to figure out if a hamiltonian has any energy eigenvalue within a certain window range which is at least inverse polynomial in ...
2
votes
0answers
80 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 ...
0
votes
0answers
88 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 ...
0
votes
0answers
71 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 ...
1
vote
0answers
58 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 ...
-1
votes
1answer
158 views

Differences between Quantum Computing and Parallelism

What are the differences between Quantum Computing and Parallelism? thanks in advance
5
votes
1answer
107 views

What is the underlying physical principle behind quantum fault tolerance in quantum computation?

What is the underlying physical principle behind quantum fault tolerance in quantum computation? I am trying to follow the mathematical steps behind quantum fault tolerance, and while I can just ...
1
vote
0answers
115 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 ...
-6
votes
1answer
117 views

Is the sub-bit model of quantum computation equivalent to other models? [closed]

In a comment to this question Peter Shor asked me for a reference about the third described in the question point of view, namely, that quantum computers can be described as computers that can ...
3
votes
1answer
82 views

Techniques for lower bounding spectral gaps in the quantum adiabatic algorithm

In the quantum adiabatic algorithm, one prepares the ground state of a Hamiltonian $H_{i}$, and then evolves the Hamiltonian slowly over time to a target Hamiltonian $H_{f}$ via the interpolation ...
2
votes
1answer
129 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 ...
4
votes
2answers
242 views

Simulation of every physical quantum system on quantum computer

Let me quote from the section 9.3 of Classical and Quantum Computation by Kitaev, Shen and Vyalyi. With high confidence, we may claim that every physical quantum system can be efficiently ...
1
vote
0answers
214 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 ...
4
votes
1answer
154 views

Is bounded-error probabilistic computation sensitive to transition types?

In the unbounded-error case, it is known that both realtime quantum and probabilistic finite automata can recognize some uncomputable languages if they are allowed to use arbitrary real numbers in ...
3
votes
2answers
234 views

Impacts of quantum computing on Theoretical Computer Science [closed]

Using quantum computers we can do calculations very fast. However from a layman's view, I want to know the impact of quantum computers have on Theoretical computer science.
17
votes
1answer
183 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 ...
0
votes
1answer
75 views

Confusion with the proof of constraints for a particular adiabatic quantum evolution

[This might be related to one of my previous unanswered questions.] This proof belongs to the paper, How to Make the Quantum Adiabatic Algorithm Fail by Edward Farhi, Jeffrey Goldstone, Sam Gutmann ...
3
votes
1answer
67 views

Questions about Farhi's pre-Adiabatic paper

I have been going through Eddie Farhi's 6-pages long pre-Adiabatic paper, An Analog Analogue of a Digital Quantum Computation. I guess I understand most of the math and physics but I am struggling ...
5
votes
0answers
146 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 ...
6
votes
0answers
180 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 ...
8
votes
0answers
127 views

Difficulty in understanding the quantum algorithm for the abelian hidden subgroup problem

I've difficulty in understanding the last steps of the AHSP algorithm. Let $G$ be an abelian group and $f$ be the function which hides the subgroup $H$. Let $G^*$ represent the dual group of $G$. ...
6
votes
2answers
426 views

Is there any task where classical computers outperform quantum computers?

Everybody knows that there are whole classes of problems which quantum computers are able to solve much faster (i.e. with fewer instructions) than classical computers. Is there any problem for which ...
19
votes
1answer
363 views

Sampling satisfiable 3-SAT formulas

Consider the following computational task: We want to sample a 3-SAT formula of $n$ variables (a variant: $n$ variables $m$ clauses) with respect to the uniform probability distribution, conditioned ...
1
vote
0answers
142 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 ...
5
votes
1answer
142 views

The computational complexity of spectral norm of a matrix

How hard is computing the spectral norm of a matrix? This paper says, ... it suffices to say that, except for few particular cases, the Matrix Norm problem is NP-hard. I expected that the ...
1
vote
1answer
135 views

Ising spin vs Pauli spin matrices [closed]

Are Ising spins scalar or operators? I am not a condensed matter physicist hence having some confusion. I have learnt about Ising models from adiabatic quantum algorithm papers. For example this ...
0
votes
0answers
822 views

Quantum annealing vs adiabatic quantum computation

I had this impression that quantum annealing is an optimization technique which may or may not produce exact solutions. On the other hand adiabatic quantum computation always gives exact solutions ...
3
votes
1answer
330 views

Is the D-Wave architecture a close implementation of quantum interactive proof?

A very high level architecture is, as mentioned here, shown in this picture. The component on the left is classical while the one on the right is the D-Wave box. I understand that in QIP, Arthur is ...
3
votes
1answer
119 views

Why spectral norms are used for computing the complexity of adiabatic Hamiltonian?

In the context of adiabatic quantum computation the spectral norm was first used in the first adiabatic paper by Farhi et. al. when he demonstrated the relation of it to the conventional quantum ...
16
votes
1answer
660 views

The complexity of sampling (approximately) the Fourier transform of a Boolean function

One thing that quantum computers can do (possibly even with just BPP + log-depth quantum circuits) is to approximate-sample the Fourier transform of a Boolean $\pm 1$-valued function in P. Here and ...
15
votes
0answers
254 views

Runtime of Grover's algorithm

What is the time complexity (not query complexity) of Grover's algorithm? It seems clear to me that it is $\Omega(\log(N) \sqrt{N})$ since there are $\Omega(\sqrt{N})$ iterations and each iteration ...
8
votes
2answers
613 views

Is adiabatic quantum computing as powerful as the circuit model?

Much of the quantum computing literature focuses on the circuit model. Adiabatic quantum computing is not based on applying a sequence of unitary operators, but on changing a time-dependent ...
11
votes
1answer
416 views

Is there a quantum NC algorithm for computing GCD?

From the comments on one of my questions on MathOverflow I get the feeling that the question regarding GCD being in $\mathsf{NC}$ vs. $\mathsf{P}$ is akin to the question regarding Integer ...
1
vote
1answer
172 views

1st & 2nd quantization from TCS

Last year I attended Scott Aaronson's talk Hawking Quantum Wares at the Classical Complexity Bazaar. Being intrigued by his argument that "[e]ven if quantum mechanics hadn't existed, theoretical ...
2
votes
2answers
228 views

Quantum oracle implementation overhead

I am a physicist getting acquainted with one of the typical constructs for formulation and analysis of quantum algorithms (such as search problems or query complexity models), namely the "oracle ...
0
votes
1answer
116 views

Finding all solutions by Grover search(not superposition)

When there are multiple marked elements, grover search provides only superposition of them. If I want to find all the marked elements, not superposition, I could try this: 1) Do Grover search, get ...
7
votes
0answers
153 views

Is there a candidate for a post-quantum one-way group action?

Is there a known family of group actions with a designated element in the set that is being acted on, where it is known how to efficiently $\:$ sample (essentially uniformly) from the groups, ...
-1
votes
2answers
422 views

Will quantum computing pave the way for native, true RNGs?

Obviously, regular computers can't generate random numbers on their own, since they're inherently systematic machines. Would quantum computing be able to run a true RNG without a seed based off user ...
17
votes
1answer
286 views

Consequences of $BQP \subseteq P/poly$?

While Adleman's theorem shows, that $\mathsf{BPP} \subseteq \mathsf{P}/\text{poly}$, I'm not aware of any literature investigating the possible inclusion of $\mathsf{BQP} \subseteq ...