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Questions tagged [quantum-computing]

Quantum computation and computational issues related to quantum mechanics

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1answer
267 views

Hardness of quantum circuit equivalence?

Given two poly-sized quantum circuits $C_1$ and $C_2$ on $n$ qubits with a universal gate set generated by some finite set of one and two qubit gates. I'm thinking of the gates $\langle H, T, CNOT\...
6
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1answer
260 views

Proof that Entanglement Cannot Increase the Capacity of a Noiseless Classical Channel

I am aware that quantum entanglement cannot increase the asymptotic capacity of a noiseless classical channel. However, can anyone provide some type of reference in the literature that contains a ...
6
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1answer
207 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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1answer
1k views

Applications of HHL's algorithm for solving linear equations

In HHL's algorithm for solving a system of linear equations (HHL = Harrow, Hassidim and Lloyd) the output is a quantum state rather than explicit information. Has anyone been able to apply knowledge ...
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2answers
352 views

Energy cost of adiabatic quantum computation

I'm not sure whether this question is completely on-topic, since it is a physics-related question. But I'll ask anyway and apologize if I'm off-topic. In Adiabatic Quantum Computation is Equivalent ...
6
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1answer
231 views

Evidence that there is some problem in BQP distinct from BPP?

Are there any evidences (1 physics, 2 mathematics AND 3 computer science) that particular problems such as integer factorization, discrete logarithm are in BQP but not in BPP? There do not seem to be ...
6
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1answer
4k 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 ...
6
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1answer
360 views

Quantum capacity for ensemble of Pauli channels

In Preskill's quantum computing notes Chapter 7 approximate page 82, he shows that a Pauli channel has capacity $Q \geq 1-H(p_I,p_X,p_Y,p_Z)$ where $H$ is Shannon entropy and $p_I, p_X, p_Y, p_Z$ are ...
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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 ...
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4answers
2k views

Factoring as a decision problem

I've seen in multiple places stating that factoring is in BQP and referencing Shor's algorithm, but Shor's algorithm is not solving a decision problem. How can factoring be restated in a decision ...
5
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1answer
248 views

Quantum Channel Decoding

Let a quantum channel $\Phi(\cdot)$ between two Hilbert spaces $\mathcal{H}_{in}$ and $\mathcal{H}_{out}$. What is the quantum channel $\Phi_{inv}(\cdot)$ that best reverses $\Phi(\cdot)$ ? $\forall $...
5
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1answer
207 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 ...
5
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1answer
171 views

Communicating a string of zeros and ones quantumly

Alice wants to communicate an arbitrary $x \in \{0 ,1\}^n$ to Bob. Alice and Bob communicate in rounds, in each round Alice (or Bob) applies a unitary transformation on his/her part and transmits a ...
5
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1answer
447 views

Quantum algorithms for determining whether two sets intersect

Grover's algorithm is a quantum algorithm that is able to locate a special record in an $N$ element unsorted database in $\Theta(\sqrt{N})$ time. What quantum algorithms are known to determine whether ...
5
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1answer
253 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 $O(\text{poly}(...
5
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1answer
348 views

How efficiently can a 1-sparse Hamiltonian be simulated (quantum mechanically)?

In quantum computation there is a fair amount of interest in the task of simulating quantum physics. One instance of this is the problem of simulating the evolution of a system under the action of ...
5
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1answer
132 views

Known properties of a specific class of quantum states

Recently, I have been studying a quantum protocol for the "Hidden Matching" problem that makes use of states that can be expressed as $|\psi\rangle=\frac{1}{\sqrt{n}}\sum_{i=1}^n (-1)^{x_i}|i\rangle$,...
5
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1answer
871 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 ...
5
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1answer
261 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 ...
5
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1answer
153 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 ...
5
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1answer
182 views

Things that imply BQP Derandomization

I am aware that it is generally believed that P = BPP, but BQP != P (since factoring is in BQP, and factoring seems hard.) For BPP, we have the hardness vs randomness result: which states that ...
5
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1answer
502 views

Is there any problem which is in AWPP but conjectured to be not in BQP?

Is there any known problem which is in $\mathsf{AWPP}$ but conjectured to be not in $\mathsf{BQP}$? What about relative to an oracle? Is there any known problem in $\mathsf{MQ^2}$ which is ...
5
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1answer
367 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 ...
5
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1answer
176 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 ...
5
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1answer
256 views

How Much Computing Power would be Required to Fully Simulate a Cubic Meter?

Imagine you want to simulate a cubic meter down to the particle. By following the Standard Model and other basic physical equations, how much computing power would be required to do this, in say, a ...
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0answers
605 views

Learning quantum CS [duplicate]

Possible Duplicate: What is the quantum computational model? What is the best way to study quantum branch of CS for the person with rather advanced background in classical CS? Does one need to ...
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6answers
5k views

Ternary (and beyond) computation and quantum computing?

Binary math is at the heart of most computing, in large part because of the ease with which two energy states can be achieved. I have always thought that having more states could improve computing ...
4
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1answer
637 views

If BQP contains NP, does this mean that P=NP?

There is a question raised by Scott Aaronson in one of his papers [1]: "Could we show that if NP ⊆ BQP, then the polynomial hierarchy collapses?". Assuming the answer is yes, and it is also know that ...
4
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2answers
427 views

Major advance for measurement based quantum computing?

http://arxiv.org/abs/1211.3405 The Measurement Based Quantum Computing Search Algorithm is Faster than Grover's Algorithm If this recent paper is true, it seems like a major advance for ...
4
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1answer
220 views

Why is shifting bits different from shifting qubits?

In classical circuit complexity, shifting bits is considered gratis; all you have to do is reorganizing wires between corresponding gates. By contrast, shifting qubits is typically done by using a ...
4
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1answer
194 views

Quantum oracle for non-negative vector

I was wondering if anyone knew on whether it is possible to construct a quantum oracle that was able to detect whether a given state vector was "non-negative"? Essentially I have a classical problem ...
4
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2answers
491 views

Are two-qubit unitaries necessary for universal quantum computation?

I was going through Fast Universal Quantum Computation with Railroad-switch Local Hamiltonians by Daniel Nagaj. In the first sentence of the fifth paragraph on the fourth page, he said, Two-qubit ...
4
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1answer
653 views

Qubits and permutation symmetry

To put it straight - are qubits fermions, bosons or else? For example, the Bell states that are frequently used in quantum computations have different symmetry (00 + 11 is symmetric, 10 - 01 is ...
4
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1answer
181 views

Results comparing BQP and NEXP

Are there oracle results with $$P=NP\neq BQP=NEXP\mbox{ and }P=NP\neq BQP\neq NEXP?$$ Also is there a $PCP$ characterization of $BQP$ like $$PCP(O(poly(n)),1)=PCP(O(poly(n)),O(poly(n)))=NEXP?$$
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2answers
327 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 ...
4
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1answer
345 views

theorems for universal set of quantum gates for SU(d)

It seems that there is a theorem that for prime dimension d, the set of Clifford gates and one non-Clifford gate together forms a universal set of quantum gates for SU(d). It also seems that for a ...
4
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1answer
69 views

Is it possible to MAC a quantum state with a classical key under reasonable assumption?

Assume that classical one-way functions secure against quantum adversaries exist. Is it possible, given a quantum state $Q$ and classical secret key $k$, produce a quantum state $AuthQ$ such that: ...
4
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1answer
243 views

Is it possible to design an efficient approximation algorithm for one NP-complete problem based on Shor's algorithm?

Is it possible to design an efficient approximation algorithm for an $\sf{NP\text{-}complete}$ problem based on reductions from Shor's algorithm? Are known any (classical) approximation algorithms ...
4
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1answer
178 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 $H(s)...
4
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1answer
347 views

Quantum cellular automata

This questions is cross-posted from MathOverflow A little background: As far as I know there is no standard definition of a quantum cellular automaton in the literature. Different authors use ...
4
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1answer
159 views

Probabilistic and quantum analog of $FP$ and $FNP$?

Is there any analog of the computational classes $FP$ and $FNP$ with probabilistic or quantum Turing machines? If so, what are the relation with other computational classes?
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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 ...
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0answers
116 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-...
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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 ...
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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 ...
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0answers
269 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
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 ...
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3answers
3k 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 ...
3
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2answers
306 views

Consequences of $NP\subseteq P/poly$ to $BQP$

A post here Consequences of $BQP \subseteq P/poly$? queried on Consequences of $BQP \subseteq P/poly$. It is not known if $NP\subseteq BQP$. In general, what are the consequences of $NP\subseteq P/...