Questions tagged [quantum-computing]

Quantum computation and computational issues related to quantum mechanics

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QPIP minimal client quantum capabilities

It is conjectured that classical (BPP) client blind quantum computing is implausible according to Aaronson et al: https://www.researchgate.net/publication/...
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1answer
252 views

Is there any quantum analog of the VP vs. VNP problem?

From Wikipedia: $\mathsf{VP}$: The class VP is the algebraic analog of P; it is the class of polynomials $f$ of polynomial degree that have polynomial size circuits over a fixed field $K$. $\...
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Why exactly are complexity theorists interested in closed timelike curves?

Context: There are several papers that study the implications of closed timelike curves (CTCs) to quantum complexity. In 2008, Aaronson and Watrous published their famous paper on this topic which ...
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1answer
118 views

Lower bound on alternations needed in $BQP$ versus $PH$ result?

What is the fastest $f(n)$ the relatively new result of oracle separation of $\mathsf{BQP}$ from $\mathsf{PH}$ provides such that ${\#\mathsf{SAT}}\not\subseteq\mathsf{FP}^{\mathsf{PH}[O(f(n))]}$ ...
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List of quantum-inspired algorithms

Advances in quantum computing have led to the development of new classical algorithms. Notable recent examples are quantum-inspired algorithms for linear algebra: A quantum-inspired classical ...
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93 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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2answers
456 views

Notation for a Conditional Hamiltonian Evolution Operator

I am reading Harrow, Hassidim, and Lloyd's paper Quantum algorithms for linear systems of equations. On the third page of that paper, they write Next we apply the conditional Hamiltonian evolution $...
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167 views

In light of Raz and Tal's results, what can we say about whether there's a BQP problem for each level of the polynomial hierarchy?

[cross-posted on QCSE a couple of weeks ago] Every Venn diagram or Hasse diagram I see illustrating the "standard model" of computational complexity describes a universe of $\mathsf{PSPACE}$ problems,...
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1answer
161 views

String theory based computations

I was reading Arora and Barak's book on computational complexity and in the section on 'criticism on Turing machine model and the class P' along with quantum computer it also mentions possibilities of ...
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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
112 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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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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What would a very simple quantum program look like?

In light of the announcement of the world's first programmable quantum photonic chip, I was wondering just what software for a computer that uses quantum entanglement would be like. One of the first ...
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1answer
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QMA definition of difference between probabilities intuition

I'm reading about the complexity classes related to quantum computation, currently I'm studying QMA class. A language is in QMA(c,s) if there exists a polynomial time verifier and polynomial $p(n)$ ...
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335 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^{...
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0answers
69 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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3answers
238 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 size....
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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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163 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 ...
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95 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 ...
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2answers
204 views

Which cryptographic protocols are secure against quantum computer attacks?

Are there any cryptosystems that we know that would be secure against an attack by a quantum computer? Are there problems which are known or suspected to be hard for quantum computers, and can these ...
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0answers
52 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 ...
9
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1answer
240 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, ...
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1answer
212 views

Fast classical simulation of quantum algorithms

Are there examples of cases where the classical simulation of a quantum algorithm for a problem outperforms the best previously known classical algorithm for this problem? "Outperforms" doesn't have ...
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711 views

Analytic solutions in semidefinite programming (SDP)

From my experience in the application of semidefinite programming (SDP) to quantum information, I have learnt that the solution to an SDP can sometimes be expressed as an analytic formula. For example,...
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1answer
81 views

Quantum circuit simulation divergence in results

I'm learning about quantum computing in order to code a simulator. I tried the following circuit in Quirk And ran the same circuit using OPENQASM 2.0: Notice that the input is |11> in both cases, ...
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1answer
349 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 ...
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1answer
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Problems in BQP but conjectured to be outside P

Wikipedia listed four problems that are in $BQP$ but conjectured to be outside $P$: Integer factorization; Discrete logarithm; Simulation of quantum systems; Computing the Jones polynomial at certain ...
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136 views

Complement for joint POVMs?

I'm trying to relate some notions of set theory to POVMs. I firstly explain the scenario with set theory and then in the POVM setting. For some finite $N \in \mathbb{N}$, let $A_i$ and $B_i$ for $i=1,...
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1answer
124 views

Papers on using resource states to implement QFT efficiently

I recently stumbled onto the idea of using a pre-existing re-usable phase gradient to implement the QFT, instead of having to keep re-applying exponentially precise phase gates. I'm looking for papers ...
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216 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 ...
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7answers
24k views

Universities for Quantum Computing / Information?

Which universities have a strong quantum computing curriculum, and offer some type of quantum computing/information courses/research? The aim here is to collect a useful list for someone considering ...
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2answers
743 views

Problems with no known quantum advantage

I was wondering what the list of current natural computational problems is for which there is no known complexity advantage in using a quantum computer. To start things off, I think computation of ...
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1answer
182 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
80 views

PromiseBQP and expectation values of operators

This question is regarding The Equivalence of Searching and Sampling by Aaronson. In page 4 he makes the following statement, ... a difficult and unsolved meta-question is whether PromiseBPP = ...
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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 ...
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6answers
4k 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 ...
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2answers
247 views

How can I get $\sum_n e^{i a_n} |n\rangle$ from $\sum_n a_n |n\rangle$?

Suppose that I have a normalized quantum state $\sum_n a_n |n\rangle$, is there a quantum operation/circuit so that I can get $\frac{1}{N} \sum_n e^{i a_n} |n\rangle$ at output? How?
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1answer
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States and Probability distributions that the 5-qubits IBM computer can produce

Update (January 2018) A new very interesting paper with various experiments on the IBM machine is Five Experimental Tests on the 5-Qubit IBM Quantum Computer by Diego García-Martín, Germán Sierra. ...
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Why is BQPSPACE in PSPACE if it can have doubly exponentially long running times?

The standard proof that BQPSPACE is in PSPACE relies on a Savitch game type analysis on path integrals. However, it assumes the time running length for BQPSPACE is at most exponentially long. This is ...
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Is $CAPP \in P$ known to collapse some quantum complexity classes to classical ones?

Lets define the class $ZBQP = \{ L \mid \exists \textit{P-uniform circuit family } \{C_i\}, \forall n \in \mathbb{N}, |x| = n, |\langle 0|C_n|x \rangle - I(x \in L)| \leq 9/10 \Longleftrightarrow x \...
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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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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 ...
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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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57 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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1answer
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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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95 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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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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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 ...
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1answer
4k views

Oracle Construction for Grover's Algorithm

In Mike and Ike's "Quantum Computation and Quantum Information", Grover's algorithm is explained in great detail. However, in the book, and in all explanations I have found online for Grover's ...