Questions tagged [quantum-computing]

Quantum computation and computational issues related to quantum mechanics

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An algebro-combinatorial argument that P = NP

Also asked in normal CS stack exchange. I have long been fascinated by this question and recently wrote an article about it. The version of computation described in the article is similar to those ...
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1answer
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Qubit gates in google supremacy

The gates in quantum supremacy experiment are nearest-neighbor and have spatial locality. Would this additional information help bolster IBM's argument to perhaps simulate quantum supremacy experiment ...
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102 views

How exactly is solving the random circuit sampling problem a computation in the Church-Turing thesis sense? [closed]

Note: This has been cross-posted to Quantum Computing SE. If we assume $\mathsf{BQP} \neq \mathsf{BPP}$, then we can say with reasonable certainty that Google's random sampling experiment falsifies ...
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Quantum advantage beyond the black-box model

The common quantum algorithms I know of can be all explained using black-box model (i.e., query model): Grover's search. An $O(\sqrt{n})$-query algorithm that computes the OR of $n$ bits. Shor's ...
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Is the wording of Google's QC Supremacy valid?

Quantum supremacy using a programmable superconducting processor was published today. Scott Aaronson posted a few weeks ago a post about this paper and it was clear we will see a Nature or Science ...
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If Shore's Algorithm can solve factorization efficiently, how can it be in NP?

having a somewhat decent knowledge about classic complexity theory but not about Quantum Complexity Theory, I really struggle to understand the following: Under the ...
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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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PPAD and Quantum

Today in New York and all over the world Christos Papadimitriou's birthday is celebrated. This is a good opportunity to ask about the relations between Christos' complexity class PPAD (and his other ...
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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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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 ...
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1answer
134 views

Given a subset of of the hypercube and an affine transform of it, find the affine map

This is a follow up to this resolved question. Suppose we are given a set of bitvectors $A\subseteq\mathbb{F}_2^d$ and an invertible affine transformed copy of it $$B=\{Mx + s\mid x\in A\}$$ for some ...
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Given a subset of the hypercube and a copy translated by s, find s

Problem: Suppose we are given an $n$ element subset $A\subseteq\{0,1\}^d$ of the $d$ dimensional hypercube and a translated copy $B= A+s$ by some secret $s\in\{0,1\}^d$. Find $s$ as fast as possible ...
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1answer
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Grover's algorithm, M out of N, when M is large

The more general version of Grover's algorithm searches for one of $M$ entries that match a criterion, out of $N$ total entries. I have seen it written that this takes $O(\sqrt{N/M})$ iterations, to ...
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58 views

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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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
127 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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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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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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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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1answer
177 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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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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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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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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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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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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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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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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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 ...
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1answer
222 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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1answer
82 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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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 ...
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2answers
207 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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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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690 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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1answer
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
84 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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183 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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123 views

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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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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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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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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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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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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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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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 ...