Questions tagged [quantum-algorithms]
For questions about quantum algorithms, that is, sequences of quantum gates, operations, and measurements, whose purpose which achieve some goal. Standard examples are Shor's and Grover's algorithms.
190 questions from the last 365 days
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Does quantum algorithm guarantee to solve a combinatorial problem?
One of the applications of quantum computing is to solve practical problems faced in other fields, such as combinatorial problems. One route is encoding the problem into a Hamiltonian and then finding ...
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equivalent expression of the uncertainty principle in the presence of quantum memory [duplicate]
I'm reading the paper The Uncertainty Principle in the Presence of Quantum Memory. In the appendix the authors say that expression (2) is equivalent to (3). However, R is a mapping performed on system ...
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How to train QNN on qiskit or ionq simulators
I am trying to train a QNN using qiskit and ionq, the method I use now is to manually feed my input data into quantum circuits:
...
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60
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How to entangle two separate set into one?
I have two sets of qubits where the information is encoded in amplitude. How can I entangle them into one to save qubits.
The information $k_0,k_1,k_2,k_3$ and $k'_0,k'_1,k'_2,k'_3$ are encoding in ...
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0
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13
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Understanding Phase Maps and Dephasing in a Periodically Driven Qubit System
I am working on a periodically driven qubit system and trying to understand the concepts of phase maps and dephasing. Here is the setup:
The initial qubit state is given by:
$\cos(\theta/2)|0\rangle+\...
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11
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5
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What is the complexity of modulo order-finding problem on classical computer?
It doesn't seem to be NP-complete. But has it been proved to be NP-hard?
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how to mix (or time average) two density matrix?
Given two density matrix $\rho_1,\rho_2$ with the same size, how to get a mix state of the two matrix,
$$
\rho = \frac12 (\rho_1+\rho_2)?
$$
e.g. there are two quantum channel both of them have 4 ...
- 39
1
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0
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I have trouble using the alternatives for some commands in older versions of qiskit
I have a code that calculates the transition amplitute between and using the ZZFeatureMap with 4 repetitions and default data mapping function. Use the qasm_simulator with shots = 8192, seed_simulator ...
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1
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1
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115
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Is there a unitary operator for this multi qubit addition?
Is there a quantum unitary operator $U$ that
takes the tensor product of the two equiprobable states
$$
\frac{1}{\sqrt{2}}\big(|a_1\rangle+|a_2\rangle\big)
$$
and
$$
\frac{1}{\sqrt{2}}\big(|b_1\...
- 79
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0
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19
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Quantum many-body real time simulation: certain states inner product having no imaginary part?
When simulating the real-time evolution of transverse ising model many-body states, I noticed that some initial states, under the evolution of different times, would produce an inner product that is ...
- 231
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1
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Regarding proof that QIP$(m, a, b)$ $\subseteq$ QIP$(m+2, 1, 1 - (a-b)^2)$
I am having trouble understanding why additional interaction is required for perfect completeness. The essential idea of the proof in this paper is that, after the original $m$ rounds, the verifier ...
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1
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0
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Qiskit trotter simulation choice of initial state under transverse field Ising hamiltonian
The code is from https://github.com/qiskit-community/qiskit-algorithms/blob/stable/0.3/docs/tutorials/13_trotterQRTE.ipynb.
While simulating many-body system evolving under a transverse field Ising ...
- 231
2
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0
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30
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Set of `reachable` states from an initial density matrix with polynomial elements
I've been reading about the Bernoulli-factory problem and I'm particularly interested in deriving the results using the density matrix formalism, i.e., given required numbers of copies of the initial ...
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Why are there fewer algorithms for continuous compared to discrete quantum computation?
Why are there significantly fewer algorithms for continuous quantum computation compared to discrete quantum computation?
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Qiskit - Parallelization of a quantum circuit
I have the following circuit, which is the implementation of a quantum oracle for a fuzzy inference engine:
As you can see this is composed of blocks, between barriers, which can be considered ...
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Reference recommendation for research in quantum algorithm and quantum machine learning?
I have finished reading Nielson and Chuang and am interested in doing research in quantum algorithm and quantum machine learning. Are there any references that introduce these topics at research level?...
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What to do about operator scalability?
Suppose I have a 32 qubit register meant to represent a classic variable. I want to apply gates to it and naturally I have to tensor product up to a 32 bit register. That means something like
$$
I_{1} ...
- 171
1
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1
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Does qubitization work for non-hermitian matrices?
In the original qubitization paper, Definition 2 for a quantum signal processor requires a Hermitian matrix with bounded spectral norm. However, lemmas 8 and 10 are extended to normal matrices in ...
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1
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QPE implementation with 4 qubits
I'm trying to implement a circuit for QPE, i start with 4 qubits but the results are incorrect (even for 3 or 5 qubits).
the used unitary gate is : ...
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3
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1
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308
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Nielsen and Chuang Exercise 5.9
Let $U$ be a unitary transform with eigenvalues $±1$, which acts on a
state $|ψ〉$. Using the phase estimation procedure, construct a quantum
circuit to collapse $|ψ〉$ into one or the other of the two ...
0
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Cannot Find referance DeutschJozsa in __init__.py
I am new to quantum computing and Python. I tried to make a quantum simulation with qiskit, but I have some import issues that I can't solve, and I decided to ask it here.
I tried to import ...
3
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2
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187
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Can Shor's algorithm be improved transfering the classical part into the quantum part?
Shor's algorithm was suggested 20 years ago. But it has still globally unavailable in real world.
In my opinion, one reason of that is shor's algorithm includes both classical part and quantum part.
...
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1
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Implementation of the CSD Decomposition for a 4x4 matrix
I am currently reading Volume I of "Principles of Quantum Computation and Information" by Benenti-Casati-Strini. There is a section in chapter 3 which covers the decomposition of any ...
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Complexity of gaussian superposition preparation in Regev's factorisation algorithm
I'm going through the Regev's factorisation algorithm, and I don't understand how, for the Gaussian state preparation, he achieves a complexity of $d(\log D+ \text{poly}(\log d))$.
He says:
"the ...
- 63
1
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1
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76
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Error during replication of results in article Evidence for the utility of quantum computing
I am a newbie to quantum computing and Qiskit. I tried practise myself with research paper called Evidence for the utility of quantum computing before fault tolerance. I run it successfully but the ...
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150
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Are there any known or obvious practical applications for good solutions to the optimal polynomial intersection problem?
I learned from Aaronson's blog about a recent preprint by Jordan, Shutty, Wootters, (our very own) Zalcman, Schmidhuber, King, Isakov, and Babbush that provides an efficient quantum algorithm to give ...
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2
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2
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75
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Construction of $f(x) = x \pmod 2$ as an oracle function
I'm trying to conceptualise how one would implement an oracle function of f(x) = x in the context of the Deutsch-Josza Algorithm. So far I understand the basic idea of implementing trivial constant ...
2
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1
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76
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Why do we need an ancilla qubits in Grover-Rodolph method to initialise state?
I'm trying to understand the method from Grover and Rudolph to initialise state based on probability distribution. There is a example described in This post, however I don't understand why we need to ...
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Correlation decay in GHZ states, IBM quantum video
I watched an IBM quantum tutorial "Hello World" video. It assumed and then demonstrated that the correlation decays with the distance between two Pauli Z observables. I'm not able to derive ...
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1
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59
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Max amount of entries in n dimensional unit ball of infinity norm, question on YiLei Chen's eprint555 Lemma 3.10 proof
On pages 23-24 of YiLei Chen's paper "Quantum Algorithms for Lattice Problems", he claims the following state's support contains at most $ 2r\log n $ entries:
$$
\left|\varphi_{1}\right\...
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2
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1
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192
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HHL eigenvalue inversion and further inverse QPE
Reading the paper (arXiv) about HHL I misunderstood the following points:
$$|{x}\rangle = A^{-1} \cdot |b\rangle = \sum^{2^nb-1}_{i=0}\lambda_i^{-1}b_i|u_i\rangle$$
How do we inverse the eigenvalues? ...
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(Asymptotically) best known quantum algorithm for Graph isomorphism problem
Technically, Babai's (2016) (classical) quasi-polynomial algorithm can be counted as a quantum algorithm with a runtime of $\textrm{2}^{(\textrm{log(n)}^{c})}$. [Side remark: There is a claim that c=3 ...
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1
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Modify a quantum state prepared with HHL [closed]
I can prepare a state $|1\rangle|x\rangle|0\rangle$ using HHL. How do I prepare $|1\rangle|x\rangle|0\rangle+|0\rangle|y\rangle|0\rangle$ or simply $|1\rangle|x\rangle|0\rangle+|0\rangle|0\rangle|0\...
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1
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Why does QPE still produce phase eigenvalues in HHL even though it operates on non-eigenvectors?
I'm trying to understand mathematical intuition of HHL algorithm using original paper (arXiv)
For now I stuck at the part of Phase estimation. If I understand correctly, if vector b is the eigenvector ...
0
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0
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68
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A basic misunderstanding regarding a quantum algorithm for finding the maximum (Ahuja & Kapoor)
My question is regarding this paper where the authors claim that their algorithm finds the maximum in an unsorted table $T[0,...,N-1]$ of size $N$ in $O(\sqrt N)$ queries to the oracle. However, it's ...
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1
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Get Minimum Binary Value from Arbitrary Blackbox Oracle Result
Suppose there are three quantum registers and one classical register.
Operand A: 3-qubit
Operand B: 3-qubit
Results C: 6-qubit
Results D: 6-bit
The operand A is deterministic (user input), and the ...
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0
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Build a query circuit that set the first bit to 0
This is a question from Chapter 2, 8(c) in Quantum Computing: Lecture notes by Ronald de Wolf.
Suppose we can make queries of the type $|i, b\rangle→ |i, b\oplus x_i\rangle$ to input $x\in\{0, 1\}^N, ...
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Is quantum computation effectiveness dependent on EPR non-locality?
Suppose 100 qubits are used to perform a quantum algorithm.
According to the EPR view, each of these 100 qubits already have pre-determined states before we start the computation, which are just ...
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Classification in QSVM 2014 model: understanding the quantum circuit
This is a QSVM circuit from this paper (fig.. 1-e). I am having hard time understanding after barrier 2(in blue line).
I get that before line one, HHL is used to find the hyper-plane parameters ...
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What is the range of expectation value in quantum machine learning
If I want to build a quantum circuit to solve a regression problem in machine learning, and the target value is 200~300. In qiskit, we can use VQR to easily implement it, and it will output the ...
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Is there a generalized quantum teleportation for n-qubit entangled states? [duplicate]
Quantum teleportation for single qubit is a fairly simple algorithm to follow. Even its extensions into the transportation of $n$ qubits is fairly simple: repeat the process $n$ times (or run $n$ ...
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4
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How to realize the index shift operation in quantum circuit?
Can we realize the index shift in a quantum circuit as we do in a classic circuit?
$\forall$ $a,b,c \in \{0,1\}$, $\left|abc\right>\mapsto\left|bca\right>$
e.g. $\left|001\right>\mapsto \left|...
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Is there any known characterization of k-Local Hamiltonian (k-LH) to distinguish if it has an efficient guiding state?
In general, k-LH promise problem, where input is given as $<H, a, b>$, is QMA complete if $a-b>1/{\textrm{poly}(n)}$.
Also, if a guiding state (say, a "good" approximation to the ...
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1
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200
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How to prepare a superposed state?
Given two arbitrary states, $|\psi\rangle\ \text{and}\ |\phi\rangle$ that are possibly unknown to the preparer, is there a way to prepare the superposition $|\psi\rangle+|\phi\rangle$ of them? (If it'...
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Can quantum computers eventually be programmed "normally"?
They tell us that eventually quantum computers will break all current encryption methods. On the other hand, current quantum computers are programmed at a very low, mathematical level and for very ...
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Expectation Value of Observable from evolved statevectors using qiskit on Hardware
I want to compute this <Zi Zj> - <Zi><Zj> for an entangled n-qubit initial state under the application of a general XY Hamiltonian for a range of ...
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1
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112
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How different quantum computing in four dimensions would be? [closed]
Would mathematic of quantum computing stay mostly similar, if one would be able to perform quantum computing in four dimensions using spin operators $S_{x}$, $S_{y}$, $S_{z}$ and $S_{w}$?
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Why is my graph wrong when trying to visualize the max-cut in qiskit?
I think my QAOA code is correctly solving the max-cut but the visualization is wrong.
I am working on solving the Max-cut problem using QAOA. I started small-scale with a 5 node bipartite graph. I ...
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108
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VarQITE from scratch: troubles understanding the Variational Quantum Time Evolution (VarQTE) algorithm from Qiskit
At the moment I am trying to implement variational imaginary time evolution in Pennylane from scratch. To get a feeling if it works, I compare the results of my own implementation with the solutions ...
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Numerical values for the volume of qubits
This paper mentions the volume of qubit in equation (9) given by:
$$Q_0=U*C_1*T_o*n_p^{(2/3)}*(v_q)^{(2/3)}$$
where
$Q_0$ is the heat entering the chamber
$U$ is the heat transfer coefficient
$C_1$ ...
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