All Questions
Tagged with algorithms quantum-mechanics
28
questions
3
votes
2
answers
172
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About how to calculate observables in Quantum Monte Carlo with complex weights
I'm rewriting a Diagrammatic Quantum Monte Carlo algorithm following Werner, P., Oka, T., & Millis, A. J. (2009). Diagrammatic Monte Carlo simulation of nonequilibrium systems. Physical Review B, ...
- 165
1
vote
0
answers
77
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Simplest quantum Monte-Carlo method for the Bose-Hubbard model
I want to use quantum Monte-Carlo results to benchmark an algorithm for the Bose-Hubbard model. There are so many QMC methods in the market, so which one is the simplest one? I want the ground state ...
- 1,957
2
votes
0
answers
207
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How Do Quantum Computers Work, Like Really [closed]
I understand in plain terms superposition and entanglement, but I'm very unclear how either of these could work as a means to increase computation power.
A helpful metaphor is that of the maze. A ...
- 129
1
vote
1
answer
336
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Number of qubits required in Shor's algorithm
People say that the number of qubits required in Shor's algorithm for factorizing $N$ should be
$2\log N$ for control register and $\log N$ for target register.
What is the reason why these numbers of ...
- 185
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0
answers
140
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Is there a comparison table for quantum algorithms like VQE, QPE, QAOA, and so on?
I have one question: Recently, I studied about several algorithms like VQE, QPE, QAOA and so on. I would like to make some comparison tables about those algorithms, their strengths and weaknesses. If ...
11
votes
1
answer
1k
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Why use Crank-Nicolson over Matrix Exponential when solving Schrödinger's equation?
For Schrödinger's equation,
$$\psi(x,t+\Delta t)=e^{-i H\Delta t}\psi(x,t)\approx\frac{1-\frac{1}{2}i H\Delta t}{1+\frac{1}{2}i H\Delta t}\psi(x,t).$$
The right-most expression is the Crank-Nicolson ...
- 779
1
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0
answers
122
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Final Hamiltonian for Adiabatic Grover
X-Posted on Quantum-Computing Stack Exchange
In quantum computation, there is a famous algorithm to search a marked item in an unstructured database called Grover's algorithm. It achieves a quadratic ...
4
votes
2
answers
1k
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How to actually find a Hartree-Fock ground state?
I am interested in finding the Hartree-Fock ground state for a system of interacting fermions (with totally local scattering, so a delta-function interaction potential). I have read through some ...
- 613
0
votes
1
answer
78
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Metropolis Algorithm Transition-Proposal Probability
I'm working my way through a short section on the Metropolis algorithm in the lecture notes on Computational Quantum Physics by Prof. Troyer.
However, I am not sure what probability distribution was ...
- 485
1
vote
1
answer
100
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Is photon interference really random? [closed]
I know that according to the many worlds interpretation, there is no randomness and rather there is a universal wave function that simulates an observer with a continuously branching timeline. My ...
- 1,668
0
votes
2
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290
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Shor's algorithm with adversary - can (delayed) erasure of value qubits cripple calculations?
Let's look at quantum subroutine of Shor's algorithm:
Hadamard gates create superposition of all (exponential number) values for input qubits.
Then we perform a classical function on them, which is ...
- 960
2
votes
1
answer
289
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Quantum Approximate Optimization Algorithm
I try to understand the 'Quantum Approximate Optimization Algorithm' (QAOA) by Farhi et al. - arXiv:1411.4028.
I understand that the solution is hidden in the unitaries, but I do not understand how ...
- 570
9
votes
2
answers
2k
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Shor's algorithm - why doesn't the final collapse of the auxiliary qubits cripple the computation?
Let's look at quantum subroutine of Shor's algorithm (image source):
Hadamard gates create superposition of all (exponential number) values for input qubits.
Then we perform a classical function ...
- 960
1
vote
0
answers
230
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Shor's algorithm - its causality and similar exploitation of QM?
Shor's algorithm is rather the most interesting quantum algorithm as it shifts a problem which is believed to need exponential classical time, to polynomial time for quantum computer, additionally ...
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votes
0
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75
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Using quantum state tomography in quantum search algorithms
Problem statement: The search space A involves elements $|0\rangle $, $|2\rangle$... $|d-1\rangle$. An oracle is provided for the function $f(x)$ where
\begin{align}
f(x)&=1 \quad x=x^{'}\in A \\
...
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