For questions about simulating either quantum computers or simulating things on quantum computers.
Questions tagged [simulation]
393 questions
79
votes
4 answers
Can a Turing machine simulate a quantum computer?
I know that a Turing machine1 can theoretically simulate "anything", but I don't know whether it could simulate something as fundamentally different as a quantum-based computer. Are there any attempts to do this, or has anybody proved it…
user7
38
votes
3 answers
Can a quantum computer simulate a normal computer?
Similar to the question Could a Turing Machine simulate a quantum computer?: given a 'classical' algorithm, is it always possible to formulate an equivalent algorithm which can be performed on a quantum computer? If yes, is there some kind of…
Glorfindel
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27
votes
1 answer
What are examples of Hamiltonian simulation problems that are BQP-complete?
Many papers assert that Hamiltonian simulation is BQP-complete
(e.g.,
Hamiltonian simulation with nearly optimal dependence on all parameters and Hamiltonian Simulation by Qubitization).
It is easy to see that Hamiltonian simulation is BQP-hard…
groupsgroupsgroups
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26
votes
1 answer
Explicit Lieb-Robinson Velocity Bounds
Lieb-Robinson bounds describe how effects are propagated through a system due to a local Hamiltonian. They are often described in the form
$$
\left|[A,B(t)]\right|\leq Ce^{vt-l},
$$
where $A$ and $B$ are operators that are separated by a distance…
DaftWullie
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25
votes
5 answers
How would I implement the quantum oracle in Deutsch's algorithm?
I am trying to simulate Deutsch's algorithm (elementary case of Deutsch-Jozsa algorithm), and I am not entirely sure how I would go about implementing the quantum oracle necessary for the algorithm to function, without defeating the purpose of the…
Jack Ceroni
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21
votes
3 answers
What would a very simple quantum program look like?
After reading the "first programmable quantum photonic chip". I was wondering just what software for a computer that uses quantum entanglement would be like.
Is there any example of code for specific quantum programming? Like pseudocode or…
Didix
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19
votes
1 answer
Why are non-Clifford gates more complex than Clifford gates?
There are two groups of quantum gates - Clifford gates and non-Clifford gates.
Representatives of Clifford gates are Pauli matrices $I$, $X$, $Y$ and $Z$, Hadamard gate $H$, $S$ gate and $CNOT$ gate. Non-Clifford gate is for example $T$ gate and…
Martin Vesely
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18
votes
1 answer
Obtaining gate $e^{-i\Delta t Z}$ from elementary gates
I am currently reading "Quantum Computation and Quantum Information" by Nielsen and Chuang. In the section about Quantum Simulation, they give an illustrative example (section 4.7.3), which I don't quite understand:
Suppose we have the Hamiltonian…
brzepkowski
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17
votes
3 answers
Building a quantum computer in simulation
If one wants to start building a quantum computer from scratch inside simulations (like how people get to build a classical computer from scratch in the Nand2Tetris course), is it possible?
If yes, what would be some possible approaches?
Also, what…
ak_nama
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16
votes
1 answer
Status of Google's quantum supremacy claim 2022
More than a year ago a couple of scientists made a splash by presenting a classical algorithm that took less than a week to simulate Sycamore's circuits on a small GPU cluster. Also, their simulations produced exact results and not estimates.
This…
MonteNero
- 3,344
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15
votes
6 answers
Is there any online Bloch sphere simulator?
While writing this answer I realized it would be really helpful if I could show the OP a video or .gif of how qubit states in Bloch spheres transform under certain unitary operations. I googled up a bit and could find only these two…
Sanchayan Dutta
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15
votes
3 answers
How to compactly represent multiple qubit states?
Since access to quantum devices capable of quantum computing is still extremely limited, it is of interest to simulate quantum computations on a classical computer. Representing the state of $n$ qubits as a vector takes $2^n$ elements, which greatly…
Kiro
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14
votes
2 answers
Why doesn't the Gottesman-Knill theorem render quantum computing almost useless?
The Gottesman-Knill theore states (from Nielsen and Chuang)
Suppose a quantum computation is performed which involves only the following elements: state preparations in the computational basis, Hadamard gates, phase gates, controlled-NOT gates,…
user2723984
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13
votes
1 answer
Where does precisely the difficulty in exponentiating a Hamiltonian $H$ in the quantum simulation problem lay?
I've read in the Nielsen's, Chuang's "Quantum Computation and Quantum Information":
Classical simulation begins with the realization that in solving a simple differential equation such as $dy/dt = f(y)$, to first order, it is known that $y(t +…
brzepkowski
- 1,069
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13
votes
2 answers
Hamiltonian simulation with complex coefficients
As part of a variational algorithm, I would like to construct a quantum circuit (ideally with pyQuil) that simulates a Hamiltonian of the form:
$H = 0.3 \cdot Z_3Z_4 + 0.12\cdot Z_1Z_3 + [...] +
- 11.03 \cdot Z_3 - 10.92 \cdot Z_4 + \mathbf{0.12i…
Mark Fingerhuth
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