Questions tagged [simulation]

For questions about simulating either quantum computers or simulating things on quantum computers.

393 questions
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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
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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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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…
26
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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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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…
21
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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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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…
18
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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…
17
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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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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
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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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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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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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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
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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…
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