# Tag Info

Accepted

### Can a Turing machine simulate a quantum computer?

Yes, a quantum computer could be simulated by a Turing machine, though this shouldn't be taken to imply that real-world quantum computers couldn't enjoy quantum advantage, i.e. a significant ...
• 1,497
Accepted

### Can a quantum computer simulate a normal computer?

Yes, it can do so in a rather trivial way: Use only reversible classical logical gates to simulate computations using boolean logic (for instance, using Toffoli gates to simulate NAND gates), use only ...
• 1,314

### What are examples of Hamiltonian simulation problems that are BQP-complete?

There are plenty of different variants, particularly with regards to the conditions on the Hamiltonian. It's a bit of a game, for example, to try and find the simplest possible class of Hamiltonians ...
• 59.3k
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### Why doesn't the Gottesman-Knill theorem render quantum computing almost useless?

To my mind, this theorem is not very well stated in this form, if taken out of context. Where it says "phase gates", this may be misleading. It means specifically just $S=\sqrt{Z}$ and not what I ...
• 59.3k

### What would a very simple quantum program look like?

One way of writing quantum programs is with QISKit. This can be used to run the programs on IBM's devices. The QISKit website suggests the following code snippet to get you going, which is an ...
• 11.3k
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• 12.2k
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### Obtaining gate $e^{-i\Delta t Z}$ from elementary gates

One way order to perform Z rotations by arbitrary angles is to approximate them with a sequence of Hadamard and T gates. If you need the approximation to have maximum error $\epsilon$, there are known ...
• 38.5k
Accepted

### Where does precisely the difficulty in exponentiating a Hamiltonian $H$ in the quantum simulation problem lay?

TL;DR: Hamiltonian simulation does not just mean "exponentiating $H$". It means finding a quantum circuit $U$ that approximates the matrix exponentiation $e^{-iHt}$. More importantly, the size of the ...
• 17.6k
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### Are almost-Clifford circuits almost easy to simulate?

Short answer: Yes, this should be possible. However, the details have to be filled out. The key is to relate this to magic monotones. There has been some development since the 2016 Bravyi-Gosset paper....
• 5,107
Accepted

### Roughly speaking, How many qubits will be needed to study (or simulate) a molecule such as: C29H31N7O?

My quick answer: something between 4 and 4000. ^_^ The number of qubits in an electronic structure calculation depends on at least three things: Your basis set. Your qubit mapping. Your algorithm. ...
• 1,206
Accepted

### is cirq suitable for simulation of quantum error correction?

I wrote most (as in >50% not as in all) of the initial versions of cirq, and was its team lead for a couple years. I wouldn't recommend using Cirq as a tool for simulating QEC codes. Cirq is first ...
• 38.5k
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### How to compactly represent multiple qubit states?

There are many possible ways to compactly represent a state, the usefulness of which strongly depends on the context. First of all, it is important to notice that it is not possible to have a ...
• 25.5k
Accepted

### Is there any source which tabulates quantum computing algorithms for simulating physical systems?

I believe what you're after is NIST's Quantum Zoo, a comprehensive catalog of quantum algorithms maintained by Stephen Jordan. Its sections include: Algebraic and Number Theoretic Algorithms (14 ...
• 1,749
AHusain's answer is absolutely correct, but perhaps lacks some detail. The circuit that you want to implement is Basically, the key is to realise that you want to apply phase $e^{i\alpha}$ to the ...