# Questions tagged [random-quantum-circuit]

For questions about quantum circuits having a small (polynomial) number of quantum gates; each gate is defined randomly. Random quantum circuits may be implementable shortly, and be used in noisy, intermediate-scale quantum (NISQ) era. Sampling from a random quantum circuit is likely to be classically hard.

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### Clifford circuit approximation to a random Clifford circuit

Given a random Clifford state on $L$ qubits (defined as an infinite depth Clifford circuit acting on the zero state), what depth Clifford circuit is required to approximate this state to a given ...
• 330
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### What's the deal with quantum random number generators?

Classical computers are usually incapable of generating true random numbers as they are based on deterministic algorithms. To overcome this challenge, one can either use pseudo-random number ...
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### Multiplication by a Haar random unitary two times

Consider a Haar random unitary $U$. I am trying to compute the value (or put a bound on) $$\mathbb{E}\left[\left|\langle 0^{n} |U^{2} |0^{n}\rangle\right|^{2}\right].$$ The ...
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1 vote
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### Approximating the average of a rational function with respect to the Haar measure

Suppose I have a state $|\psi\rangle = U|0\rangle$ where $U$ is a $d$-dimensional unitary sampled uniformly with respect the Haar measure. I'm interested in computing or approximating analytically an ...
• 4,652
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### understanding QuantumCircuit.x() function

For Code 1 qc.x(0,1) throws error but not for code 2 . Please help me to understand code 1 ...
• 181
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### What is the average amount of gates needed to implement a random Clifford gate?

Given a Clifford gate acting on $n$ qubits is implemented using its generators, what is the average number of gates needed to implement a random Clifford gate as a function of $n$?
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### What is the HOG test and how would it help proving quantum supremacy?

Proposed experiments in achieving quantum supremacy, such as with BosonSampling or using random circuits, have been described as using a (not necessarily Turing complete) quantum computer to perform ...
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