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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Randomness using simple parallel Hadamard circuit

I've recently tried to build a Random generator using 5 hadamard gates (shown as U2 below) measured to 5 classical bits in parallel as shown in the circuit image. I've executed this circuit for 8192 ...
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If two reduced density matrices are equal, does that mean that the two subsystems are the same?

Suppose we have a $3$-qubit system at time $t_0$ in the state $$\vert{\psi(t_0)}\rangle= \vert{q_0}\rangle \otimes \vert{q_1} \rangle \otimes \vert{q_2}\rangle. $$ We want to check if, for instance, ...
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How to create a Quantum circuit to implement the generation of 3-qubit uniform superposition wavefunction

I want to know experimentally or circuit wise diagram to know how to create a circuit that will produce 3-qubit uniform superposition wave function Can somebody help me in that Thank you in advance
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Help Identifying a Gate In Nielsen and Chuang

I am seeking help to identify the oracle gates listed in this example. I understand that the right-most one is a toffoli gate, but what are the other ones? Specifically, I do not understand what a ...
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1answer
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What is the role of choosing the single-qubits randomly in Google quantum supremacy experiment?

In supremacy paper and part D of section VII of supplementary information (below), it is said that there is a pseudo-random number generator that is initialized with a seed called $s$; And then the ...
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What did exactly Google do in simulating a random quantum circuit on a classical computer in supremacy experiment?

I've been working on Google quantum supremacy paper for quite some time now and I have a problem in understanding how exactly they simulate their actual random quantum circuit on a classical computer. ...
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How do we know that there exists a quantum circuit whose output distribution is #P-hard to calculate?

I am trying to understand the random quantum circuit sampling arguments for recent Google experiment, but struggling to understand why there exists a family of quantum circuit whose output ...
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1answer
201 views

How to make circuit for randomly selected gate?

I am trying to make a circuit for the randomly selected gates from a gate_list but I don't know how to put these selected gates in front of ...
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0answers
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How to randomly generate unoptimized stabilizer circuits?

I have to test a simulator with a high number of random stabilizer circuits. One way to create random stabilizer circuits is to generate random graph states and convert those to circuits, this, ...
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What is quantum gate's correponding circuit implementation? [closed]

We know that the symbol of a quantum gate like "x gate", "z gate" is an abstraction notation. For example, the Not-gate in classical computer is composed of 2 transistors. How can we know quantum gate'...
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How does successfully sampling from a random quantum circuit invalidate the Extended Church-Turing Thesis?

According to these lecture notes from Berkeley, the Extended Church-Turing Thesis (ECT) asserts that: ...any "reasonable" model of computation can be efficiently simulated on a standard model such ...
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Are 20 repetitions of Sycamore's one- and 2-qubit gates sufficient to produce a uniformly random state?

In the answer to this question about random circuits, James Wootton states: One way to see how well we [fully explore the Hilbert space] is to focus on just randomly producing $n$ qubit states. ...
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Number of qubits to achieve quantum supremacy?

Google's Sycamore paper describes achieving quantum supremacy on a $53$-qubit quantum computer. The layout of Sycamore is $n=6\times 9=54$ nearest neighbors, with one qubit nonfunctional. They apply ...
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Understanding Google's “Quantum supremacy using a programmable superconducting processor” (Part 3): sampling

In Google's 54 qubit Sycamore processor, they created a 53 qubit quantum circuit using a random selection of gates from the set $\{\sqrt{X}, \sqrt{Y}, \sqrt{W}\}$ in the following pattern: ...
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Understanding Google's “Quantum supremacy using a programmable superconducting processor” (Part 2): simplifiable and intractable tilings

In Google's 54 qubit Sycamore processor, they created a 53 qubit quantum circuit using a random selection of gates from the set $\{\sqrt{X}, \sqrt{Y}, \sqrt{W}\}$ in the following pattern: ...
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575 views

Understanding Google's “Quantum supremacy using a programmable superconducting processor” (Part 1): choice of gate set

I was recently going through the paper titled "Quantum supremacy using a programmable superconducting processor" by NASA Ames Research Centre and the Google Quantum AI team (note that the paper was ...
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Do quantum supremacy experiments repeatedly apply the same random unitary?

It is my understanding that, given a quantum computer with $n$ qubits and a way to apply $m$ single- and 2-qubit gates, quantum supremacy experiments Initialize the $n$ qubits into the all-zero's ket ...
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Sampling random circuits vs Solovay-Kitaev compiler

Suppose I want to obtain a gate sequence representing a particular 1 qubit unitary matrix. The gate set is represented by a discrete universal set, e.g. Clifford+T gates or $\{T,H\}$ gates. A well ...
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106 views

Can we amplify BPP algorithms with a random quantum circuit?

Suppose we are given a (univariate) polynomial $P$ of degree $d$, and we wish to determine if $P$ is identically $0$. A standard way to do this is to use a classical PRG to randomly sample $n$ bits, ...
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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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What exactly is “Random Circuit Sampling”?

Many people have suggested using "Random Circuit Sampling" to demonstrate quantum supremacy. But what is the precise definition of the "Random Circuit Sampling" problem? I've seen statements like "the ...