# 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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### At what depth and for what architecture are random quantum circuits $1$-designs?

I was confused about something related to quantum $1$ designs. Let us recap two facts we know about random circuit ensembles that form a $1$ design. $1$ design, for a quantum circuit over $n$ qubits, ...
60 views

### Random circuits with google cirq

For my dissertation I need to simulate random circuits and I have been trying to use google Cirq for that. Looking at the documentation I have seen how to create my own circuit and simulate it, but it ...
47 views

### Random quantum circuits and general efficient POVM measurement

Let's consider a random quantum circuit $C$, applied to the $n$ qubit initial state $|0^{n}\rangle$, producing the state $|\psi\rangle$. Consider a general efficiently implementable $m$-outcome POVM ...
63 views

### Spreading of entanglement with depth for Haar random states

Consider a Haar random quantum state of depth $d$. Consider any bipartition of this state. According to this paper (page $2$): Haar-random states on $n$ qudits are nearly maximally entangled across ...
155 views

### Spoofing XQUATH with the Feynman method

Consider the XQUATH conjecture for random quantum circuits, as mentioned here. (XQUATH, or Linear Cross-Entropy Quantum Threshold Assumption). There is no polynomial-time classical algorithm that ...
44 views

### Feynman method and polynomial time algorithm for XQUATH

Consider the Feynman algorithm for simulating quantum circuits, as given here. Consider the XQUATH conjecture for random quantum circuits from here, given by (XQUATH, or Linear Cross-Entropy Quantum ...
26 views

### What constitutes generic dynamics, and how is it different from a fully random function?

What constitutes generic dynamics? And how is it different from a fully random function? From what I understand, a fully random function is one that is "Haar" random. And generic dynamics, ...
45 views

### What is the counting argument for the number of elementary operations required for a random function?

What is the counting argument for the following statement (classical)? "A random function on n bits requires $e^{\Omega(n)}$ elementary operations." It appears in the introduction of PRL 116,...
58 views

### Random Circuit Generation in Cirq

I am trying to improve an optimization method as describe in this paper: enter link description here For that I need to create many random equivalent circuits. In my experiment I have 6 beam splitters ...
128 views

### Quantum supremacy: shallow depth Haar random circuits and unitary designs

I had a confusion about shallow depth Haar random quantum circuits. In this paper, in Section B (related works), it is mentioned that Haar random quantum circuits form approximate $2$-designs only ...
44 views

### Quantum PRGN against Hard disk Forensics

We can make use of the Qbit to make a random string of bytes then as I have an office laptop and I can do some espionage by copying the files to my local disk from the network share and upload it to ...
104 views

### Why is the Measurement Result Always 1? (expected to find uniformly random measurement)

I created a $|0\rangle$ state then applied $H$ gate to get $\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)$ and then I meausred my state. But I always found 1. I expected to find 0 and 1 uniformly random ...
106 views

### Could random quantum circuits be efficiently approximately simulated?

Google's landmark result last year was to compute a task with a quantum computer that a classical computer could not compute, and they chose random circuit sampling. Part of their justification was ...
151 views

### What is the Clifford gates selection probability distribution used in the generation of randomized benchmarking circuits?

I've read that in standard randomized benchmarking implementations the random quantum circuits are generated through random gate selection from a uniformly distributed Clifford set of either 1 or 2-...
150 views

### Implementing a circuit that returns $|01\rangle$ and $|10\rangle$ with equal probability

Using Python how can I implement a quantum circuit that returns $|01\rangle$ or $|10\rangle$ using only $CX$, $RX$ and $RY$ gates, starting with random parametric gates as parameters and optimizing it ...
189 views

### How to split a Quantum Circuit on a barrier in Qiskit?

Let's say I have a QuantumCircuit with multiple barriers as shown in the visual below: How would I split up the ...
55 views

### 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 ...
89 views

### 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, ...
60 views

### 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
184 views

### 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 ...
98 views

### 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 ...
195 views

### 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. ...
24 views

### 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 ...
308 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 ...
40 views

### 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, ...
54 views

### 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'...
196 views

### How exactly is solving the random circuit sampling problem a computation in the Church-Turing thesis sense?

Note: This has been cross-posted to CS Theory SE. If we assume $\mathsf{BQP} \neq \mathsf{BPP}$, then we can say with reasonable certainty that Google's random sampling experiment falsifies the ...
115 views

### 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 ...
235 views

### 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. ...
333 views

### 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 ...
614 views

### 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: ...
768 views

### 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: ...
730 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 ...
324 views

### 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 ...
210 views

### 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 ...
127 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, ...