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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How to benchmark approximate random unitary sampling
I'm currently studying a specific sampling "quantum advantage" (sorry for the buzzword) protocol wich consist of periodically driving a random Ising chain (https://iopscience.iop.org/article/...
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Integral over Haar measure of squared density matrix of Haar random state is proportional to the identity plus swap operator
I am having some trouble understanding why $\int d\psi (| \psi \rangle \langle \psi | )^{\otimes ^2}\propto \ I+$ SWAP , where $|\psi \rangle =U|\psi _0\rangle$ are Haar random states and $d\psi $ is ...
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Generalizing a brick-wall circuit acting on qubits to acting on qudits
Recently, I have been creating a "brick layer" circuit of random unitary gates (each acting on 2 qubits) which acts on a n qubit register using cirq. A typical circuit looks like this.
(...
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Independence in state prepared by independently drawn Haar random gates
Consider independently drawn $2 \times 2$ Haar random unitaries $U_1, U_2, \ldots, U_n$ and
$$V = U_1 \otimes U_2 \otimes \cdots U_n.$$ Consider the state $\sigma$ given by
$$\sigma = V \rho V^{*}, $$
...
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Quantum circuit simplification using classical computers
Suppose that we have this kind of circuit where the first unitary operator U is used for the state preparation while the Hadamard operator is used of state detection.
Let's say we try to run this ...
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Simulation files for noisy quantum circuits
For our study with Yosi Rinott and Tomer Shoham we need the following simple data:
Starting with a quantum circuit $C$ on $n$ qubits we need two files:
a) A file of probabilities (or amplitudes) for ...
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Does the invariance of the Haar measure still hold if you use Clifford gates to approximate the Haar random unitaries?
I am not familiar with the Clifford group - I do know that Clifford unitaries can form a unitary 3-design (from this paper) and can be used to approximate Haar random unitaries, but I don't know how ...
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Vanishing expectation value $|\langle Z_1Z_2...Z_N \rangle|$
I'm doing a research involving expectation values of different observables.
I've observed that, given a random Quantum Circuit $U$ with $N$ qubits acting on an inital state $|0\rangle$ in such a way ...
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Prove that uniformly random states have moments ${\bf E}_\psi|\langle x|\psi\rangle|^{2t}\sim1/\binom d t$
Im looking for the moments of Haar random states. Is it true that
$\textbf{E}_{\psi\sim \text{Haar}}|\langle x| \psi\rangle|^{2t}\sim \frac{1}{\binom{d}{t}}?$ How does one prove this?
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How to compute projective probabilities of a given measurement outcome using Stim?
I am looking to calculate the projective probabilities for each measurement outcome in a Clifford circuit and then output its corresponding tableau state. I am performing the measurement in the Z ...
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How to convert Tableau to Circuit in stim
I am trying to simulate random Clifford circuit. I can use stim.Tableau.random(n) to generate it, but don't know how to convert into stim.Circuit() form. It seems current v1.9 does not have to_circuit(...
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Generating random circuits with only CNOT gates using qiskit.circuit.random.random_circuit
I am trying to generate a random quantum circuit with 5 qubits using only CNOT gates. I have modified the source code of the qiskit.circuit.random.random_circuit function to only include CNOT gates (...
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A question on random quantum states and the uniform distribution
Consider an $n$ qubit Haar random quantum state $|\psi\rangle$. Consider a distribution $\mathcal{D}_1$ over $n$ bit strings defined as
$$
p_x = |\langle x| \psi \rangle|^{2},
$$
for $x \in \{0, 1\}^{...
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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 ...
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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)
\begin{equation}
\mathbb{E}\left[\left|\langle 0^{n} |U^{2} |0^{n}\rangle\right|^{2}\right].
\end{equation}
The ...
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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 ...
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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
...
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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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The phase of the eigenvalue for the LCU method and randomized product formula
If we implement the linear combination of unitary(LCU), $\tilde{U}=\sum_i p_i U_i$, onto its eigenstate, $|\psi \rangle$, we can express its eigenvalue as $re^{i\theta}$, where $\sum_ip_i=1$, $0\leq ...
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What is the relationship between the size of the Hilbert space for boson sampling and the complexity of classical simulating it?
My intuition is that the fastest classical algorithm for simulating some kind of noiseless quantum sampling process should scale roughly with the dimension of the Hilbert space: you would need to ...
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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, ...
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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 ...
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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 ...
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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
...
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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 ...
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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 ...
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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, ...
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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,...
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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 ...
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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 ...
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Computing expectation value of $|\langle z|C|0^n\rangle|^2$ over Haar random circuit
I am trying to understand the integration on page 4 of this paper. Consider a Haar random circuit $C$ and a fixed basis $z$. Each output probability of a Haar random circuit (given by $|\langle z | C |...
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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 ...
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Compute the large $n$ distribution of $|\langle z_i|\psi\rangle|^2$ over Haar random quantum states
Let $|\psi\rangle$ be a $n$ qubit Haar-random quantum state. I am trying to show that in the limit of large $n$, for each $z_{i} \in \{0, 1\}^{n}$,
$$ |\langle 0|\psi\rangle|^{2}, |\langle 1|\psi\...
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Could random quantum circuits be efficiently approximately simulated?
Google's landmark result last year was to compute a task with a quantum computer that a classical computer could not compute, and they chose random circuit sampling. Part of their justification was ...
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What is the Clifford gates selection probability distribution used in the generation of randomized benchmarking circuits?
I've read that in standard randomized benchmarking implementations the random quantum circuits are generated through random gate selection from a uniformly distributed Clifford set of either 1 or 2-...
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Implementing a circuit that returns $|01\rangle$ and $|10\rangle$ with equal probability
Using Python how can I implement a quantum circuit that returns $|01\rangle$ or $|10\rangle$ using only $CX$, $RX$ and $RY$ gates, starting with random parametric gates as parameters and optimizing it ...
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How to split a Quantum Circuit on a barrier in Qiskit?
Let's say I have a QuantumCircuit with multiple barriers as shown in the visual below:
How would I split up the ...
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Randomness using simple parallel Hadamard circuit
I've recently tried to build a Random generator using 5 hadamard gates (shown as U2 below) measured to 5 classical bits in parallel as shown in the circuit image.
I've executed this circuit for 8192 ...
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If two reduced density matrices are equal, does that mean that the two subsystems are the same?
Suppose we have a $3$-qubit system at time $t_0$ in the state
$$\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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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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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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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 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 ...
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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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