Random unitaries in extremely low depth
We prove that random quantum circuits on any geometry, including a 1D line, can form
approximate unitary designs over $ n $ qubits in $\log n $ depth. In a similar manner, we …
approximate unitary designs over $ n $ qubits in $\log n $ depth. In a similar manner, we …
Exact spectral gaps of random one-dimensional quantum circuits
The spectral gap of local random quantum circuits is a fundamental property that determines
how close the moments of the circuit's unitaries match those of a Haar random distribution …
how close the moments of the circuit's unitaries match those of a Haar random distribution …
Classically estimating observables of noiseless quantum circuits
A Angrisani, A Schmidhuber, MS Rudolph… - arXiv preprint arXiv …, 2024 - arxiv.org
We present a classical algorithm for estimating expectation values of arbitrary observables
on most quantum circuits across all circuit architectures and depths, including those with all …
on most quantum circuits across all circuit architectures and depths, including those with all …
Approximate Unitary -Designs from Shallow, Low-Communication Circuits
N LaRacuente, F Leditzky - arXiv preprint arXiv:2407.07876, 2024 - arxiv.org
Random unitaries are useful in quantum information and related fields but hard to generate
with limited resources. An approximate unitary $ k $-design is an ensemble of unitaries and …
with limited resources. An approximate unitary $ k $-design is an ensemble of unitaries and …
Random ensembles of symplectic and unitary states are indistinguishable
A unitary state $ t $-design is an ensemble of pure quantum states whose moments match
up to the $ t $-th order those of states uniformly sampled from a $ d $-dimensional Hilbert …
up to the $ t $-th order those of states uniformly sampled from a $ d $-dimensional Hilbert …
Efficient Quantum Pseudorandomness from Hamiltonian Phase States
Quantum pseudorandomness has found applications in many areas of quantum information,
ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum …
ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum …
Quantum and Classical Dynamics with Random Permutation Circuits
Understanding thermalisation in quantum many-body systems is among the most enduring
problems in modern physics. A particularly interesting question concerns the role played by …
problems in modern physics. A particularly interesting question concerns the role played by …
Characterization of Randomness in Quantum Circuits of Continuous Gate Sets
Y Mitsuhashi, R Suzuki, T Soejima… - arXiv preprint arXiv …, 2024 - arxiv.org
In the accompanying paper of arXiv: 2408. XXXXX, we have established the method of
characterizing the maximal order of approximate unitary designs generated by symmetric …
characterizing the maximal order of approximate unitary designs generated by symmetric …
Embedded Complexity and Quantum Circuit Volume
Z Du, ZW Liu, X Ma - arXiv preprint arXiv:2408.16602, 2024 - arxiv.org
Quantum circuit complexity is a pivotal concept in quantum information, quantum many-body
physics, and high-energy physics. While extensively studied for closed systems, the …
physics, and high-energy physics. While extensively studied for closed systems, the …
Anti-Concentration for the Unitary Haar Measure and Applications to Random Quantum Circuits
We prove a Carbery-Wright style anti-concentration inequality for the unitary Haar measure,
by showing that the probability of a polynomial in the entries of a random unitary falling into …
by showing that the probability of a polynomial in the entries of a random unitary falling into …