Fast quantum circuit cutting with randomized measurements
- URL: http://arxiv.org/abs/2207.14734v1
- Date: Fri, 29 Jul 2022 15:13:04 GMT
- Title: Fast quantum circuit cutting with randomized measurements
- Authors: Angus Lowe, Matija Medvidovi\'c, Anthony Hayes, Lee J. O'Riordan,
Thomas R. Bromley, Juan Miguel Arrazola, Nathan Killoran
- Abstract summary: We propose a new method to extend the size of a quantum computation beyond the number of physical qubits available on a single device.
This is accomplished by randomly inserting measure-and-prepare channels to express the output state of a large circuit as a separable state across distinct devices.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We propose a new method to extend the size of a quantum computation beyond
the number of physical qubits available on a single device. This is
accomplished by randomly inserting measure-and-prepare channels to express the
output state of a large circuit as a separable state across distinct devices.
Our method employs randomized measurements, resulting in a sample overhead that
is $\widetilde{O}(4^k / \varepsilon ^2)$, where $\varepsilon $ is the accuracy
of the computation and $k$ the number of parallel wires that are "cut" to
obtain smaller sub-circuits. We also show an information-theoretic lower bound
of $\Omega(2^k / \varepsilon ^2)$ for any comparable procedure. We use our
techniques to show that circuits in the Quantum Approximate Optimization
Algorithm (QAOA) with $p$ entangling layers can be simulated by circuits on a
fraction of the original number of qubits with an overhead that is roughly
$2^{O(p\kappa)}$, where $\kappa$ is the size of a known balanced vertex
separator of the graph which encodes the optimization problem. We obtain
numerical evidence of practical speedups using our method applied to the QAOA,
compared to prior work. Finally, we investigate the practical feasibility of
applying the circuit cutting procedure to large-scale QAOA problems on
clustered graphs by using a $30$-qubit simulator to evaluate the variational
energy of a $129$-qubit problem as well as carry out a $62$-qubit optimization.
Related papers
- A two-circuit approach to reducing quantum resources for the quantum lattice Boltzmann method [41.66129197681683]
Current quantum algorithms for solving CFD problems use a single quantum circuit and, in some cases, lattice-based methods.
We introduce the a novel multiple circuits algorithm that makes use of a quantum lattice Boltzmann method (QLBM)
The problem is cast as a stream function--vorticity formulation of the 2D Navier-Stokes equations and verified and tested on a 2D lid-driven cavity flow.
arXiv Detail & Related papers (2024-01-20T15:32:01Z) - Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$.
We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
arXiv Detail & Related papers (2024-01-17T18:59:38Z) - Simulation of IBM's kicked Ising experiment with Projected Entangled
Pair Operator [71.10376783074766]
We perform classical simulations of the 127-qubit kicked Ising model, which was recently emulated using a quantum circuit with error mitigation.
Our approach is based on the projected entangled pair operator (PEPO) in the Heisenberg picture.
We develop a Clifford expansion theory to compute exact expectation values and use them to evaluate algorithms.
arXiv Detail & Related papers (2023-08-06T10:24:23Z) - Quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian [0.5097809301149342]
We show that a na"ive partitioning and low-order splitting formula can yield, through our divide and conquer formalism, superior scaling to qubitization for large $Lambda$.
We also give new algorithmic and circuit level techniques for gate optimization including a new way of implementing a group of multi-controlled-X gates.
arXiv Detail & Related papers (2023-06-19T23:20:30Z) - Even shorter quantum circuit for phase estimation on early
fault-tolerant quantum computers with applications to ground-state energy
estimation [5.746732081406236]
We develop a phase estimation method with a distinct feature.
The total cost of the algorithm satisfies the Heisenberg-limited scaling $widetildemathcalO(epsilon-1)$.
Our algorithm may significantly reduce the circuit depth for performing phase estimation tasks on early fault-tolerant quantum computers.
arXiv Detail & Related papers (2022-11-22T03:15:40Z) - Digital-analog co-design of the Harrow-Hassidim-Lloyd algorithm [0.0]
Harrow-Hassidim-Lloyd quantum algorithm was proposed to solve linear systems of equations $Avecx = vecb$.
There is not an explicit quantum circuit for the subroutine which maps the inverse of the problem matrix $A$ into an ancillary qubit.
We present a co-designed quantum processor which reduces the depth of the algorithm.
arXiv Detail & Related papers (2022-07-27T13:58:13Z) - Quantum Goemans-Williamson Algorithm with the Hadamard Test and
Approximate Amplitude Constraints [62.72309460291971]
We introduce a variational quantum algorithm for Goemans-Williamson algorithm that uses only $n+1$ qubits.
Efficient optimization is achieved by encoding the objective matrix as a properly parameterized unitary conditioned on an auxilary qubit.
We demonstrate the effectiveness of our protocol by devising an efficient quantum implementation of the Goemans-Williamson algorithm for various NP-hard problems.
arXiv Detail & Related papers (2022-06-30T03:15:23Z) - Quantum State Preparation with Optimal Circuit Depth: Implementations
and Applications [10.436969366019015]
We show that any $Theta(n)$-depth circuit can be prepared with a $Theta(log(nd)) with $O(ndlog d)$ ancillary qubits.
We discuss applications of the results in different quantum computing tasks, such as Hamiltonian simulation, solving linear systems of equations, and realizing quantum random access memories.
arXiv Detail & Related papers (2022-01-27T13:16:30Z) - How to simulate quantum measurement without computing marginals [3.222802562733787]
We describe and analyze algorithms for classically computation measurement of an $n$-qubit quantum state $psi$ in the standard basis.
Our algorithms reduce the sampling task to computing poly(n)$ amplitudes of $n$-qubit states.
arXiv Detail & Related papers (2021-12-15T21:44:05Z) - Random quantum circuits transform local noise into global white noise [118.18170052022323]
We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime.
For local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy benchmark) between the output distribution $p_textnoisy$ of a generic noisy circuit instance shrink exponentially.
If the noise is incoherent, the output distribution approaches the uniform distribution $p_textunif$ at precisely the same rate.
arXiv Detail & Related papers (2021-11-29T19:26:28Z) - Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings.
In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$.
We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
arXiv Detail & Related papers (2020-02-25T19:18:36Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.