Efficient parallelization of quantum basis state shift
- URL: http://arxiv.org/abs/2304.01704v2
- Date: Tue, 10 Oct 2023 12:46:04 GMT
- Title: Efficient parallelization of quantum basis state shift
- Authors: Ljubomir Budinski, Ossi Niemim\"aki, Roberto Zamora-Zamora, Valtteri
Lahtinen
- Abstract summary: We optimize the state shift algorithm by incorporating the shift in different directions in parallel.
This provides a significant reduction in the depth of the quantum circuit in comparison to the currently known methods.
We focus on the one-dimensional and periodic shift, but note that the method can be extended to more complex cases.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Basis state shift is central to many quantum algorithms, most notably the
quantum walk. Efficient implementations are of major importance for achieving a
quantum speedup for computational applications. We optimize the state shift
algorithm by incorporating the shift in different directions in parallel. This
provides a significant reduction in the depth of the quantum circuit in
comparison to the currently known methods, giving a linear scaling in the
number of gates versus working qubits in contrast to the quadratic scaling of
the state-of-the-art method based on the quantum Fourier transform. For a
one-dimensional array of size $2^n$ for $n > 4$, we derive the total number of
$15n + 74$ two-qubit $CX$ gates in the parallel circuit, using a total of
$2n-2$ qubits including an ancilla register for the decomposition of
multi-controlled gates. We focus on the one-dimensional and periodic shift, but
note that the method can be extended to more complex cases.
Related papers
- Parallel Quantum Computing Simulations via Quantum Accelerator Platform Virtualization [44.99833362998488]
We present a model for parallelizing simulation of quantum circuit executions.
The model can take advantage of its backend-agnostic features, enabling parallel quantum circuit execution over any target backend.
arXiv Detail & Related papers (2024-06-05T17:16:07Z) - Efficient implementation of discrete-time quantum walks on quantum computers [0.0]
We propose an efficient and scalable quantum circuit implementing the discrete-time quantum walk (DTQW) model.
For $t$ time-steps of the DTQW, the proposed circuit requires only $O(n2 + nt)$ two-qubit gates compared to the $O(n2 t)$ of the current most efficient implementation.
arXiv Detail & Related papers (2024-02-02T19:11:41Z) - Universal qudit gate synthesis for transmons [44.22241766275732]
We design a superconducting qudit-based quantum processor.
We propose a universal gate set featuring a two-qudit cross-resonance entangling gate.
We numerically demonstrate the synthesis of $rm SU(16)$ gates for noisy quantum hardware.
arXiv Detail & Related papers (2022-12-08T18:59:53Z) - 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) - A quantum processor based on coherent transport of entangled atom arrays [44.62475518267084]
We show a quantum processor with dynamic, nonlocal connectivity, in which entangled qubits are coherently transported in a highly parallel manner.
We use this architecture to realize programmable generation of entangled graph states such as cluster states and a 7-qubit Steane code state.
arXiv Detail & Related papers (2021-12-07T19:00:00Z) - Efficient multi-qubit subspace rotations via topological quantum walks [1.0486921990935787]
The rotation of subspaces by a chosen angle is a fundamental quantum computing operation.
We propose a fast, high-fidelity way to implement such operations via topological quantum walks.
This procedure can be implemented in superconducting qubits, ion-traps and Rydberg atoms with star-type connectivity.
arXiv Detail & Related papers (2021-11-12T02:10:56Z) - Halving the cost of quantum multiplexed rotations [0.0]
We improve the number of $T$ gates needed for a $b$-bit approximation of a multiplexed quantum gate with $c$ controls.
Our results roughly halve the cost of state-of-art electronic structure simulations based on qubitization of double-factorized or tensor-hypercontracted representations.
arXiv Detail & Related papers (2021-10-26T06:49:44Z) - Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems.
By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
arXiv Detail & Related papers (2021-08-03T17:49:09Z) - Improving the Performance of Deep Quantum Optimization Algorithms with
Continuous Gate Sets [47.00474212574662]
Variational quantum algorithms are believed to be promising for solving computationally hard problems.
In this paper, we experimentally investigate the circuit-depth-dependent performance of QAOA applied to exact-cover problem instances.
Our results demonstrate that the use of continuous gate sets may be a key component in extending the impact of near-term quantum computers.
arXiv Detail & Related papers (2020-05-11T17:20:51Z) - Quantum Gram-Schmidt Processes and Their Application to Efficient State
Read-out for Quantum Algorithms [87.04438831673063]
We present an efficient read-out protocol that yields the classical vector form of the generated state.
Our protocol suits the case that the output state lies in the row space of the input matrix.
One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
arXiv Detail & Related papers (2020-04-14T11:05:26Z) - Computational advantage from quantum superposition of multiple temporal
orders of photonic gates [0.0]
A control quantum system can coherently determine the order in which a target quantum system undergoes $N$ gate operations.
We experimentally demonstrate the quantum $N$-switch with $N=4$ gates acting on a photonic-polarization qubit.
This is the first observation of a quantum superposition of more than $N=2$ temporal orders.
arXiv Detail & Related papers (2020-02-18T19:00:01Z)
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.