Efficient implementation of discrete-time quantum walks on quantum computers
- URL: http://arxiv.org/abs/2402.01854v2
- Date: Tue, 9 Apr 2024 12:39:59 GMT
- Title: Efficient implementation of discrete-time quantum walks on quantum computers
- Authors: Luca Razzoli, Gabriele Cenedese, Maria Bondani, Giuliano Benenti,
- Abstract summary: 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.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum walks have proven to be a universal model for quantum computation and to provide speed-up in certain quantum algorithms. The discrete-time quantum walk (DTQW) model, among others, is one of the most suitable candidates for circuit implementation, due to its discrete nature. Current implementations, however, are usually characterized by quantum circuits of large size and depth, which leads to a higher computational cost and severely limits the number of time steps that can be reliably implemented on current quantum computers. In this work, we propose an efficient and scalable quantum circuit implementing the DTQW on the $2^n$-cycle based on the diagonalization of the conditional shift operator. For $t$ time-steps of the DTQW, the proposed circuit requires only $O(n^2 + nt)$ two-qubit gates compared to the $O(n^2 t)$ of the current most efficient implementation based on quantum Fourier transforms. We test the proposed circuit on an IBM quantum device for a Hadamard DTQW on the $4$- and $8$-cycle characterized by periodic dynamics and recurrent generation of maximally entangled single-particle states. Experimental results are meaningful well beyond the regime of few time steps, paving the way for reliable implementation and use on quantum computers.
Related papers
- Robust Implementation of Discrete-time Quantum Walks in Any Finite-dimensional Quantum System [2.646968944595457]
discrete-time quantum walk (DTQW) model one of most suitable choices for circuit implementation.
In this paper, we have successfully cut down the circuit cost concerning gate count and circuit depth by half.
For the engineering excellence of our proposed approach, we implement DTQW in any finite-dimensional quantum system with akin efficiency.
arXiv Detail & Related papers (2024-08-01T13:07:13Z) - Quantum Compiling with Reinforcement Learning on a Superconducting Processor [55.135709564322624]
We develop a reinforcement learning-based quantum compiler for a superconducting processor.
We demonstrate its capability of discovering novel and hardware-amenable circuits with short lengths.
Our study exemplifies the codesign of the software with hardware for efficient quantum compilation.
arXiv Detail & Related papers (2024-06-18T01:49:48Z) - On Reducing the Execution Latency of Superconducting Quantum Processors via Quantum Program Scheduling [48.142860424323395]
We introduce the Quantum Program Scheduling Problem (QPSP) to improve the utility efficiency of quantum resources.
Specifically, a quantum program scheduling method concerning the circuit width, number of measurement shots, and submission time of quantum programs is proposed to reduce the execution latency.
arXiv Detail & Related papers (2024-04-11T16:12:01Z) - QuantumSEA: In-Time Sparse Exploration for Noise Adaptive Quantum
Circuits [82.50620782471485]
QuantumSEA is an in-time sparse exploration for noise-adaptive quantum circuits.
It aims to achieve two key objectives: (1) implicit circuits capacity during training and (2) noise robustness.
Our method establishes state-of-the-art results with only half the number of quantum gates and 2x time saving of circuit executions.
arXiv Detail & Related papers (2024-01-10T22:33:00Z) - Classical variational optimization of PREPARE circuit for quantum phase
estimation of quantum chemistry Hamiltonians [0.8009842832476994]
We propose a method for constructing $textttPREPARE$ circuits for quantum phase estimation of a molecular Hamiltonian in quantum chemistry.
The $textttPREPARE$ circuit generates a quantum state which encodes the coefficients of the terms in the Hamiltonian as probability amplitudes.
arXiv Detail & Related papers (2023-08-26T05:32:38Z) - Efficient parallelization of quantum basis state shift [0.0]
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.
arXiv Detail & Related papers (2023-04-04T11:01:08Z) - 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) - Depth-efficient proofs of quantumness [77.34726150561087]
A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify quantum advantage of an untrusted prover.
In this paper, we give two proof of quantumness constructions in which the prover need only perform constant-depth quantum circuits.
arXiv Detail & Related papers (2021-07-05T17:45:41Z) - Fast Swapping in a Quantum Multiplier Modelled as a Queuing Network [64.1951227380212]
We propose that quantum circuits can be modeled as queuing networks.
Our method is scalable and has the potential speed and precision necessary for large scale quantum circuit compilation.
arXiv Detail & Related papers (2021-06-26T10:55:52Z) - 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)
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.