Efficient phase-factor evaluation in quantum signal processing
- URL: http://arxiv.org/abs/2002.11649v2
- Date: Sat, 10 Jul 2021 06:51:23 GMT
- Title: Efficient phase-factor evaluation in quantum signal processing
- Authors: Yulong Dong, Xiang Meng, K. Birgitta Whaley, Lin Lin
- Abstract summary: Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrixs on quantum computers.
There is so far no classically stable algorithm allowing computation of the phase factors that are needed to build QSP circuits.
We present here an optimization based method that can accurately compute the phase factors using standard double precision arithmetic operations.
- Score: 1.3614427997190908
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Quantum signal processing (QSP) is a powerful quantum algorithm to exactly
implement matrix polynomials on quantum computers. Asymptotic analysis of
quantum algorithms based on QSP has shown that asymptotically optimal results
can in principle be obtained for a range of tasks, such as Hamiltonian
simulation and the quantum linear system problem. A further benefit of QSP is
that it uses a minimal number of ancilla qubits, which facilitates its
implementation on near-to-intermediate term quantum architectures. However,
there is so far no classically stable algorithm allowing computation of the
phase factors that are needed to build QSP circuits. Existing methods require
the usage of variable precision arithmetic and can only be applied to
polynomials of relatively low degree. We present here an optimization based
method that can accurately compute the phase factors using standard double
precision arithmetic operations. We demonstrate the performance of this
approach with applications to Hamiltonian simulation, eigenvalue filtering, and
the quantum linear system problems. Our numerical results show that the
optimization algorithm can find phase factors to accurately approximate
polynomials of degree larger than $10,000$ with error below $10^{-12}$.
Related papers
- Benchmarking digital quantum simulations above hundreds of qubits using quantum critical dynamics [42.29248343585333]
We benchmark quantum hardware and error mitigation techniques on up to 133 qubits.
We show reliable control up to a two-qubit gate depth of 28, featuring a maximum of 1396 two-qubit gates.
Results are transferable to applications such as Hamiltonian simulation, variational algorithms, optimization, or quantum machine learning.
arXiv Detail & Related papers (2024-04-11T18:00:05Z) - Truncation technique for variational quantum eigensolver for Molecular
Hamiltonians [0.0]
variational quantum eigensolver (VQE) is one of the most promising quantum algorithms for noisy quantum devices.
We propose a physically intuitive truncation technique that starts the optimization procedure with a truncated Hamiltonian.
This strategy allows us to reduce the required number of evaluations for the expectation value of Hamiltonian on a quantum computer.
arXiv Detail & Related papers (2024-02-02T18:45:12Z) - Realization of quantum signal processing on a noisy quantum computer [0.4593579891394288]
We propose a strategy to run an entire QSP protocol on noisy quantum hardware by carefully reducing overhead costs at each step.
We test the protocol by running the algorithm on the Quantinuum H1-1 trapped-ion quantum computer powered by Honeywell.
Our results are the first step in the experimental realization of QSP-based quantum algorithms.
arXiv Detail & Related papers (2023-03-09T19:00:17Z) - End-to-end resource analysis for quantum interior point methods and portfolio optimization [63.4863637315163]
We provide a complete quantum circuit-level description of the algorithm from problem input to problem output.
We report the number of logical qubits and the quantity/depth of non-Clifford T-gates needed to run the algorithm.
arXiv Detail & Related papers (2022-11-22T18:54:48Z) - Efficient Classical Computation of Quantum Mean Values for Shallow QAOA
Circuits [15.279642278652654]
We present a novel graph decomposition based classical algorithm that scales linearly with the number of qubits for the shallow QAOA circuits.
Our results are not only important for the exploration of quantum advantages with QAOA, but also useful for the benchmarking of NISQ processors.
arXiv Detail & Related papers (2021-12-21T12:41:31Z) - Quantum algorithm for stochastic optimal stopping problems with
applications in finance [60.54699116238087]
The famous least squares Monte Carlo (LSM) algorithm combines linear least square regression with Monte Carlo simulation to approximately solve problems in optimal stopping theory.
We propose a quantum LSM based on quantum access to a process, on quantum circuits for computing the optimal stopping times, and on quantum techniques for Monte Carlo.
arXiv Detail & Related papers (2021-11-30T12:21:41Z) - Variational Quantum Optimization with Multi-Basis Encodings [62.72309460291971]
We introduce a new variational quantum algorithm that benefits from two innovations: multi-basis graph complexity and nonlinear activation functions.
Our results in increased optimization performance, two increase in effective landscapes and a reduction in measurement progress.
arXiv Detail & Related papers (2021-06-24T20:16:02Z) - Quantum mean value approximator for hard integer value problems [19.4417702222583]
We show that an optimization can be improved substantially by using an approximation rather than the exact expectation.
Together with efficient classical sampling algorithms, a quantum algorithm with minimal gate count can thus improve the efficiency of general integer-value problems.
arXiv Detail & Related papers (2021-05-27T13:03:52Z) - Logical Abstractions for Noisy Variational Quantum Algorithm Simulation [25.515765956985188]
Existing quantum circuit simulators do not address the common traits of variational algorithms.
We present a quantum circuit simulation toolchain based on logical abstractions targeted for simulating variational algorithms.
arXiv Detail & Related papers (2021-03-31T17:20:13Z) - Classical variational simulation of the Quantum Approximate Optimization
Algorithm [0.0]
We introduce a method to simulate layered quantum circuits consisting of parametrized gates.
A neural-network parametrization of the many-qubit wave function is used.
For the largest circuits simulated, we reach 54 qubits at 4 QAOA layers.
arXiv Detail & Related papers (2020-09-03T15:55:27Z)
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.