We show how phase and amplitude estimation algorithms can be parallelized. This can reduce the gate depth of the quantum circuits to that of a single Grover operator with a small overhead. Further, we show that for quantum amplitude estimation, the parallelization can lead to vast improvements in resilience against quantum errors. The resilience is not caused by the lower gate depth, but by the structure of the algorithm. Even in cases with errors that make it impossible to read out the exact or approximate solutions from conventional amplitude estimation, our parallel approach provided the correct solution with high probability. The results on error resilience hold for the standard version and for low depth versions of quantum amplitude estimation. Methods presented are subject of a patent application [Quantum computing device: Patent application EP 21207022.1].We show how phase and amplitude estimation algorithms can be parallelized. This can reduce the gate depth of the quantum circuits to that of a single Grover operator with a small overhead. Further, we show that for quantum amplitude estimation, the parallelization can lead to vast improvements in resilience against quantum errors. The resilience is not caused by the lower gate depth, but by the structure of the algorithm. Even in cases with errors that make it impossible to read out the exact or approximate solutions from conventional amplitude estimation, our parallel approach provided the correct solution with high probability. The results on error resilience hold for the standard version and for low depth versions of quantum amplitude estimation. Methods presented are subject of a patent application [Quantum computing device: Patent application EP 21207022.1].

arXiv:2204.01337Apr 4, 20220 citations

Parallelizing gates with high-dimensional ancillas

Brown, Kendon

Conference on Lasers and Electro-OpticsJan 1, 20120 citations

The Future of Parallel Computation

Selim G. Akl, Marius Nagy

Springer eBooksJan 1, 20099 citations

Low depth virtual distillation of quantum circuits by deterministic circuit decomposition

Akib Karim, Shaobo Zhang, Muhammad Usman

Virtual distillation using measurements of multiple copies of a quantum circuit have recently been proposed as a method of noise mitigation of expectation values. Circuit decompositions known as B gates were found only for 1-local Hamiltonians, however practical problems for chemistry require n -local Hamiltonians, which cannot be corrected with B gates. We discover low depth circuit decompositions for expectation values for n -local Pauli strings by combining multiple projections to recover the correct measurement statistics or expectation values. Our method adds linear entangling gates with the number of qubits, but it requires extra measurements. Furthermore, in applications to find ground states such as the variational quantum eigensolver (VQE) algorithm, the variational principle is required which states that the energy cannot go below the ground-state energy. We find that the variational principle is violated when using B gates and is preserved if we use our low depth decomposition on all expectation values. We perform a demonstration on real devices, and we show that our decomposition can mitigate real experimental noise in VQE for the H 2 molecule with a two-qubit tapered mapping, H 3 with three qubits, and H 2 with four qubits. Our decomposition provides a way to perform duplicate circuit virtual distillation on real devices at significantly lower depth and for arbitrary observables. Published by the American Physical Society 2024Virtual distillation using measurements of multiple copies of a quantum circuit have recently been proposed as a method of noise mitigation of expectation values. Circuit decompositions known as B gates were found only for 1-local Hamiltonians, however practical problems for chemistry require n -local Hamiltonians, which cannot be corrected with B gates. We discover low depth circuit decompositions for expectation values for n -local Pauli strings by combining multiple projections to recover the correct measurement statistics or expectation values. Our method adds linear entangling gates with the number of qubits, but it requires extra measurements. Furthermore, in applications to find ground states such as the variational quantum eigensolver (VQE) algorithm, the variational principle is required which states that the energy cannot go below the ground-state energy. We find that the variational principle is violated when using B gates and is preserved if we use our low depth decomposition on all expectation values. We perform a demonstration on real devices, and we show that our decomposition can mitigate real experimental noise in VQE for the H 2 molecule with a two-qubit tapered mapping, H 3 with three qubits, and H 2 with four qubits. Our decomposition provides a way to perform duplicate circuit virtual distillation on real devices at significantly lower depth and for arbitrary observables. Published by the American Physical Society 2024

arXiv:2402.18874Physical Review ResearchAug 27, 20242 citations

Parallelizing quantum circuits

Anne Broadbent, Elham Kashefi

arXiv:0704.1736Theoretical Computer ScienceJan 7, 2009115 citations

Changing the circuit-depth complexity of measurement-based quantum computation with hypergraph states

Mariami Gachechiladze, Otfried Gühne, Akimasa Miyake

While the circuit model of quantum computation defines its logical depth or ``computational time'' in terms of temporal gate sequences, the measurement-based model could allow totally different temporal ordering and parallelization of logical gates. By developing techniques to analyze Pauli measurements on multiqubit hypergraph states generated by the controlled-controlled-Z (ccz) gates, we introduce a deterministic scheme of universal measurement-based computation. In contrast to the cluster-state scheme where the Clifford gates are parallelizable, our scheme enjoys massive parallelization of ccz and swap gates, so that the computational depth grows with the number of global applications of Hadamard gates, or, in other words, with the number of changing computational bases. A logarithmic-depth implementation of an $N$ -times controlled-Z gate illustrates a trade-off between space and time complexity.While the circuit model of quantum computation defines its logical depth or ``computational time'' in terms of temporal gate sequences, the measurement-based model could allow totally different temporal ordering and parallelization of logical gates. By developing techniques to analyze Pauli measurements on multiqubit hypergraph states generated by the controlled-controlled-Z (ccz) gates, we introduce a deterministic scheme of universal measurement-based computation. In contrast to the cluster-state scheme where the Clifford gates are parallelizable, our scheme enjoys massive parallelization of ccz and swap gates, so that the computational depth grows with the number of global applications of Hadamard gates, or, in other words, with the number of changing computational bases. A logarithmic-depth implementation of an $N$-times controlled-Z gate illustrates a trade-off between space and time complexity.

arXiv:1805.12093Physical Review AMay 2, 201939 citations

N

-times controlled-Z gate illustrates a trade-off between space and time complexity.