Shallow unitary decompositions of quantum Fredkin and Toffoli gates for connectivity-aware equivalent circuit averaging

• URL: http://arxiv.org/abs/2305.18128v3
• Date: Tue, 27 Feb 2024 18:55:34 GMT
• Title: Shallow unitary decompositions of quantum Fredkin and Toffoli gates for connectivity-aware equivalent circuit averaging
• Authors: Pedro M. Q. Cruz, Bruno Murta
• Abstract summary: Controlled-SWAP and controlled-controlled-NOT gates are at the heart of the original proposal of reversible classical computation. We provide several logically equivalent circuits for the Toffoli and Fredkin gates under all-to-all and linear qubit connectivity. We also demonstrate the remarkable effectiveness of the obtained decompositions at mitigating coherent errors on near-term quantum computers.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The controlled-SWAP and controlled-controlled-NOT gates are at the heart of the original proposal of reversible classical computation by Fredkin and Toffoli. Their widespread use in quantum computation, both in the implementation of classical logic subroutines of quantum algorithms and in quantum schemes with no direct classical counterparts, has made it imperative early on to pursue their efficient decomposition in terms of the lower-level gate sets native to different physical platforms. Here, we add to this body of literature by providing several logically equivalent circuits for the Toffoli and Fredkin gates under all-to-all and linear qubit connectivity, the latter with two different routings for control and target qubits. Besides achieving the lowest CNOT counts in the literature for all these configurations, we also demonstrate the remarkable effectiveness of the obtained decompositions at mitigating coherent errors on near-term quantum computers via equivalent circuit averaging. We first quantify the performance of the method in silico with a coherent-noise model before validating it experimentally on a superconducting quantum processor. In addition, we consider the case where the three qubits on which the Toffoli or Fredkin gates act nontrivially are not adjacent, proposing a novel scheme to reorder them that saves one CNOT for every SWAP. This scheme also finds use in the shallow implementation of long-range CNOTs. Our results highlight the importance of considering different entangling gate structures and connectivity constraints when designing efficient quantum circuits.

Related papers

• Fault-tolerant quantum architectures based on erasure qubits [49.227671756557946]
  We exploit the idea of erasure qubits, relying on an efficient conversion of the dominant noise into erasures at known locations. We propose and optimize QEC schemes based on erasure qubits and the recently-introduced Floquet codes. Our results demonstrate that, despite being slightly more complex, QEC schemes based on erasure qubits can significantly outperform standard approaches.
  arXiv  Detail & Related papers  (2023-12-21T17:40:18Z)
• Kerr-effect-based quantum logical gates in decoherence-free subspace [1.194799054956877]
  decoherence-free subspace (DFS) introduced can effectively decrease the influence of decoherence effect. We propose some schemes for setting up a family of quantum control gates, including controlled-NOT (CNOT), Toffoli, and Fredkin gates for two or three logical qubits.
  arXiv  Detail & Related papers  (2023-06-09T02:18:01Z)
• Hybrid Gate-Pulse Model for Variational Quantum Algorithms [33.73469431747376]
  Current quantum programs are mostly compiled on the gate-level, where quantum circuits are composed of quantum gates. pulse-level optimization has gained more attention from researchers due to their advantages in terms of circuit duration. We present a hybrid gate-pulse model that can mitigate these problems.
  arXiv  Detail & Related papers  (2022-12-01T17:06:35Z)
• Hardware-Conscious Optimization of the Quantum Toffoli Gate [11.897854272643634]
  This manuscript expands the analytical and numerical approaches for optimizing quantum circuits at this abstraction level. We present a procedure for combining the strengths of analytical native gate-level optimization with numerical optimization. Our optimized Toffoli gate implementation demonstrates an $18%$ reduction in infidelity compared with the canonical implementation.
  arXiv  Detail & Related papers  (2022-09-06T17:29:22Z)
• Decomposition of Matrix Product States into Shallow Quantum Circuits [62.5210028594015]
  tensor network (TN) algorithms can be mapped to parametrized quantum circuits (PQCs) We propose a new protocol for approximating TN states using realistic quantum circuits. Our results reveal one particular protocol, involving sequential growth and optimization of the quantum circuit, to outperform all other methods.
  arXiv  Detail & Related papers  (2022-09-01T17:08:41Z)
• Coherent effects contribution to a fast gate fidelity in ion quantum computer [47.187609203210705]
  We develop a numerical model for full simulation of coherence effects using a linear ion microtrap array and a 2D microtrap array. We have also studied the dependency of the gate fidelity on the laser power fluctuations.
  arXiv  Detail & Related papers  (2021-12-12T12:53:00Z)
• Approaching the theoretical limit in quantum gate decomposition [0.0]
  We propose a novel numerical approach to decompose general quantum programs in terms of single- and two-qubit quantum gates with a $CNOT$ gate count. Our approach is based on a sequential optimization of parameters related to the single-qubit rotation gates involved in a pre-designed quantum circuit used for the decomposition.
  arXiv  Detail & Related papers  (2021-09-14T15:36:22Z)
• 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)
• QUANTIFY: A framework for resource analysis and design verification of quantum circuits [69.43216268165402]
  QUANTIFY is an open-source framework for the quantitative analysis of quantum circuits. It is based on Google Cirq and is developed with Clifford+T circuits in mind. For benchmarking purposes QUANTIFY includes quantum memory and quantum arithmetic circuits.
  arXiv  Detail & Related papers  (2020-07-21T15:36:25Z)
• 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)

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.