Depth-2 QAC circuits cannot simulate quantum parity

• URL: http://arxiv.org/abs/2005.12169v1
• Date: Mon, 25 May 2020 15:32:16 GMT
• Title: Depth-2 QAC circuits cannot simulate quantum parity
• Authors: Daniel Pad\'e (University of South Carolina), Stephen Fenner (University of South Carolina), Daniel Grier (IQC), Thomas Thierauf (Aalen University)
• Abstract summary: We show that the quantum parity gate on $n > 3$ qubits cannot be cleanly simulated by a quantum circuit. This is the best known and first nontrivial separation between the parity gate and circuits of this form.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that the quantum parity gate on $n > 3$ qubits cannot be cleanly simulated by a quantum circuit with two layers of arbitrary C-SIGN gates of any arity and arbitrary 1-qubit unitary gates, regardless of the number of allowed ancilla qubits. This is the best known and first nontrivial separation between the parity gate and circuits of this form. The same bounds also apply to the quantum fanout gate. Our results are incomparable with those of Fang et al. [3], which apply to any constant depth but require a sublinear number of ancilla qubits on the simulating circuit.

Related papers

• Universal quantum computation using atoms in cross-cavity systems [0.0]
  We theoretically investigate a single-step implementation of both a universal two- (CNOT) and three-qubit (quantum Fredkin) gates in a cross-cavity setup. Within a high-cooper regime, the system exhibits an atomic-state-dependent $pi$-phase gate involving the two-mode single-photon bright and dark states.
  arXiv  Detail & Related papers  (2023-08-28T20:09:54Z)
• A vertical gate-defined double quantum dot in a strained germanium double quantum well [48.7576911714538]
  Gate-defined quantum dots in silicon-germanium heterostructures have become a compelling platform for quantum computation and simulation. We demonstrate the operation of a gate-defined vertical double quantum dot in a strained germanium double quantum well. We discuss challenges and opportunities and outline potential applications in quantum computing and quantum simulation.
  arXiv  Detail & Related papers  (2023-05-23T13:42:36Z)
• Fast pseudorandom quantum state generators via inflationary quantum gates [3.5072186061740904]
  We propose a mechanism for reaching pseudorandom quantum states, computationally indistinguishable from Haar random, with shallow log-n depth quantum circuits. We prove that IQ-gates cannot be implemented with 2-qubit gates, but can be realized either as a subset of 2-qudit-gates in $U(d2)$ with $dge 3$ and $d$ prime, or as special 3-qubit gates.
  arXiv  Detail & Related papers  (2023-04-19T18:00:01Z)
• Quantum process tomography of continuous-variable gates using coherent states [49.299443295581064]
  We demonstrate the use of coherent-state quantum process tomography (csQPT) for a bosonic-mode superconducting circuit. We show results for this method by characterizing a logical quantum gate constructed using displacement and SNAP operations on an encoded qubit.
  arXiv  Detail & Related papers  (2023-03-02T18:08:08Z)
• Optimizing the number of CNOT gates in one-dimensional nearest-neighbor quantum Fourier transform circuit [0.0]
  We construct a one-dimensional nearest-neighbor circuit of quantum Fourier transform (QFT) It is found that our method reduces the number of CNOT gates by 60%. Our results for the one-dimensional nearest-neighbor circuit can be applied to quantum amplitude estimation.
  arXiv  Detail & Related papers  (2022-08-30T13:24:16Z)
• Gaussian initializations help deep variational quantum circuits escape from the barren plateau [87.04438831673063]
  Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years. However, quantum circuits with random structures have poor trainability due to the exponentially vanishing gradient with respect to the circuit depth and the qubit number. This result leads to a general belief that deep quantum circuits will not be feasible for practical tasks.
  arXiv  Detail & Related papers  (2022-03-17T15:06:40Z)
• 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)
• Quantum simulation of $\phi^4$ theories in qudit systems [53.122045119395594]
  We discuss the implementation of quantum algorithms for lattice $Phi4$ theory on circuit quantum electrodynamics (cQED) system. The main advantage of qudit systems is that its multi-level characteristic allows the field interaction to be implemented only with diagonal single-qudit gates.
  arXiv  Detail & Related papers  (2021-08-30T16:30:33Z)
• 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)
• Two-qubit sweet spots for capacitively coupled exchange-only spin qubits [0.0]
  We study capacitive coupling between two triple quantum dot spin qubits encoded in the $S = 1/2$, $S_z = -1/2$ decoherence-free subspace -- the exchange-only (EO) spin qubits. We report exact gate sequences for CPHASE and CNOT gates, and demonstrate theoretically, the existence of multiple two-qubit sweet spots (2QSS) in the parameter space of capacitively coupled EO qubits.
  arXiv  Detail & Related papers  (2021-03-29T15:05:07Z)
• 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)

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.