Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Continuous time quantum walks performing quantum gates via higher energy states

Dmitry Solenov

Published Dec 20, 2015• 1 citation
OpenAlex

Abstract

It has recently been noticed that quantum gates can be performed faster and can utilize interaction between qubits more effectively if performed via continuous time quantum walks through states outside of the computational basis. We formulate general requirements for such walks and illustrate them with examples of single-, two- and three-qubit gates, including Hadamard, Control-NOT, and Toffoli gates. Continuous-time quantum walks on graphs involved in these gates are investigated.

Related papers

Quantum gates via continuous time quantum walks in multiqubit systems with non-local auxiliary states

Dmitry Solenov

Non-local higher-energy auxiliary states have been successfully used to entangle pairs of qubits in different quantum computing systems. Typically a longer-span non-local state or sequential application of few-qubit entangling gates are needed to produce a non-trivial multiqubit gate. In many cases a single non-local state that span over the entire system is difficult to use due to spectral crowding or impossible to have. At the same time, many multiqubit systems can naturally develop a network of multiple nonlocal higher-energy states that span over few qubits each. We show that continuous time quantum walks can be used to address this problem by involving multiple such states to perform local and entangling operations concurrently on many qubits. This introduces an alternative approach to multiqubit gate compression based on available physical resources. We formulate general requirements for such walks and discuss configurations of non-local auxiliary states that can emerge in quantum computing architectures based on self-assembled quantum dots, defects in diamond, and superconducting qubits, as examples. Specifically, we discuss a scalable multiqubit quantum register constructed as a single chain with nearest-neighbor interactions. We illustrate how quantum walks can be configured to perform single-, two- and three-qubit gates, including Hadamard, Control-NOT, and Toffoli gates. Continuous time quantum walks on graphs involved in these gates are investigated.

arXiv:1512.06399•Quantum Information and Computation•Apr 1, 2017•2 citations

Quantum walks as mathematical foundation for quantum gates

Dmitry Solenov

It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit designs and can be formulated for very general field-matter interactions. It is shown that, most generally, gates are described by a set of coined quantum walks. Rotating wave and resonant approximations for field-matter interaction simplify the walks, factorizing the coin, and leading to pure continuous time quantum walk description. The walks reside on a graph formed by the Hilbert space of all involved qubits and auxiliary states, if present. Physical interactions between different parts of the system necessary to propagate entanglement through such graph---quantum network---enter via reduction of symmetries in graph edges. Description for several single- and two-qubit gates are given as examples.

arXiv:1906.11701•Quantum Information and Computation•Mar 1, 2020•1 citation

Isolated vertices in continuous-time quantum walks on dynamic graphs

Thomas G. Wong

It was recently shown that continuous-time quantum walks on dynamic graphs, i.e., sequences of static graphs whose edges change at specific times, can implement a universal set of quantum gates. This result treated all isolated vertices as having self-loops, so they all evolved by a phase under the quantum walk. In this paper, we permit isolated vertices to be loopless or looped, and loopless isolated vertices do not evolve at all under the quantum walk. Using this distinction, we construct simpler dynamic graphs that implement the Pauli gates and a set of universal quantum gates consisting of the Hadamard, $T$, and controlled-not gates, and these gates are easily extended to multiqubit systems. For example, the $T$ gate is simplified from a sequence of six graphs to a single graph, and the number of vertices is reduced by a factor of 4. We also construct a generalized phase gate, of which $Z$, $S$, and $T$ are specific instances. Finally, we validate our implementations by numerically simulating a quantum circuit consisting of layers of one- and two-qubit gates, similar to those in recent quantum supremacy experiments, using a quantum walk.

arXiv:1908.00507•Physical Review A•Dec 18, 2019•11 citations

Implementing Quantum Gates With Length-3 Dynamic Graphs

Ibukunoluwa Adebimpe Adisa

The continuous-time quantum walk is a quantum version of a random walk that evolves by Schrodinger's equation. With the Hamiltonian equal to the adjacency matrix of a sequence of graphs, called a dynamic graph, continuous-time quantum walks have been shown to implement quantum gates, including the T gate, Hadamard gate, and the Controlled{NOT gate. Since these gates make up a universal set of quantum gates, they can implement any other arbitrary quantum gate up to an arbitrary approximation. This process, however, can be tedious and ine cient. To alleviate this, we have developed a parameterized dynamic graph on which a continuous-time quantum walk can implement any arbitrary single-qubit quantum gate, and we have also extended this result to implement any two-qubit controlled-unitary quantum gate. These dynamic graphs have at most length three. Using these, we implemented Draper's quantum addition circuit, which is based on the quantum Fourier transform, using a continuous-time quantum walk on a dynamic graph.

•May 4, 2021•0 citations

Coherent modification of entanglement: benefits due to extended Hilbert space

Dmitry Solenov

A quantum computing system is typically represented by a set of non-interacting (local) two-state systems—qubits. Many physical systems can naturally have more accessible states, both local and non-local. We show that the resulting non-local network of states connecting qubits can be efficiently addressed via continuous time quantum random walks, leading to substantial speed-up of multiqubit entanglement manipulations. We discuss a three-qubit Toffoli gate and a system of superconducting qubits as an illustration.

arXiv:1511.08254•Quantum Information and Computation•Sep 1, 2016•2 citations

Continuous-time quantum walks on dynamic graphs

Rebekah Herrman, Travis S. Humble

Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the case of dynamic graphs, in which an ordered sequence of graphs governs free evolution of the quantum walk. We then consider how perfect state transfer during the quantum walk can be used to design dynamic graphs that implement a universal set of quantum logic gates. We give explicit examples for a complete logical basis, and we validate implementations using numerical simulations for quantum teleportation and addition circuits. Finally, we discuss the potential for realizing CTQWs on dynamic graphs using actively controlled quantum optical waveguides.

arXiv:1902.01346•Physical Review A•Jul 8, 2019•20 citations
It has recently been noticed that quantum gates can be performed faster and can utilize interaction between qubits more effectively if performed via continuous time quantum walks through states outside of the computational basis. We formulate general requirements for such walks and illustrate them with examples of single-, two- and three-qubit gates, including Hadamard, Control-NOT, and Toffoli gates. Continuous-time quantum walks on graphs involved in these gates are investigated.
Non-local higher-energy auxiliary states have been successfully used to entangle pairs of qubits in different quantum computing systems. Typically a longer-span non-local state or sequential application of few-qubit entangling gates are needed to produce a non-trivial multiqubit gate. In many cases a single non-local state that span over the entire system is difficult to use due to spectral crowding or impossible to have. At the same time, many multiqubit systems can naturally develop a network of multiple nonlocal higher-energy states that span over few qubits each. We show that continuous time quantum walks can be used to address this problem by involving multiple such states to perform local and entangling operations concurrently on many qubits. This introduces an alternative approach to multiqubit gate compression based on available physical resources. We formulate general requirements for such walks and discuss configurations of non-local auxiliary states that can emerge in quantum computing architectures based on self-assembled quantum dots, defects in diamond, and superconducting qubits, as examples. Specifically, we discuss a scalable multiqubit quantum register constructed as a single chain with nearest-neighbor interactions. We illustrate how quantum walks can be configured to perform single-, two- and three-qubit gates, including Hadamard, Control-NOT, and Toffoli gates. Continuous time quantum walks on graphs involved in these gates are investigated.
It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit designs and can be formulated for very general field-matter interactions. It is shown that, most generally, gates are described by a set of coined quantum walks. Rotating wave and resonant approximations for field-matter interaction simplify the walks, factorizing the coin, and leading to pure continuous time quantum walk description. The walks reside on a graph formed by the Hilbert space of all involved qubits and auxiliary states, if present. Physical interactions between different parts of the system necessary to propagate entanglement through such graph---quantum network---enter via reduction of symmetries in graph edges. Description for several single- and two-qubit gates are given as examples.
It was recently shown that continuous-time quantum walks on dynamic graphs, i.e., sequences of static graphs whose edges change at specific times, can implement a universal set of quantum gates. This result treated all isolated vertices as having self-loops, so they all evolved by a phase under the quantum walk. In this paper, we permit isolated vertices to be loopless or looped, and loopless isolated vertices do not evolve at all under the quantum walk. Using this distinction, we construct simpler dynamic graphs that implement the Pauli gates and a set of universal quantum gates consisting of the Hadamard, TTT, and controlled-not gates, and these gates are easily extended to multiqubit systems. For example, the TTT gate is simplified from a sequence of six graphs to a single graph, and the number of vertices is reduced by a factor of 4. We also construct a generalized phase gate, of which ZZZ, SSS, and TTT are specific instances. Finally, we validate our implementations by numerically simulating a quantum circuit consisting of layers of one- and two-qubit gates, similar to those in recent quantum supremacy experiments, using a quantum walk.
The continuous-time quantum walk is a quantum version of a random walk that evolves by Schrodinger's equation. With the Hamiltonian equal to the adjacency matrix of a sequence of graphs, called a dynamic graph, continuous-time quantum walks have been shown to implement quantum gates, including the T gate, Hadamard gate, and the Controlled{NOT gate. Since these gates make up a universal set of quantum gates, they can implement any other arbitrary quantum gate up to an arbitrary approximation. This process, however, can be tedious and ine cient. To alleviate this, we have developed a parameterized dynamic graph on which a continuous-time quantum walk can implement any arbitrary single-qubit quantum gate, and we have also extended this result to implement any two-qubit controlled-unitary quantum gate. These dynamic graphs have at most length three. Using these, we implemented Draper's quantum addition circuit, which is based on the quantum Fourier transform, using a continuous-time quantum walk on a dynamic graph.
A quantum computing system is typically represented by a set of non-interacting (local) two-state systems—qubits. Many physical systems can naturally have more accessible states, both local and non-local. We show that the resulting non-local network of states connecting qubits can be efficiently addressed via continuous time quantum random walks, leading to substantial speed-up of multiqubit entanglement manipulations. We discuss a three-qubit Toffoli gate and a system of superconducting qubits as an illustration.
Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the case of dynamic graphs, in which an ordered sequence of graphs governs free evolution of the quantum walk. We then consider how perfect state transfer during the quantum walk can be used to design dynamic graphs that implement a universal set of quantum logic gates. We give explicit examples for a complete logical basis, and we validate implementations using numerical simulations for quantum teleportation and addition circuits. Finally, we discuss the potential for realizing CTQWs on dynamic graphs using actively controlled quantum optical waveguides.