Universal hybrid quantum computing in trapped ions

Sutherland, R. T.; Srinivas, R.

doi:10.1103/physreva.104.032609

Cited by 5 publications

(3 citation statements)

References 64 publications

(116 reference statements)

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“…These quantum gates can be considered as alternative building blocks to quantum computation that might be realizable in quantum optics, trapped ion systems and superconducting circuits [17][18][19]24,25]. These gates can also be used to implement alternative quantum realizations of DQC1, quantum phase estimation, Shor's factoring algorithm [19] and sensing [26].…”

Section: Quantum Iterative Methods For Discrete Linear Dynamical Systemsmentioning

confidence: 99%

“…On the other hand, |x0falsefalse⟩ is a finite false(d+1false)-dimensional quantum state, realized by a discrete log2⁡false(Dfalse) number of qubits. The evolution of |wfalse~false(tfalse)falsefalse⟩CV-DV is governed by a hybrid CV-DV quantum gate exp⁡false(−iHCV-DVtfalse) |wfalse~false(tfalse)falsefalse⟩CV-DV=exp⁡false(−iHCV-DVtfalse)|wfalse~false(0false)falsefalse⟩CV-DV,1emHCV-DV=H⊗qfalse^.These quantum gates can be considered as alternative building blocks to quantum computation that might be realizable in quantum optics, trapped ion systems and superconducting circuits [17–19,24,25]. These gates can also be used to implement alternative quantum realizations of DQC1, quantum phase estimation, Shor’s factoring algorithm [19] and sensing [26].…”

Section: Quantum Iterative Methods For Discrete Linear Dynamical Systemsmentioning

confidence: 99%

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Quantum simulation of discrete linear dynamical systems and simple iterative methods in linear algebra

Jin,

Liu

2024

Proc. R. Soc. A.

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Quantum simulation is capable of simulating certain dynamical systems in continuous time—Schrödinger’s equations being the most direct and well known—more efficiently than classical simulation. Any linear dynamical system can in fact be transformed into a system of Schrödinger’s equations via a method called Schrödingerisation (Jin et al. 2022. Quantum simulation of partial differential equations via Schrödingerisation. ( https://arxiv.org/abs/2212.13969 ) and Jin et al. 2023. Phys. Rev. A 108 , 032603. ( doi:10.1103/PhysRevA.108.032603 )). We show how Schrödingerisation allows quantum simulation to be directly used for the simulation of continuous-time versions of general (explicit) iterative schemes or discrete linear dynamical systems. In particular, we use this new method to solve linear systems of equations and for estimating the maximum eigenvector and eigenvalue of a matrix, respectively. This method is applicable using either discrete-variable quantum systems or on hybrid continuous-variable and discrete-variable quantum systems. This framework provides an interesting alternative to solve linear algebra problems using quantum simulation.

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Section: Quantum Iterative Methods For Discrete Linear Dynamical Systemsmentioning

confidence: 99%

Section: Quantum Iterative Methods For Discrete Linear Dynamical Systemsmentioning

confidence: 99%

Quantum simulation of discrete linear dynamical systems and simple iterative methods in linear algebra

Jin,

Liu

2024

Proc. R. Soc. A.

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“…Geometric phase gates take many forms and can be used to generate spin [33] as well as phonon [34] interactions beyond 2nd order. In this work, however, we consider a subset of geometric phase gates typically used for high-fidelity two-qubit gates, which we represent with the Hamiltonian:…”

Section: Theorymentioning

confidence: 99%

Laser-free trapped ion entangling gates with AESE: adiabatic elimination of spin-motion entanglement

Tyler Sutherland,

Foss-Feig

2024

New J. Phys.

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We discuss a laser-free, two-qubit geometric phase gate technique for generating high-fidelity entanglement between two trapped ions. The scheme works by ramping the spin-dependent force on and off slowly relative to the gate detunings, which adiabatically eliminates the spin-motion entanglement (AESE). We show how gates performed with AESE can eliminate spin-motion entanglement with multiple modes simultaneously, without having to specifically tune the control field detunings. This is because the spin-motion entanglement is suppressed by operating the control fields in a certain parametric limit, rather than by engineering an optimized control sequence. We also discuss physical implementations that use either electronic or ferromagnetic magnetic field gradients. In the latter, we show how to “AESE” the system by smoothly turning on the effective spin-dependent force by shelving from a magnetic field insensitive state to a magnetic field sensitive state slowly relative to the gate mode frequencies. We show how to do this with a Rabi or adiabatic rapid passage transition. Finally, we show how gating with AESE significantly decreases the gate’s sensitivity to common sources of motional decoherence, making it easier to perform high-fidelity gates at Doppler temperatures.

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Synthetic $${{\mathbb{Z}}}_{2}$$ gauge theories based on parametric excitations of trapped ions

Bǎzǎvan,

Saner,

Tirrito

et al. 2024

Commun Phys

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Resource efficient schemes for the quantum simulation of lattice gauge theories can benefit from hybrid encodings of gauge and matter fields that use the native degrees of freedom, such as internal qubits and motional phonons in trapped-ion devices. We propose to use a parametric scheme to induce a tunneling of the phonons conditioned to the internal qubit state which, when implemented with a single trapped ion, corresponds to a minimal $${{\mathbb{Z}}}_{2}$$ Z 2 gauge theory. To evaluate the feasibility of this scheme, we perform numerical simulations of the state-dependent tunneling using realistic parameters, and identify the leading sources of error in future experiments. We discuss how to generalize this minimal case to more complex settings by increasing the number of ions, moving from a single link to a $${{\mathbb{Z}}}_{2}$$ Z 2 plaquette, and to an entire $${{\mathbb{Z}}}_{2}$$ Z 2 chain. We present analytical expressions for the gauge-invariant dynamics and the corresponding confinement, which are benchmarked using matrix product state simulations.

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Universal hybrid quantum computing in trapped ions

Cited by 5 publications

References 64 publications

Quantum simulation of discrete linear dynamical systems and simple iterative methods in linear algebra

Quantum simulation of discrete linear dynamical systems and simple iterative methods in linear algebra

Laser-free trapped ion entangling gates with AESE: adiabatic elimination of spin-motion entanglement

Synthetic $${{\mathbb{Z}}}_{2}$$ gauge theories based on parametric excitations of trapped ions

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