We show experimentally that a broad class of interactions involving quantum harmonic oscillators can be made stronger (amplified) using a unitary squeezing protocol. While our demonstration uses the motional and internal states of a single trapped 25Mg+ ion, the scheme applies generally to Hamiltonians involving just a single harmonic oscillator as well as Hamiltonians coupling the oscillator to another quantum degree of freedom such as a qubit, covering a large range of systems of interest in quantum information and metrology applications. Importantly, the protocol does not require knowledge of the parameters of the Hamiltonian to be amplified, nor does it require a well-defined phase relationship between the squeezing interaction and the rest of the system dynamics, making it potentially useful in instances where certain aspects of a signal or interaction may be unknown or uncontrolled, such as searches for novel forms of dark matter. Published by the American Physical Society 2024We show experimentally that a broad class of interactions involving quantum harmonic oscillators can be made stronger (amplified) using a unitary squeezing protocol. While our demonstration uses the motional and internal states of a single trapped 25Mg+ ion, the scheme applies generally to Hamiltonians involving just a single harmonic oscillator as well as Hamiltonians coupling the oscillator to another quantum degree of freedom such as a qubit, covering a large range of systems of interest in quantum information and metrology applications. Importantly, the protocol does not require knowledge of the parameters of the Hamiltonian to be amplified, nor does it require a well-defined phase relationship between the squeezing interaction and the rest of the system dynamics, making it potentially useful in instances where certain aspects of a signal or interaction may be unknown or uncontrolled, such as searches for novel forms of dark matter. Published by the American Physical Society 2024

arXiv:2304.05529PRX QuantumApr 17, 202418 citations

Amplification of quadratic Hamiltonians

Christian Arenz, Denys I. Bondar, Daniel Klaus Burgarth +2 more

Speeding up the dynamics of a quantum system is of paramount importance for quantum technologies. However, in finite dimensions and without full knowledge of the details of the system, it is easily shown to be impossible. In contrast we show that continuous variable systems described by a certain class of quadratic Hamiltonians can be sped up without such detailed knowledge. We call the resultant procedure Hamiltonian amplification (HA). The HA method relies on the application of local squeezing operations allowing for amplifying even unknown or noisy couplings and frequencies by acting on individual modes. Furthermore, we show how to combine HA with dynamical decoupling to achieve amplified Hamiltonians that are free from environmental noise. Finally, we illustrate a significant reduction in gate times of cavity resonator qubits as one potential use of HA.Speeding up the dynamics of a quantum system is of paramount importance for quantum technologies. However, in finite dimensions and without full knowledge of the details of the system, it is easily shown to be impossible. In contrast we show that continuous variable systems described by a certain class of quadratic Hamiltonians can be sped up without such detailed knowledge. We call the resultant procedure Hamiltonian amplification (HA). The HA method relies on the application of local squeezing operations allowing for amplifying even unknown or noisy couplings and frequencies by acting on individual modes. Furthermore, we show how to combine HA with dynamical decoupling to achieve amplified Hamiltonians that are free from environmental noise. Finally, we illustrate a significant reduction in gate times of cavity resonator qubits as one potential use of HA.

May 25, 202013 citations

Dynamical decoupling and homogenization of continuous variable systems

Christian Arenz, Daniel Klaus Burgarth, Robin Hillier

For finite-dimensional quantum systems, such as qubits, a well established strategy to protect such systems from decoherence is dynamical decoupling. However many promising quantum devices, such as oscillators, are infinite dimensional, for which the question if dynamical decoupling could be applied remained open. Here we first show that not every infinite-dimensional system can be protected from decoherence through dynamical decoupling. Then we develop dynamical decoupling for continuous variable systems which are described by quadratic Hamiltonians. We identify a condition and a set of operations that allow us to map a set of interacting harmonic oscillators onto a set of non-interacting oscillators rotating with an averaged frequency, a procedure we call homogenization. Furthermore we show that every quadratic system-environment interaction can be suppressed with two simple operations acting only on the system. Using a random dynamical decoupling or homogenization scheme, we develop bounds that characterize how fast we have to work in order to achieve the desired uncoupled dynamics. This allows us to identify how well homogenization can be achieved and decoherence can be suppressed in continuous variable systems.For finite-dimensional quantum systems, such as qubits, a well established strategy to protect such systems from decoherence is dynamical decoupling. However many promising quantum devices, such as oscillators, are infinite dimensional, for which the question if dynamical decoupling could be applied remained open. Here we first show that not every infinite-dimensional system can be protected from decoherence through dynamical decoupling. Then we develop dynamical decoupling for continuous variable systems which are described by quadratic Hamiltonians. We identify a condition and a set of operations that allow us to map a set of interacting harmonic oscillators onto a set of non-interacting oscillators rotating with an averaged frequency, a procedure we call homogenization. Furthermore we show that every quadratic system-environment interaction can be suppressed with two simple operations acting only on the system. Using a random dynamical decoupling or homogenization scheme, we develop bounds that characterize how fast we have to work in order to achieve the desired uncoupled dynamics. This allows us to identify how well homogenization can be achieved and decoherence can be suppressed in continuous variable systems.

Mar 3, 201713 citations

Entanglement generation and Hamiltonian simulation in continuous-variable systems

Barbara Kraus, Klemens Hammerer, G. Giedke +1 more

Several recent experiments have demonstrated the promise of atomic ensembles for quantum teleportation and quantum memory. In these cases, the collective internal state of the atoms is well described by continuous variables corresponding to the operators ${X}_{1}{,P}_{1}$ and the interaction with the optical field ${(X}_{2}{,P}_{2})$ by a quadratic Hamiltonian ${X}_{1}{X}_{2}.$ We show how this interaction can be used optimally to create entanglement and squeezing. We derive conditions for the efficient simulation of quadratic Hamiltonians and the engineering of all Gaussian operations and states.Several recent experiments have demonstrated the promise of atomic ensembles for quantum teleportation and quantum memory. In these cases, the collective internal state of the atoms is well described by continuous variables corresponding to the operators ${X}_{1}{,P}_{1}$ and the interaction with the optical field ${(X}_{2}{,P}_{2})$ by a quadratic Hamiltonian ${X}_{1}{X}_{2}.$ We show how this interaction can be used optimally to create entanglement and squeezing. We derive conditions for the efficient simulation of quadratic Hamiltonians and the engineering of all Gaussian operations and states.

arXiv:quant-ph/0210136Physical Review AApr 22, 200364 citations

Dynamical decoupling and homogenization of continuous variable systems

Christian Arenz, Daniel Klaus Burgarth, Robin Hillier

Abstract For finite-dimensional quantum systems, such as qubits, a well established strategy to protect such systems from decoherence is dynamical decoupling. However many promising quantum devices, such as oscillators, are infinite dimensional, for which the question if dynamical decoupling could be applied remained open. Here we first show that not every infinite-dimensional system can be protected from decoherence through dynamical decoupling. Then we develop dynamical decoupling for continuous variable systems which are described by quadratic Hamiltonians. We identify a condition and a set of operations that allow us to map a set of interacting harmonic oscillators onto a set of non-interacting oscillators rotating with an averaged frequency, a procedure we call homogenization. Furthermore we show that every quadratic system-environment interaction can be suppressed with two simple operations acting only on the system. Using a random dynamical decoupling or homogenization scheme, we develop bounds that characterize how fast we have to work in order to achieve the desired uncoupled dynamics. This allows us to identify how well homogenization can be achieved and decoherence can be suppressed in continuous variable systems.Abstract For finite-dimensional quantum systems, such as qubits, a well established strategy to protect such systems from decoherence is dynamical decoupling. However many promising quantum devices, such as oscillators, are infinite dimensional, for which the question if dynamical decoupling could be applied remained open. Here we first show that not every infinite-dimensional system can be protected from decoherence through dynamical decoupling. Then we develop dynamical decoupling for continuous variable systems which are described by quadratic Hamiltonians. We identify a condition and a set of operations that allow us to map a set of interacting harmonic oscillators onto a set of non-interacting oscillators rotating with an averaged frequency, a procedure we call homogenization. Furthermore we show that every quadratic system-environment interaction can be suppressed with two simple operations acting only on the system. Using a random dynamical decoupling or homogenization scheme, we develop bounds that characterize how fast we have to work in order to achieve the desired uncoupled dynamics. This allows us to identify how well homogenization can be achieved and decoherence can be suppressed in continuous variable systems.

arXiv:1605.05908Journal of Physics A Mathematical and TheoreticalFeb 13, 201714 citations

Spectral Gap Amplification

R. D. Somma, S. Boixo

Many problems can be solved by preparing a specific eigenstate of some Hamiltonian $H$ . The generic cost of quantum algorithms for these problems is determined by the inverse spectral gap of $H$ for that eigenstate and the cost of evolving with $H$ for some fixed time. The goal of spectral gap amplification is to construct a Hamiltonian $H'$ with the same eigenstate as $H$ but a bigger spectral gap, requiring that constant-time evolutions with $H'$ and $H$ are implemented with nearly the same cost. We show that a quadratic spectral gap amplification is possible when $H$ satisfies a frustration-free property and give $H'$ for these cases. This results in quantum speedups for optimization problems. It also yields improved constructions for adiabatic simulations of quantum circuits and for the preparation of projected entangled pair states, which play an important role in quantum many-body physics. Defining a suitable black-box model, we establish that the quadratic amplification is optimal for frustration-free Hamiltonians and that no spectral gap amplification is possible, in general, if the frustration-free property is removed. A corollary is that finding a similarity transformation between a stoquastic Hamiltonian and the corresponding stochastic matrix is hard in the black-box model, setting limits to the power of some classical methods that simulate quantum adiabatic evolutions.Many problems can be solved by preparing a specific eigenstate of some Hamiltonian $H$. The generic cost of quantum algorithms for these problems is determined by the inverse spectral gap of $H$ for that eigenstate and the cost of evolving with $H$ for some fixed time. The goal of spectral gap amplification is to construct a Hamiltonian $H'$ with the same eigenstate as $H$ but a bigger spectral gap, requiring that constant-time evolutions with $H'$ and $H$ are implemented with nearly the same cost. We show that a quadratic spectral gap amplification is possible when $H$ satisfies a frustration-free property and give $H'$ for these cases. This results in quantum speedups for optimization problems. It also yields improved constructions for adiabatic simulations of quantum circuits and for the preparation of projected entangled pair states, which play an important role in quantum many-body physics. Defining a suitable black-box model, we establish that the quadratic amplification is optimal for frustration-free Hamiltonians and that no spectral gap amplification is possible, in general, if the frustration-free property is removed. A corollary is that finding a similarity transformation between a stoquastic Hamiltonian and the corresponding stochastic matrix is hard in the black-box model, setting limits to the power of some classical methods that simulate quantum adiabatic evolutions.

arXiv:1110.2494SIAM Journal on ComputingJan 1, 201350 citations

{X}_{1}{,P}_{1}

and the interaction with the optical field

{(X}_{2}{,P}_{2})

by a quadratic Hamiltonian

{X}_{1}{X}_{2}.

We show how this interaction can be used optimally to create entanglement and squeezing. We derive conditions for the efficient simulation of quadratic Hamiltonians and the engineering of all Gaussian operations and states.

Many problems can be solved by preparing a specific eigenstate of some Hamiltonian

H

. The generic cost of quantum algorithms for these problems is determined by the inverse spectral gap of

H

for that eigenstate and the cost of evolving with

H

for some fixed time. The goal of spectral gap amplification is to construct a Hamiltonian

H'

with the same eigenstate as

H

but a bigger spectral gap, requiring that constant-time evolutions with

H'

and

H

are implemented with nearly the same cost. We show that a quadratic spectral gap amplification is possible when

H

satisfies a frustration-free property and give

H'

for these cases. This results in quantum speedups for optimization problems. It also yields improved constructions for adiabatic simulations of quantum circuits and for the preparation of projected entangled pair states, which play an important role in quantum many-body physics. Defining a suitable black-box model, we establish that the quadratic amplification is optimal for frustration-free Hamiltonians and that no spectral gap amplification is possible, in general, if the frustration-free property is removed. A corollary is that finding a similarity transformation between a stoquastic Hamiltonian and the corresponding stochastic matrix is hard in the black-box model, setting limits to the power of some classical methods that simulate quantum adiabatic evolutions.