ABSTRACT We investigate quantum control of an oscillator mode off-resonantly coupled to an ancill... more ABSTRACT We investigate quantum control of an oscillator mode off-resonantly coupled to an ancillary qubit. In the strong dispersive regime, we may drive the qubit conditioned on number states of the oscillator, which together with displacement operations can achieve universal control of the oscillator. Based on our proof of universal control, we provide explicit constructions for arbitrary state preparation and arbitrary unitary operation of the oscillator. Moreover, we present an efficient procedure to prepare the number state $\left|n\right\rangle$ using only $O\left(\sqrt{n}\right)$ operations. We also compare our scheme with known quantum control protocols for coupled qubit-oscillator systems. This universal control scheme of the oscillator can readily be implemented using superconducting circuits.
We study a reservoir engineering scheme whose steady-state space consists of superpositions of $d... more We study a reservoir engineering scheme whose steady-state space consists of superpositions of $d$ well-separated coherent states. We show that universal computation on this space can be achieved by two types of adiabatic holonomic gates. The first type consists of moving a coherent state around a closed path in phase space, resulting in a relative Berry phase between that state and the other states. The second type consists of colliding two coherent states, resulting in coherent population transfer between them. The $d = 2$ case is realizable in systems which support tunable nonlinearities, such as trapped ions and circuit QED.
We construct a new class of quantum error-correcting codes for a bosonic mode which are advantage... more We construct a new class of quantum error-correcting codes for a bosonic mode which are advantageous for applications in quantum memories, communication, and scalable computation. These 'binomial quantum codes' are formed from a finite superposition of Fock states weighted with binomial coefficients. The binomial codes can exactly correct errors that are polynomial up to a specific degree in bosonic creation and annihilation operators, including amplitude damping and displacement noise as well as boson addition and dephasing errors. For realistic continuous-time dissipative evolution, the codes can perform approximate quantum error correction to any given order in the timestep between error detection measurements. We present an explicit approximate quantum error recovery operation based on projective measurements and unitary operations. The binomial codes are tailored for detecting boson loss and gain errors by means of measurements of the generalized number parity. We discuss optimization of the binomial codes and demonstrate that by relaxing the parity structure, codes with even lower unrecoverable error rates can be achieved. The binomial codes are related to existing two-mode bosonic codes but offer the advantage of requiring only a single bosonic mode to correct amplitude damping as well as the ability to correct other errors. Our codes are similar in spirit to 'cat codes' based on superpositions of the coherent states, but offer several advantages such as smaller mean number, exact rather than approximate orthonormality of the code words, and an explicit unitary operation for repumping energy into the bosonic mode. The binomial quantum codes are realizable with current superconducting circuit technology and they should prove useful in other quantum technologies, including bosonic quantum memories, photonic quantum communication, and optical-to-microwave up-and down-conversion.
There is particular value in having wavefunctions for few-body systems that are compact but never... more There is particular value in having wavefunctions for few-body systems that are compact but nevertheless have the features needed to capture the essence of the correlation effects. These desiderata are inherently in conflict and cannot be simultaneously reconciled when the wavefunction is described in terms of orbitals. However, explicit use of the interparticle distances leads to more efficient expansions; when all these distances are included as exponentials it is found that the expansions converge extremely rapidly, but only when the nonlinear parameters occurring therein are very carefully optimized. The present contribution reports the use of such expansions. For typical three-body systems (the He isoelectric series), with wavefunctions containing four terms (configurations), ground-state energies are obtained with errors between 32 and 38 microhartrees, and other properties, including those arising entirely from electron correlation, are given with very small errors. For a four-body system (the Li atom), a four-term wavefunction yields a ground-state energy within 350 microhartrees of the correct value.
The large available Hilbert space and high coherence of cavity resonators make these systems an i... more The large available Hilbert space and high coherence of cavity resonators make these systems an interesting resource for storing encoded quantum bits. To perform a quantum gate on this encoded information, however, complex nonlinear operations must be applied to the many levels of the oscillator simultaneously. In this work, we introduce the selective number-dependent arbitrary phase (snap) gate, which imparts a different phase to each Fock-state component using an off-resonantly coupled qubit. We show that the snap gate allows control over the quantum phases by correcting the unwanted phase evolution due to the Kerr effect. Furthermore, by combining the snap gate with oscillator displacements, we create a one-photon Fock state with high fidelity. Using just these two controls, one can construct arbitrary unitary operations, offering a scalable route to performing logical manipulations on oscillator-encoded qubits.
Collisions between Xe@C60 and sheets of graphite of various dimensions were simulated. A Tersoff ... more Collisions between Xe@C60 and sheets of graphite of various dimensions were simulated. A Tersoff many-body potential modeled the interactions between carbon atoms and a Lennard-Jones potential simulated the xenon-carbon interactions. The simulations were compared to experiment and with simulations which implemented other potentials. The results indicate that a relatively small graphite film can be an accurate approximation for a nearly infinite sheet of graphite.
This work addresses Lindbladians admitting attractive subspaces in which time evolution is exclus... more This work addresses Lindbladians admitting attractive subspaces in which time evolution is exclusively unitary. Such subspaces can be used to store, protect, and process quantum information. We derive an analytical formula for the left eigenmatrices of such Lindbladians corresponding to pure imaginary eigenvalues. This formula resolves how Lindbladian evolution affects the perturbative response and geometrical features of the attractive subspaces. We show that all Hamiltonian and certain jump operator perturbations induce (to first order) exclusively unitary evolution on the subspaces. Similarly, the holonomy induced on such subspaces after (adiabatic) traversal of a closed path in the parameter space is unitary. We derive a new Riemannian metric tensor in the parameter space induced by a large family of attractive subspaces. The adiabatic curvature (related to holonomies) and the metric tensor (related to the path length) are shown to be parts of a Lindblad quantum geometric tensor, generalizing this structure to Lindbladians possessing one or more mixed steady states. We derive a Kubo formula governing linear response of the attractive subspaces to Hamiltonian perturbations and determine cases in which this formula reduces to a Hamiltonian-based Kubo formula. As an application, we show that (for gapped systems) the zero-frequency Hall conductivity is unaffected by many types of Markovian dissipation. Finally, we show that the energy scale governing leakage out of the attractive subspaces, resulting from either corrections to adiabatic evolution or Hamiltonian perturbations, is different from the conventional Lindbladian dissipative gap. In certain cases, this scale is equivalent to the excitation gap of a related Hamiltonian. We summarize our key results by introducing "four-corners" notation and presenting two properties of generic subspaces, the "no-leak" and "clean-leak" properties.
Compact, but relatively accurate wavefunctions for the ground state of the Li atom were obtained ... more Compact, but relatively accurate wavefunctions for the ground state of the Li atom were obtained through the use of a limited basis of exponentially correlated functions with optimized nonlinear parameters. In contrast to our earlier work, the basis contains pre-exponential factors that improve the rate of convergence of the basis-set expansion. The matrix elements needed in the present work were
New photovoltaic and photocatalysis applications have been recently proposed based on the hybrid ... more New photovoltaic and photocatalysis applications have been recently proposed based on the hybrid Ru(II)-bipyridine-complex/semiconductor quantum dot systems. In order to attach the Ru(II) complex to the surface of a semiconductor, a linking bridge -- a carboxyl group -- needs to be added to one or two of the 2,2'-bipyridine (bpy) ligands. Such changes in the ligand structure affect electronic and
ABSTRACT We investigate quantum control of an oscillator mode off-resonantly coupled to an ancill... more ABSTRACT We investigate quantum control of an oscillator mode off-resonantly coupled to an ancillary qubit. In the strong dispersive regime, we may drive the qubit conditioned on number states of the oscillator, which together with displacement operations can achieve universal control of the oscillator. Based on our proof of universal control, we provide explicit constructions for arbitrary state preparation and arbitrary unitary operation of the oscillator. Moreover, we present an efficient procedure to prepare the number state $\left|n\right\rangle$ using only $O\left(\sqrt{n}\right)$ operations. We also compare our scheme with known quantum control protocols for coupled qubit-oscillator systems. This universal control scheme of the oscillator can readily be implemented using superconducting circuits.
We study a reservoir engineering scheme whose steady-state space consists of superpositions of $d... more We study a reservoir engineering scheme whose steady-state space consists of superpositions of $d$ well-separated coherent states. We show that universal computation on this space can be achieved by two types of adiabatic holonomic gates. The first type consists of moving a coherent state around a closed path in phase space, resulting in a relative Berry phase between that state and the other states. The second type consists of colliding two coherent states, resulting in coherent population transfer between them. The $d = 2$ case is realizable in systems which support tunable nonlinearities, such as trapped ions and circuit QED.
We construct a new class of quantum error-correcting codes for a bosonic mode which are advantage... more We construct a new class of quantum error-correcting codes for a bosonic mode which are advantageous for applications in quantum memories, communication, and scalable computation. These 'binomial quantum codes' are formed from a finite superposition of Fock states weighted with binomial coefficients. The binomial codes can exactly correct errors that are polynomial up to a specific degree in bosonic creation and annihilation operators, including amplitude damping and displacement noise as well as boson addition and dephasing errors. For realistic continuous-time dissipative evolution, the codes can perform approximate quantum error correction to any given order in the timestep between error detection measurements. We present an explicit approximate quantum error recovery operation based on projective measurements and unitary operations. The binomial codes are tailored for detecting boson loss and gain errors by means of measurements of the generalized number parity. We discuss optimization of the binomial codes and demonstrate that by relaxing the parity structure, codes with even lower unrecoverable error rates can be achieved. The binomial codes are related to existing two-mode bosonic codes but offer the advantage of requiring only a single bosonic mode to correct amplitude damping as well as the ability to correct other errors. Our codes are similar in spirit to 'cat codes' based on superpositions of the coherent states, but offer several advantages such as smaller mean number, exact rather than approximate orthonormality of the code words, and an explicit unitary operation for repumping energy into the bosonic mode. The binomial quantum codes are realizable with current superconducting circuit technology and they should prove useful in other quantum technologies, including bosonic quantum memories, photonic quantum communication, and optical-to-microwave up-and down-conversion.
There is particular value in having wavefunctions for few-body systems that are compact but never... more There is particular value in having wavefunctions for few-body systems that are compact but nevertheless have the features needed to capture the essence of the correlation effects. These desiderata are inherently in conflict and cannot be simultaneously reconciled when the wavefunction is described in terms of orbitals. However, explicit use of the interparticle distances leads to more efficient expansions; when all these distances are included as exponentials it is found that the expansions converge extremely rapidly, but only when the nonlinear parameters occurring therein are very carefully optimized. The present contribution reports the use of such expansions. For typical three-body systems (the He isoelectric series), with wavefunctions containing four terms (configurations), ground-state energies are obtained with errors between 32 and 38 microhartrees, and other properties, including those arising entirely from electron correlation, are given with very small errors. For a four-body system (the Li atom), a four-term wavefunction yields a ground-state energy within 350 microhartrees of the correct value.
The large available Hilbert space and high coherence of cavity resonators make these systems an i... more The large available Hilbert space and high coherence of cavity resonators make these systems an interesting resource for storing encoded quantum bits. To perform a quantum gate on this encoded information, however, complex nonlinear operations must be applied to the many levels of the oscillator simultaneously. In this work, we introduce the selective number-dependent arbitrary phase (snap) gate, which imparts a different phase to each Fock-state component using an off-resonantly coupled qubit. We show that the snap gate allows control over the quantum phases by correcting the unwanted phase evolution due to the Kerr effect. Furthermore, by combining the snap gate with oscillator displacements, we create a one-photon Fock state with high fidelity. Using just these two controls, one can construct arbitrary unitary operations, offering a scalable route to performing logical manipulations on oscillator-encoded qubits.
Collisions between Xe@C60 and sheets of graphite of various dimensions were simulated. A Tersoff ... more Collisions between Xe@C60 and sheets of graphite of various dimensions were simulated. A Tersoff many-body potential modeled the interactions between carbon atoms and a Lennard-Jones potential simulated the xenon-carbon interactions. The simulations were compared to experiment and with simulations which implemented other potentials. The results indicate that a relatively small graphite film can be an accurate approximation for a nearly infinite sheet of graphite.
This work addresses Lindbladians admitting attractive subspaces in which time evolution is exclus... more This work addresses Lindbladians admitting attractive subspaces in which time evolution is exclusively unitary. Such subspaces can be used to store, protect, and process quantum information. We derive an analytical formula for the left eigenmatrices of such Lindbladians corresponding to pure imaginary eigenvalues. This formula resolves how Lindbladian evolution affects the perturbative response and geometrical features of the attractive subspaces. We show that all Hamiltonian and certain jump operator perturbations induce (to first order) exclusively unitary evolution on the subspaces. Similarly, the holonomy induced on such subspaces after (adiabatic) traversal of a closed path in the parameter space is unitary. We derive a new Riemannian metric tensor in the parameter space induced by a large family of attractive subspaces. The adiabatic curvature (related to holonomies) and the metric tensor (related to the path length) are shown to be parts of a Lindblad quantum geometric tensor, generalizing this structure to Lindbladians possessing one or more mixed steady states. We derive a Kubo formula governing linear response of the attractive subspaces to Hamiltonian perturbations and determine cases in which this formula reduces to a Hamiltonian-based Kubo formula. As an application, we show that (for gapped systems) the zero-frequency Hall conductivity is unaffected by many types of Markovian dissipation. Finally, we show that the energy scale governing leakage out of the attractive subspaces, resulting from either corrections to adiabatic evolution or Hamiltonian perturbations, is different from the conventional Lindbladian dissipative gap. In certain cases, this scale is equivalent to the excitation gap of a related Hamiltonian. We summarize our key results by introducing "four-corners" notation and presenting two properties of generic subspaces, the "no-leak" and "clean-leak" properties.
Compact, but relatively accurate wavefunctions for the ground state of the Li atom were obtained ... more Compact, but relatively accurate wavefunctions for the ground state of the Li atom were obtained through the use of a limited basis of exponentially correlated functions with optimized nonlinear parameters. In contrast to our earlier work, the basis contains pre-exponential factors that improve the rate of convergence of the basis-set expansion. The matrix elements needed in the present work were
New photovoltaic and photocatalysis applications have been recently proposed based on the hybrid ... more New photovoltaic and photocatalysis applications have been recently proposed based on the hybrid Ru(II)-bipyridine-complex/semiconductor quantum dot systems. In order to attach the Ru(II) complex to the surface of a semiconductor, a linking bridge -- a carboxyl group -- needs to be added to one or two of the 2,2'-bipyridine (bpy) ligands. Such changes in the ligand structure affect electronic and
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Papers by Victor Albert