Session N07: Quantum Control in Manybody Systems

Generation of optimal states for single-qubit rotations

We show how the interaction of a single-mode quantum field with a sequence of identically prepared two-level atoms converges to a field state that has some remarkable properties: starting from the given initial atomic state, it performs an error- and entanglement-free rotation in the Bloch sphere, while remaining unchanged itself.  Starting from a random initial state, it minimizes the average rotation error.  We discuss the similarities with the recently-introduced transcoherent states [1], and relate the preparation process to a recent proposal [2] for “cleaning up” a quantum field so as to be able to reuse it for quantum logic operations.

[1] A. Z. Goldberg, A. M. Steinberg, and K. Heshami “Field states for effecting optimal coherent rotations on single or multiple qubits,” Quantum 7, 963 (2023).

[2] J. Ikonen, J. Salmilehto and Mikko Möttönen, “Energy-efficient quantum computing,” npj Quantum Information 3:17 (2017).   

Harry Potter's Invisibility Cloak and Quantum Spoofing

To observe, we capture the reflection of electromagnetic waves that come from light sources (emitter) on objects in our eyes (receiver). A magical garment such as Harry Potter's invisibility cloak should absorb that light and emit carefully crafted electromagnetic waves to fool us into believing that something isn't there. Of course, we are assuming that a scientific explanation like that makes sense in the Wizarding world. In the context of radar, one would call that magical item a spoofer, a third party that absorbs and emits those carefully crafted electromagnetic waves to false an object's position, shape, speed, etc. The difference between these situations is that, in radar, the receiver is also the emitter of the electromagnetic waves. That difference gives the emitter an edge as it can encode information (into the pulse shape and spectral content) to distinguish a truly reflected signal from the one generated by a spoofer. Indeed, one may look for Harry Potter using a lantern that emits light where one of two non-orthogonal quantum states is encoded. The invisibility cloak should measure the state and return the same one to generate the spoofing. However, the success of that state's determination is probabilistic. Assuming that magic doesn't break quantum mechanics, the emitter may detect when the state doesn't match, break the charm, and detect Harry Potter. Nevertheless, the receiver also has to do a measurement with a probabilistic outcome to determine that. Recently, Blakely et al. [1] introduced this concept of quantum spoofing and demonstrated an advantage with respect to a classical version of the problem. In their approach, that advantage appears when limiting themselves to a small number of photons. Here, we aim to demonstrate that the quantum advantage remains for a large number of photons. We also derive analytically the quantum states needed to attain that advantage. In our approach, single photon sources are not required for a proof-of-principle experiment, thus opening the door for an experimental implementation in a standard quantum optics lab and facilitating further development of quantum radar technology.

J.N. Blakely and S.D. Pethel, Physical Review Research 4, 023178 (2022)   

Protecting Quantum Information via Destructive Interference of Correlated Noise

Decoherence remains a major challenge for quantum technologies. Several important strategies, such as decoherence-free spaces, clock transitions, dynamical decoupling, and composite pulses, reduce the effect of noise, lowering decoherence and control error rates. Each strategy takes advantage of a certain “resource” to protect quantum information.

In this work, we propose and experimentally demonstrate a protection strategy that leverages a new kind of resource – the cross-correlation of two noise sources, e.g. control fields. Such cross-correlations exist when the control fields are generated from the same source or pass through the same transmission line.

As an example, we modify the continuous concatenated dynamical decoupling control scheme. As we show, introducing a frequency shift to one of the control fields, which is proportional to the degree of cross-correlation, results in destructive interference of the cross-correlated noise. Our scheme results in a tenfold increase in the coherence time of a single NV center in diamond, and outperforms the widely used XY8 sequence. Furthermore, we demonstrate the magnetometry of GHz signals with record sensitivity and robust qubit operations.

In light of recent characterizations of noise cross-correlations in quantum systems, our contribution opens a new avenue in the field of noise protection for quantum technologies.   

General Amplitude Modulation for Robust Trapped-Ion Entangling Gates

Trapped-ion systems are a promising route toward the realization of both near-term and universal quantum computers. However, one of the pressing challenges is improving the fidelity of two-qubit entangling gates. These operations are often implemented by addressing individual ions with laser pulses using the Molmer-Sorensen (MS) protocol. Amplitude modulation (AM) is a well-studied extension of this protocol, where the amplitude of the laser pulses is controlled as a function of time. We present an analytical study of the effect of gate-timing errors on the fidelity of MS gates with AM, using a Fourier series expansion to maintain the generality of the laser amplitude's functional form. Imposing conditions on these Fourier coefficients produces trade-offs between the laser power, gate time, and fidelity. Numerical optimization is then employed to identify the minimum-power pulse at a given level of fidelity. Our central result is that we improve the leading order dependence on gate timing errors from O(Delta t^2) to O(Delta t^6) with the addition of one linear constraint on the Fourier coefficients. This occurs without a significant increase in the average laser power or the gate time. A set of constraints is also presented that can be used, in principle, to achieve arbitrarily high orders of insensitivity to gate-timing errors.   

Fast, high-fidelity laser-free gates on trapped-ion qubits at Oxford Ionics

Electronic control of trapped-ion qubits using oscillating magnetic field gradients has delivered some of the highest-fidelity quantum gates ever reported [1, 2]. However, two-qubit entangling operations using this method are typically slower than laser-based gates, limiting overall computing speeds. We demonstrate high-fidelity two-qubit entangling gates with a duration of 100 µs using a chip trap with an integrated microwave antenna, thereby reaching the typical speed of laser-based gates in a highly scalable architecture.

[1] T. P. Harty et al., Phys. Rev. Lett. 117, 140501 (2016)

[2] R. Srinivas et al., Nature 597, pp 209-213 (2021)   

Passive dynamical decoupling of trapped ion qubits and qudits

We propose a method to dynamically decouple every magnetically sensitive hyperfine sublevel of a trapped ion from magnetic field noise, simultaneously, using integrated circuits to adiabatically rotate its local quantization field. These integrated circuits allow passive adjustment of the effective polarization of any external (control or noise) field. By rotating the ion's quantization direction relative to this field's polarization, we can perform 'passive' dynamical decoupling (PDD), inverting the linear Zeeman sensitivity of every hyperfine sublevel. This dynamically decouples the entire ion, rather than just a qubit subspace. Fundamentally, PDD drives the transition mf ---> -mf for every magnetic quantum number mf in the system--with only one operation--indicating it applies to qudits with constant overhead in the dimensionality of the qudit. We show how to perform pulsed and continuous PDD, weighing each technique's insensitivity to external magnetic fields versus their sensitivity to diabaticity and control errors. Finally, we show that we can tune the sinusoidal oscillation of the quantization axis to a motional mode of the crystal in order to perform a laser-free two qubit gate that is insensitive to magnetic field noise.   

Erasure-cooling, control, and hyper-entanglement of motion in optical tweezers

We experimentally demonstrate how quantized motional degrees of freedom in optical tweezers can be used as quantum information carriers. By converting motional excitations into erasure errors and removing them, we can prepare atoms into motional ground state with close to 99% efficiency. This cooling mechanism, erasure-cooling, is the first step in coherent manipulation of motional states. With this, we can perform mid-circuit readout of certain optical qubits while shelving other qubits into motional superposition states. In parallel, with Rydberg gates, we entangle the motion of two atoms in separate tweezers and generate hyper-entanglement, a simultaneous Bell state of motional and optical qubits. With multiple concrete examples, this work shows how controlling motion enriches the toolbox of quantum information processing with neutral atoms, opening up unique prospects for metrology enhanced by mid-circuit readout and a large class of quantum operations enabled via hyper-entanglement.   

Quantum teleportation of many-body spin states in a two-dimensional trapped ions crystal

We propose to use phonon-mediated interactions as an entanglement resource to perform teleportation of many-body spin states. The spin ensembles correspond to different nuclear spin degrees of freedom of a two-dimensional ion crystal created in a Penning trap. In each ensemble, an electronic spin degree of freedom is used to encode a qubit that couples to the vibrational mode of the crystal. The strong magnetic field native to the Penning trap generates large enough energy splittings for the preparation and read out of each of the different spin ensembles without affecting the others. Emulating continuous variable quantum teleportation protocols that rely on two-mode-squeezing and beam-splitting operations, we theoretically discuss how to engineer suitable effective spin-spin interactions between three spin ensembles to implement a teleportation circuit. Exact numerical simulations of the circuit confirm the protocol performs teleportation of the many-body spin state with good fidelity for realistic experimental conditions in arrays from a few tens to a few hundred ions. Our analysis demonstrates that teleportation of spin-coherent and entangled spin-squeezed states as well as their phase-displaced versions is possible in this setting and opens new opportunities for quantum information processing in a Penning trap where single ion resolution is not trivial.   

Experimental Study of Universal Scaling in Super-radiant Quantum Phase Transitions with a Single Trapped Ion

Abstract:

Phase transitions typically manifest under thermodynamic conditions, where the emergence of a universal scaling function near a critical point serves as a pivotal sign of phase transition. Recently, the quantum Rabi model (QRM) has been highlighted for its ability to undergo quantum phase transitions from normal to super-radiant phases, with a simple system of a qubit and a harmonic oscillator mode [1,2]. QRM's order parameters can reveal universal scaling functions when approaching to the critical point, which, however, it has not been observed in experiment. Here we employ a single trapped ion to realize the QRM, and measure the order parameters of squeezing parameters and excitation of super-radiance and their corresponding universal scaling function. We speed up the process by optimizing the adiabatic evolution trajectories to overcome the limitation of coherence time of vibrational mode. This methodology offers a quantitative study of quantum phase transition and an avenue for exploring quantum sensing using QRM.

 

Reference:

[1] Myung-Joong Hwang, et al., Phys. Rev. Lett. 115, 180404 (2015).

[2] Ricardo Puebla, et al., Phys. Rev. Lett. 118, 073001 (2017).