Session S15: Quantum Networks and Open Systems

Interacting Photons in Curved Space Using Superconducting Circuits

After close to two decades of research and development, superconducting circuits have emerged as a rich platform for both quantum computation and quantum simulation. In this talk, we will discuss a new domain of quantum simulation with superconducting circuits: interacting photons in curved (non-Euclidean) space. By constructing two-dimensional lattices of microwave coplanar waveguide cavities with spatially-varying hopping rates and resonant frequencies, we demonstrate that we can simulate photons propagating in non-Euclidean space. Furthermore, superconducting circuits allow us to engineer effective photon-photon interactions using high kinetic inductance nonlinearites and transmon qubits--introducing the exciting prospect of studying strongly-interacting photons in curved geometries.   

Open-System Quantum Error Correction Conditions

In this work, we present QEC conditions for a system undergoing open-system dynamics. Here, we describe the noise on the system as originating from a joint completely-positive, trace-preserving map on the system-bath composite, after which we trace out bath degrees of freedom. Our noise model can be viewed as an intermediate picture between the standard system-only quantum channel model and a system-bath Hamiltonian noise model: It goes beyond a Markovian description for the system dynamics, and yet retains a quantum dynamical semigroup structure for the problem. Our general noise model fits naturally into many physical scenarios where one has a relatively strong coupling between the system and an "intermediate" bath, which also couples weakly to a large dissipative bath. Despite the physical motivation from an intermediate bath, our noise model is mathematically general however, and in turn contains both system-only quantum channel model and system-bath Hamiltonian noise model as extreme cases.

We derive and study the QEC conditions for our general noise model, with the emphasis that the recovery operation acts on the system only. When the noise is only approximately correctable, we obtain a lower bound for the performance of the QEC, as quantified by worst-case fidelity.   

Energy-Constrained Two-Way Assisted Private and Quantum Capacities of Quantum Channels

With the rapid growth of quantum technologies, knowing the fundamental characteristics of quantum systems and protocols is essential to their effective implementation. The maximum rates at which a quantum channel can reliably transfer private and quantum information are respectively called the private and quantum capacities. Our contribution begins by formalizing the notion of energy-constrained private and quantum communication with the assistance of local operations and classical communication (LOCC). We then define the energy-constrained squashed entanglement of a channel and prove that it upper bounds the energy-constrained LOCC-assisted private and quantum capacities of an arbitrary channel with an arbitrary Hamiltonian when the channel and Hamiltonian are subject to certain physically well motivated conditions. We shift our focus to actual bosonic channels as an example of our general theory and prove that the two-mode squeezed vacuum optimizes the squashed entanglement for any single-mode phase-insensitive Gaussian channel whenever the squashing channel is constrained to be phase-insensitive and Gaussian. Finally, we extend the theory to the broadcast setting with one sender and multiple receivers.   

Holographic Spin Networks from Tensor Network States

Tensor networks are a powerful tool for describing many body systems, they reduce the complexity of storing and computing many-body states by restricting the state space to have a restricted entanglement structure. The multiscale entanglement renormalization ansatz (MERA) is one such example of tensor network state designed to approximate many body states with conformal symmetries (i.e. spin chains). For 1D periodic states the MERA can be visualized as a disc where the quantum state is on the boundary and the tensor network is embedded into the bulk of the disc, reminiscent of the holographic principle where theories of quantum gravity are expected to be encodable onto the system's boundary.

In this presentation I will discuss a toy model we have developed, focusing on the MERA but extendible to any tensor network state, motivated by the holographic principle. Adding degrees of freedom into the bulk of the network we discuss relationships between properties of the boundary and the bulk of the tensor network with a motivation towards adapting tools from the holographic principle for use in strongly correlated many-body systems. To do this we compute correlation functions, Wilson loops, and entropic quantities in the bulk for a number of critical spin chains with on-site symmetries.   

Measurement-based linear optics

A major challenge in optical quantum processing is implementing large, stable interferometers. We offer a novel approach: virtual, measurement-based interferometers that are programed on the fly solely by the choice of homodyne measurement angles. The proposed continuous-variable cluster state architecture can be implemented on an unprecedented scale from compact experimental setups using either temporal or frequency modes. Our protocol minimizes noise due to finite squeezing. Furthermore, we show that this noise can be coaxed into appearing as pure photon loss per simulated optical element, where the efficiency of the interferometer is set by the overall squeezing parameter of the experiment. We compare our proposal to existing (physical) interferometers and consider its performance for BosonSampling, which could demonstrate postclassical computational power in the near future. We prove its efficiency in time and squeezing (energy) in this setting.

This talk is based on Phys. Rev. Lett. 118, 110503 (2017).   

Efficiently controlling qubit networks

Future quantum devices often rely on favourable scaling with respect to the system components. To achieve desirable scaling, it is therefore crucial to implement unitary transformations in an efficient manner. We develop an upper bound for the minimum time required to implement a unitary transformation on a generic qubit network in which each of the qubits is subject to local time dependent controls. The set of gates is characterized that can be implemented in a time that scales at most polynomially in the number of qubits. Furthermore, we show how qubit systems can be concatenated through controllable two body interactions, making it possible to implement the gate set efficiently on the combined system. Finally a system is identified for which the gate set can be implemented with fewer controls. The considered model is particularly important, since it describes electron-nuclear spin interactions in NV centers.   

Using Tikhonov Regularization Method to Solve the Hamiltonian in an Inverse Problem for a Quantum Spin System

Tikhonov regularization is a popular method for solving linear discrete ill-posed problems. This method can conveniently solve small-scale problems with the aid of the generalized singular value decomposition. However, it is impractical to use this decomposition for large-scale problems. We develop a new matrix decomposition method that are well suited for the solution of large-scale problems. This method can be applied to the inverse problem where we are given a set of desired orthogonal wave functions and we are trying to construct the parent Hamiltonian for a quantum spin system.   

Improving Performance of an Analog Electronic Device Using Quantum Error Correction

The development of the field of quantum information processing has resulted in countless techniques which exploit the properties of quantum mechanical systems in order to perform useful computational tasks. In this talk we discuss a particular application of protocols developed in the field quantum error correction (QEC) to a seemingly disparate field. The usefulness of analog classical systems for computation is generally thought to be complicated by the susceptibility of these devices to noise and the lack of a clear framework for achieving fault-tolerance. We present results for the application of quantum error correction techniques to a prototype analog computational device called a quantum emulation device (QED). It is shown that for the gates tested (Z, X and SH) there is a marked improvement in the performance characteristics. Gate performance after QEC, as measured by the average log-fidelity (-log₁₀(1-F)), increases by 2.15. This corresponds to a reduction in the infidelity of the gate operations by more than two orders of magnitude on average.   

Finding decoherence-free subspaces numerically

For a particular subspace or subsystem, if the quantum information is preserved by a noise with exact symmetry then it is known as a decoherence free subspace or subsystem (DFS). A numerical method was proposed to identify such a DFS by Wang, Byrd and Jacobs (Phys. Rev. A 87, 012338 (2013)). An algebraic form that gives the structure of the DFS is decomposed into simple components and these components are then further decomposed into irreducible components. These irreducible components are then used to find a unitary transform that leaves the algebraic form invariant under such a transformation. We applied the same numerical method to find DFS's with more than 1 qubit. If a particular noise process is given then this numerical method could be used to find the subspace or subsystem that is not affected by the noise or is the least affected by the noise. The latter is known as a minimal-noise subspace or subsystem (MNS).   

Noise suppression via generalized-Markovian processes

It is by now well established that noise itself can be useful for performing quantum information processing tasks.
We present results which show how one can effectively reduce the error rate associated with a noisy quantum channel, by counteracting its detrimental effects with another form of noise.
In particular, we consider the interplay between a purely Markovian (Lindblad) dynamics, and a more general form of dissipation, which we refer to as generalized-Markovian noise. This noise has an associated memory kernel and the resulting dynamics is described by an integro-differential equation (i.e., it has a non-Markov character).
The overall dynamics are characterized by decay rates which depend not only on the original dissipative time-scales, but also on the new integral kernel. We find that one can engineer this kernel such that the overall rate of decay is lowered by the addition of such a noise term.
We provide numerical results for several physical models, including a dephasing channel, and qubit in a thermal environment.
These results help to qualitatively explain the physical mechanism behind this error suppression scheme, whereby the system is periodically decoupled from the background noise.   

Temperature Dependence of Spin Relaxation and Charge Noise in Silicon Spin Qubits

Large-scale quantum computing is pursued by a wide variety of scientific disciplines. While leading solid-state approaches focus on decreasing the operation temperature to almost zero Kelvin, a crucial question is if the available cooling power will then be sufficient to increase the number of qubits to the required thousands or millions.
Here, we work towards hot-qubits, using electron spins in silicon quantum dots, and characterize the temperature dependence of the spin relaxation time and the charge noise. We have fabricated quantum dot devices on isotopically purified silicon that can host up to four qubits in a linear array. We deplete one quantum dot to the single-electron regime and we are able to readout the spin state in single shot mode. We map out the magnetic field and temperature dependence of the spin lifetime, measuring T₁ times larger than 1 ms beyond 1 K. From the temperature dependence study we conclude that the relaxation rate at high temperatures is determined by two-phonon Raman transitions, rather than Orbach processes, up to 1 K. We also investigate the effect of temperature on the charge noise, measured as current fluctuations of a SET, and find consistency with a linear temperature dependence up to 4K.