Session F33: Quantum Characterization, Verification, and Validation II

Live

Qutrits present an alternative to qubits for implementing quantum computation by using three-, rather than two-level systems, and have proven useful to explore connections between high-energy physics and quantum information science. Leveraging this extra level can also be used to extend the reach of current quantum hardware. In this talk, we present a scheme to generalize Randomized Benchmarking (RB) protocols to qutrits, and we experimentally implement them on a 5-transmon processor. More specifically, we measure the performance of our single-qutrit gate with RB and interleaved RB. We then use cycle benchmarking to assess the performance of our CSUM gate - the generalization of the CNOT for qutrits.   

Live

In the present work, Grover's search algorithm is used to study performance of state-of-the-art quantum platforms, such as LLNL Quantum Design and Integration Testbed (QuDIT), Rigetti and IBM-Q. The algorithm is suited for three and four level quantum systems, thus, it is implemented on 2 qubits on Rigetti and IBM platforms and on a single transmon on the LLNL QuDIT. The population of the desired state is measured for different number of Grover's iterations and the results are compared to the analytically derived solution. The performance of the algorithm depends on the number of the system states, the marked state of the Oracle and the number of iterations. The observed fidelity loss is noticeably less for the LLNL QuDIT, as a small number of specially designed control pulses is used instead of a large sequence of native gates. For better understanding of the nature of the coherent and decoherent processes causing the fidelity decay, the algorithm is decomposed to main blocks and all of them are tested individually.   

Live

In this work, we deal with the verification that the state generated by a quantum network corresponds to the desired target, with no assumptions on the adopted experimental platform, i.e. device-independently. Such a task is known as self-testing and its experimental implementations have been limited so far, by the fact that the majority of the existing protocols have low noise tolerance. In our case, we develop self-testing methods to deal with real imperfect conditions and show their applications to two experimentally implemented quantum networks.
In detail, our target is the tensor product of two maximally entangled two-qubit states and we provide lower bounds on the fidelity between the generated states and such an ideal state, extending previous self-testing techniques.
On the experimental side, we implement two quantum network building blocks, involving two independent sources, on a photonic platform. Firstly, a parallel configuration in which two parties share two quantum states and a tripartite configuration where a central party shares two states with peripheral nodes. Given their versatility, the techniques we show can be applied to the certification of larger networks of different topologies, for quantum communication, cryptography and randomness generation protocols.   

Live

As quantum computational power increases, the key challenge for each platform is to demonstrate the quantum computational advantage that a given quantum device has over a classical one (‘quantum supremacy’). An essential aspect of this problem is verifying a claimed quantum advantage. Since a no-go theorem [1] forbids sample-efficient, device-independent verification for most QA platforms, the way forward is to construct a reasonable error model of a device, and measure the parameters of that model. In this work, we accomplish this for boson sampling [2], where the task is to sample from the output distribution of photons in a large linear optical network in the number basis.

We show that the level of imperfections in a boson sampler can be reconstructed from a sparse set of samples. We find the level of the various noise sources which are present in a data set from the largest boson sampler currently reported [3]. Our method combined with previous results [4] enables a test whether a given boson sampler has the required quality to demonstrate a quantum advantage.

[1] Hangleiter et al, Phys. Rev. Lett 122, 210502 (2019)
[2] Aaronson, Arkhipov, Theory Comput. 9, 143 (2013).
[3] Wang et al., Phys. Rev. Lett. 123 250503 (2019).
[4] Renema et al., Phys. Rev. Lett. 120, 220502 (2018).   

Live

Verifying that quantum devices work in a properly quantum way has become of high relevance since the availability of the first small-scale quantum processors; an important requirement for such devices is the ability to create entanglement. To understand how entanglement evolves under physical operations acting on quantum states, we consider the problem of separability of quantum channels via the Choi matrix representation. We explore three classes of separability across different cuts between systems and ancillae and we provide a solution based on the mapping of the coordinates of the Choi state (in a fixed basis) to a truncated moment sequence (tms) y. This results in a necessary and sufficient condition for a channel to be separable or entanglement breaking. The algorithm we provide gives definiteness in the answer to the channel separability problem using semidefinite programming. The computational complexity and the performance depend on the number of variables n in the tms and on the size of the matrices involved in the semidefinite program. We investigate separability of 2-qubit and single-qutrit channels; in the latter case we can provide an answer in cases where more straight-forward separability criteria based on positive but not completely positive maps fail.   

Live

Precise calibration of quantum devices is necessary for reliable quantum information processing. Full characterization and tuning a quantum system without making any assumption require resources that scale exponentially with the system size. Here, we assume a model for the noisy evolution of a quantum system, and by using a machine learning technique known as meta-learning to train an optimizer that finds model parameters with less resources than other gradient-based optimization algorithms. The training of our algorithm is done efficiently on smaller systems. However, the learned optimizer is transferable to larger and different systems.   

Live

Quantum state reconstruction is an important element enabling diagnosis and improvement of quantum control. As larger states are controlled, care needs to be taken to mitigate experimental imperfections and the number of measurements required to perform state reconstruction becomes crucial. Significant gains can be found by choosing the appropriate basis in which to make measurements. In this talk I will discuss experimental techniques to characterize extended quantum harmonic oscillator states, focusing on measurements of the Wigner characteristic function. The latter allowed for a factor of 20 improvement in measurement time for the reconstruction of the motional state of a trapped ion [1] and enabled tomography of a microwave resonator weakly coupled to a transmon qubit [2].
[1]: C. Flühmann et al. PRL 125, 043602 (2020)
[2]: P. Campagne-Ibarcq et al. Nature 584, 368-372 (2020)   

Live

Measuring only one qubit in a composite quantum system is described by projectors on half-dimensional subspaces of the full Hilbert space. Despite the limitation these measurements can be combined with unitary operations in order to perform full quantum state tomography (QST). Moreover, for a system of qubits, measurement operators can be arranged in a fashion optimal for QST, i.e. such that the corresponding subspaces are mutually unbiased [1].
Here, we consider a qubit-qutrit system, e.g. formed by the N-14 nuclear spin-1 and two states of the electron spin in a nitrogen-vacancy center in diamond where the electronic state could be measured using resonance fluorescence. We formulate the search for the most efficient QST scheme as a high-dimensional optimization problem and approach this problem numerically as we did previously for QST schemes with rank-1 measurement operators [2]. For the rank-3 operators considered here, we find that our numerical solution approximates the result of mutually unbiased subspaces.

[1] Bodmann, Haas, Proc. Amer. Math. Soc. 146, 2601 (2018)
[2] Ivanova-Rohling, Rohling, Phys. Rev. A 100, 032332 (2019)   

Live

We show that it is possible to uniquely reconstruct a generic many-body local Hamiltonian from a single pair of initial and final states related by time evolution with the Hamiltonian. We then propose a practical version of the protocol involving multiple pairs of such initial/final states. Using the eigenstate thermalization hypothesis, we provide bounds on the protocol's performance and stability against errors from measurements and in the ansatz of the Hamiltonian. The protocol is efficient (requiring experimental resources scaling polynomially with system size in general and constant with system size given translation symmetry) and thus enables analog and digital quantum simulators to verify implementation of a putative Hamiltonian.   

Live

A key obstacle to achieve optimal control performance is the interaction between the target system and its unknown environment. Thus, obtaining a quantitative characterization of such environment is instrumental. We introduce a new framework for resource-efficient characterization and control of non-Markovian open quantum systems, which allows for the integration of given, experimentally motivated, control capabilities and constraints. This is achieved by developing a transfer filter-function formalism based on the notion of a frame and by tying the choice of frame to the available control. While recovering the standard frequency-based filter-function formalism as a special instance, this control-adapted generalization affords intrinsic flexibility and allows us to overcome limitations of existing approaches. In particular, we show how to implement quantum noise spectroscopy in the presence of non-stationary noise sources, and how to achieve control-driven model reduction for noise-tailored optimized quantum gate design.   

Not Participating

Abstract: This is the second part of the work ``Frame-based filter-function formalism for quantum characterization and control".

The frame-formalism [https://arxiv.org/abs/2008.13216] leads to a model-reduced representation of the open quantum system dynamics and permitting efficient integration of the control capabilities from the outset, allowing the streamlining of the tasks of characterization and optimal control of open quantum systems.

We demonstrate via numerical simulations an experimentally motivated open multi-qubit system with piecewise noisy control. We show how one can characterize exactly what is needed to execute optimal control given the available control, and demonstrate how very high fidelities can be achieved with only minimal assumptions. We present the model-reduction properties of the formalism by showing only a minimal loss of performance when compared to the (unrealistic) scenario in which full information about the open quantum system is available.