SQuInT 2022 Program
Full Program | Thursday | Friday | Saturday | All Sessions | Posters | Talks
SESSION 9b: Algorithms in NISQ era (Islands Ballroom II)Chair: (Jun Takahashi (UNM)) | |
| 3:45 pm - 4:15 pm | Frederic Sauvage, Los Alamos National Laboratory Building spatial symmetries into parameterized quantum circuits for faster training | Abstract. Practical success of quantum learning models hinges on having a suitable structure for the parameterized quantum circuit employed . Such structure is defined both by the types of gates employed and by the correlations of their parameters. While much research has been devoted to devising adequate gate-sets, typically respecting some symmetries of the problem, very little is known about how their parameters should be structured. In this work, we show that an ideal parameter structure naturally emerges when carefully considering spatial symmetries (i.e., the symmetries that are permutations of parts of the system under study). Namely, we consider the automorphism group of the problem Hamiltonian, leading us to develop a circuit construction that is equivariant under this symmetry group. The benefits of our novel circuit structure, called ORB, are numerically probed in several ground-state problems. We find a consistent improvement (in terms of circuit depth, number of parameters required, and gradient magnitudes) compared to literature circuit constructions. |
| 4:15 pm - 4:45 pm | Nic Ezzell, University of Southern California Quantum mixed state compiling and the quantum low-rank approximation problem | Abstract. We present a variational quantum algorithm (VQA) to compile mixed states which is suitable for near-term hardware. Our algorithm can be viewed as a practical means to solve the quantum low-rank approximation problem which we formally defined and solved as part of a related work. Alternatively, our algorithm is a generalization of previous VQAs that aimed at learning preparation circuits for pure states. We choose to compile a target mixed state using two types of an ansätze; the first is based on learning a purification of the state and the second on representing it as a convex combination of pure states. In both cases, the resources required to store and manipulate the compiled state grow with the rank of the approximation. Thus, by learning a lower rank approximation of the target state, our algorithm provides a means of compressing a state for more efficient processing. As a byproduct of our algorithm, one effectively learns the principal components of the target state, and hence our algorithm further provides a new method for principal component analysis. We investigate the efficacy of our algorithm through extensive numerical implementations, showing that typical random states and thermal states of many body systems may be learnt this way. Finally, we implement our algorithm on real hardware and show how it can be used to study hardware noise-induced states. |
| 4:45 pm - 5:15 pm | Alicia Magann, Sandia National Laboratories Feedback-based quantum algorithms | Abstract. Variational quantum algorithms (VQAs) are a significant focus of the quantum computing community. These algorithms operate by wrapping a classical optimization loop around a parameterized quantum circuit, and iteratively searching for the parameter configuration that produces the best solution to the problem under consideration. A critical challenge in VQAs is the difficulty of this classical optimization problem, which can become intractable as the number of quantum circuit parameters increases. I will introduce feedback-based quantum algorithms (FQAs) as an alternative paradigm that is optimization-free and applicable to a broad range of applications. Within this paradigm, quantum circuit parameter values are assigned in a layer-wise manner using a deterministic, measurement-based feedback law derived from quantum Lyapunov control principles. The use of feedback in this manner guarantees a monotonic improvement in solution quality with respect to the depth of the quantum circuit. I will overview quantum Lyapunov control theory as a motivation for this framework and go on to discuss concrete formulations of FQAs for applications including quantum simulation and combinatorial optimization. I will conclude by presenting results from a hardware implementation and numerical investigations of convergence, scalability, and robustness. Sandia National Labs is managed and operated by NTESS under DOE NNSA contract DENA0003525. SAND2022-10773 A. |
| 5:15 pm - 5:45 pm | Jacob Watkins, Michigan State University Simulating time-dependent Hamiltonians with finite-dimensional clocks | Abstract. To date, several simulation methods have been proposed that achieve optimal scaling for time-independent Hamiltonians. However, no such algorithm has been developed that saturates these lower bounds for a non-trivial time-dependent Hamiltonian. We solve this problem by providing a new approach for approximating an ordered operator exponential using an ordinary operator exponential acting on a larger, finite-dimensional Hilbert space, which we call a “clock space”. This approach allows us to translate results for simulating time-independent systems to the time-dependent case. Our result solves two open problems in simulation. First, we provide a rigorous way to generate time-dependent product and multiproduct formulas using translations on the clock, constructing a new family of multiproduct formulas for time-dependent Hamiltonians that yield both commutator scaling and poly-logarithmic error. Our construction outperforms existing methods for simulating physically local, time-dependent Hamiltonians. Second, we extend the application of qubitization to time-dependent Hamiltonians and achieve the current best computational scaling for linear time dependencies, matching the value for time-independent qubitization. We show that as the number of auxiliary qubits grows, the error in the ordered operator exponential vanishes, as well as the entanglement between the clock and the system of interest. |
| 5:45 pm - 6:15 pm | Matthias C. Caro, California Institute of Technology Out-of-distribution generalization for learning quantum dynamics and dynamical simulation | Abstract. Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). In this work, we prove the first out-of-distribution generalization guarantees in QML, where we require a trained model to perform well even on testing data drawn from a distribution different from the training data distribution. Namely, we establish out-of-distribution generalization for the task of learning an unknown unitary using a quantum neural network and for a broad class of training and testing distributions. In particular, we show that one can learn the action of a unitary on entangled states using only product state training data. Since product states can be prepared using only single-qubit gates, this advances the near-term prospects of QML for learning quantum dynamics, and further opens up new methods for both the classical and quantum compilation of quantum circuits. Based on these insights, we propose a QML-based algorithm for simulating quantum dynamics on near-term quantum hardware and rigorously prove its resource-efficiency in terms of qubit and training data requirements. We also demonstrate the viability of this algorithm through numerical experiments, both in classical simulations and on quantum hardware. Finally, we embed this algorithm in a broader framework for using QML methods for quantum dynamical simulation on NISQ devices. |
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Akimasa Miyake, Associate Professor
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SQuInT Co-Organizer
Hartmut Haeffner, Associate Professor, UC Berkeley
hhaeffner@berkeley.edu
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Dwight Zier
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505 277-1850
SQuInT Program Committee
Alberto Alonso, Postdoc, UC Berkeley
Philip Blocher, Postdoc, UNM
Neha Yadav, Postdoc, UC Berkeley
Cunlu Zhou, Postdoc, UNM
SQuInT Founder
Ivan Deutsch, Regents' Professor, CQuIC Director
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