# Daan Camps

Daan Camps is a staff member in the Advanced Technology Group at NERSC. His work focuses on integrating emerging quantum technologies in future generation HPC systems.

**Recent software projects:**

- FunFact: Concise expressions of tensor algebra through an Einstein notation-based syntax with applications in quantum circuit optimization, tensor decomposition and neural network compression.
- QCLAB: First fully-featured quantum circuit simulator for MATLAB users.
- QCLAB++: Fully templated C++ package for simulating quantum circuits.
- F3C and F3C++: Fast Free Fermion Compiler for compiling time-evolution quantum circuits of spin Hamiltonians that can be mapped to free fermions.
- QPIXL++: C++ package for generating compressed quantum circuits for image representations.

More info at: campsd.github.io

## Research Interests

- Numerical Linear Algebra
- (Non-Linear) Tensor Factorization Methods
- Quantum Algorithms
- Quantum Circuit Synthesis
- Scientific Machine Learning and Optimization
- Randomized Algorithms
- Numerical Software and Numerical Analysis

## Positions

**Staff**, Advanced Technologies Group, NERSC, Berkeley Lab, April 2022 - Present., Computational Research Division, Berkeley Lab, November 2019 - April 2022.**Postdoctoral**Scholar**PhD Researcher**, Department of Computer Science, KU Leuven, September 2015 - September 2019.

## Education

**Doctor of Philosophy (PhD): Computer Science**

2015-2019, KU Leuven, Belgium.**Master of Engineering: Mathematical Engineering**2011-2013, KU Leuven, Belgium.**Master of Science: Astronomy**

2009-2011, KU Leuven, Belgium.**Bachelor of Science: Physics**

2006-2010, UHasselt, Belgium.

## Journal Articles

### Jan Balewski, Mercy G. Amankwah, Roel Van Beeumen, E. Wes Bethel, Talita Perciano, Daan Camps, "Quantum-parallel vectorized data encodings and computations on trapped-ions and transmons QPUs", January 19, 2023,

### Thijs Steel, Daan Camps, Karl Meerbergen, Raf Vandebril, "A Multishift, Multipole Rational QZ Method with Aggressive Early Deflation", SIAM Journal on Matrix Analysis and Applications, February 19, 2021, 42:753-774, doi: 10.1137/19M1249631

In the article “A Rational QZ Method” by D. Camps, K. Meerbergen, and R. Vandebril [SIAM J. Matrix Anal. Appl., 40 (2019), pp. 943--972], we introduced rational QZ (RQZ) methods. Our theoretical examinations revealed that the convergence of the RQZ method is governed by rational subspace iteration, thereby generalizing the classical QZ method, whose convergence relies on polynomial subspace iteration. Moreover the RQZ method operates on a pencil more general than Hessenberg---upper triangular, namely, a Hessenberg pencil, which is a pencil consisting of two Hessenberg matrices. However, the RQZ method can only be made competitive to advanced QZ implementations by using crucial add-ons such as small bulge multishift sweeps, aggressive early deflation, and optimal packing. In this paper we develop these techniques for the RQZ method. In the numerical experiments we compare the results with state-of-the-art routines for the generalized eigenvalue problem and show that the presented method is competitive in terms of speed and accuracy.

### Daan Camps, Roel Van Beeumen, "Approximate quantum circuit synthesis using block encodings", PHYSICAL REVIEW A, November 11, 2020, 102, doi: 10.1103/PhysRevA.102.052411

One of the challenges in quantum computing is the synthesis of unitary operators into quantum circuits with polylogarithmic gate complexity. Exact synthesis of generic unitaries requires an exponential number of gates in general. We propose a novel approximate quantum circuit synthesis technique by relaxing the unitary constraints and interchanging them for ancilla qubits via block encodings. This approach combines smaller block encodings, which are easier to synthesize, into quantum circuits for larger operators. Due to the use of block encodings, our technique is not limited to unitary operators and can be applied for the synthesis of arbitrary operators. We show that operators which can be approximated by a canonical polyadic expression with a polylogarithmic number of terms can be synthesized with polylogarithmic gate complexity with respect to the matrix dimension.

### Daan Camps, Thomas Mach, Raf Vandebril, David Watkins, "On pole-swapping algorithms for the eigenvalue problem", ETNA - Electronic Transactions on Numerical Analysis, September 18, 2020, 52:480-508, doi: 10.1553/etna_vol52s480

Pole-swapping algorithms, which are generalizations of the QZ algorithm for the generalized eigenvalue problem, are studied. A new modular (and therefore more flexible) convergence theory that applies to all pole-swapping algorithms is developed. A key component of all such algorithms is a procedure that swaps two adjacent eigenvalues in a triangular pencil. An improved swapping routine is developed, and its superiority over existing methods is demonstrated by a backward error analysis and numerical tests. The modularity of the new convergence theory and the generality of the pole-swapping approach shed new light on bi-directional chasing algorithms, optimally packed shifts, and bulge pencils, and allow the design of novel algorithms.

### D. Camps, R. Van Beeumen, C. Yang, "Quantum Fourier Transform Revisited", Numerical Linear Algebra and Applications, September 15, 2020, 28:e2331, doi: https://doi.org/10.1002/nla.2331

### Miroslav Urbanek, Daan Camps, Roel Van Beeumen, Wibe A. de Jong, "Chemistry on quantum computers with virtual quantum subspace expansion", Journal of Chemical Theory and Computation, August 21, 2020, 16:5425–5431, doi: 10.1021/acs.jctc.0c00447

### Daan Camps, Karl Meerbergen, Raf Vandebril, "A rational QZ method", SIAM J. Matrix Anal. Appl., January 1, 2019, 40:943--972, doi: 10.1137/18M1170480

### Daan Camps, Karl Meerbergen, Raf Vandebril, "An implicit filter for rational Krylov using core transformations", Linear Algebra Appl., 2019, 561:113--140, doi: 10.1016/j.laa.2018.09.021

### Daan Camps, Nicola Mastronardi, Raf Vandebril, Paul Van Dooren, "Swapping 2 × 2 blocks in the Schur and generalized Schur form", Journal of Computational and Applied Mathematics, 2019, doi: https://doi.org/10.1016/j.cam.2019.05.022

### Borbala Hunyadi, Daan Camps, Laurent Sorber, Wim Van Paesschen, Maarten De Vos, Sabine Van Huffel, Lieven De Lathauwer, "Block term decomposition for modelling epileptic seizures", EURASIP Journal on Advances in Signal Processing, 2014, 2014, doi: 10.1186/1687-6180-2014-139

## Conference Papers

### Jan Balewski, Daan Camps, Katherine Klymko, Andrew Tritt, "Efficient Quantum Counting and Quantum Content-Addressable Memory for DNA similarity", accepted at the IEEE23 quantum week conference, August 1, 2023,

We present QCAM, a quantum analogue of Content-Addressable Memory (CAM), useful for finding matches in two sequences of bit-strings. Our QCAM implementation takes advantage of Grover's search algorithm and proposes a highly-optimized quantum circuit implementation of the QCAM oracle. Our circuit construction uses the parallel uniformly controlled rotation gates, which were used in previous work to generate QBArt encodings. These circuits have a high degree of quantum parallelism which reduces their critical depth. The optimal number of repetitions of the Grover iterator used in QCAM depends on the number of true matches and hence is input dependent. We additionally propose a hardware-efficient implementation of the quantum counting algorithm (HEQC) that can infer the optimal number of Grover iterations from the measurement of a single observable. We demonstrate the QCAM application for computing the Jaccard similarity between two sets of k-mers obtained from two DNA sequences.