7,855 research outputs found
Benchmarking the performance of portfolio optimization with QAOA
We present a detailed study of portfolio optimization using different
versions of the quantum approximate optimization algorithm (QAOA). For a given
list of assets, the portfolio optimization problem is formulated as quadratic
binary optimization constrained on the number of assets contained in the
portfolio. QAOA has been suggested as a possible candidate for solving this
problem (and similar combinatorial optimization problems) more efficiently than
classical computers in the case of a sufficiently large number of assets.
However, the practical implementation of this algorithm requires a careful
consideration of several technical issues, not all of which are discussed in
the present literature. The present article intends to fill this gap and
thereby provide the reader with a useful guide for applying QAOA to the
portfolio optimization problem (and similar problems). In particular, we will
discuss several possible choices of the variational form and of different
classical algorithms for finding the corresponding optimized parameters.
Viewing at the application of QAOA on error-prone NISQ hardware, we also
analyze the influence of statistical sampling errors (due to a finite number of
shots) and gate and readout errors (due to imperfect quantum hardware).
Finally, we define a criterion for distinguishing between "easy" and "hard"
instances of the portfolio optimization problemComment: 28 pages, 8 figure
Quantum Portfolios
Quantum computation holds promise for the solution of many intractable
problems. However, since many quantum algorithms are stochastic in nature they
can only find the solution of hard problems probabilistically. Thus the
efficiency of the algorithms has to be characterized both by the expected time
to completion {\it and} the associated variance. In order to minimize both the
running time and its uncertainty, we show that portfolios of quantum algorithms
analogous to those of finance can outperform single algorithms when applied to
the NP-complete problems such as 3-SAT.Comment: revision includes additional data and corrects minor typo
Portfolio Optimization with Digitized-Counterdiabatic Quantum Algorithms
We consider digitized-counterdiabatic quantum computing as an advanced
paradigm to approach quantum advantage for industrial applications in the NISQ
era. We apply this concept to investigate a discrete mean-variance portfolio
optimization problem, showing its usefulness in a key finance application. Our
analysis shows a drastic improvement in the success probabilities of the
resulting digital quantum algorithm when approximate counterdiabatic techniques
are introduced. Along these lines, we discuss the enhanced performance of our
methods over variational quantum algorithms like QAOA and DC-QAOA.Comment: 8 pages, 4 figure
Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer
We solve a multi-period portfolio optimization problem using D-Wave Systems'
quantum annealer. We derive a formulation of the problem, discuss several
possible integer encoding schemes, and present numerical examples that show
high success rates. The formulation incorporates transaction costs (including
permanent and temporary market impact), and, significantly, the solution does
not require the inversion of a covariance matrix. The discrete multi-period
portfolio optimization problem we solve is significantly harder than the
continuous variable problem. We present insight into how results may be
improved using suitable software enhancements, and why current quantum
annealing technology limits the size of problem that can be successfully solved
today. The formulation presented is specifically designed to be scalable, with
the expectation that as quantum annealing technology improves, larger problems
will be solvable using the same techniques.Comment: 7 pages; expanded and update
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