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Työväentutkimus Vuosikirja

Approximate State Preparation for Noisy Quantum Computers

Tom Rindell

Published Oct 25, 2025• 0 citations
OpenAlex

Abstract

Any quantum computation begins with some process of state preparation where the prepared state functions as the input value for the computation. For most states, preparation becomes exceedingly more demanding as the number of qubits increases. Moreover, the noise present in the gate operations further complicates the process by contributing to the decoherence of the state. This thesis studies possible approaches to address these problems. For a reader not familiar with the basic principles of quantum computing, Chapter 2 should provide a sufficient summary in order to follow through the rest of the thesis. In Chapter 3 a standard method of state preparation is presented in detail for 2 and 4-qubit cases and then generalized for an arbitrary number of qubits. However in order to present a comprehensive coverage, the necessary gate decompositions for state preparation are first presented and proved. The number of required quantum gates for the preparation of a general state increases exponentially in the number of qubits. Each gate introduces a small error in the computation, the cumulative effect of which can make the decoherence in the final state very severe. Therefore it is perhaps more suitable to prepare a less complex approximation of the target state with fewer gates to obtain better fidelity in the presence of noise. For this purpose, two methods are presented: low-rank state preparation algorithm (LRSP) and a genetic algorithm. LRSP provides a systematic way to generate circuits for approximate state preparation; however, for any given state LRSP can make only very specific approximations, giving us a very limited range of circuits to work with. For this reason our work introduces a genetic algorithm to iterate over the LRSP circuits and to provide a wider range of candidate circuits for approximate state preparation. Using this approach we prepared a range of approximate state preparation circuits for 1000 different Haar-random states and ran them with simulated noise on IBM Qiskit FakeVigo backend. We found that the numerical results matched closely with our theoretical prediction and showed that when run on a noisy quantum computer, the highest fidelity is obtained not for the exact state preparation circuit but for a shorter approximate circuit.

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Any quantum computation begins with some process of state preparation where the prepared state functions as the input value for the computation. For most states, preparation becomes exceedingly more demanding as the number of qubits increases. Moreover, the noise present in the gate operations further complicates the process by contributing to the decoherence of the state. This thesis studies possible approaches to address these problems. For a reader not familiar with the basic principles of quantum computing, Chapter 2 should provide a sufficient summary in order to follow through the rest of the thesis. In Chapter 3 a standard method of state preparation is presented in detail for 2 and 4-qubit cases and then generalized for an arbitrary number of qubits. However in order to present a comprehensive coverage, the necessary gate decompositions for state preparation are first presented and proved. The number of required quantum gates for the preparation of a general state increases exponentially in the number of qubits. Each gate introduces a small error in the computation, the cumulative effect of which can make the decoherence in the final state very severe. Therefore it is perhaps more suitable to prepare a less complex approximation of the target state with fewer gates to obtain better fidelity in the presence of noise. For this purpose, two methods are presented: low-rank state preparation algorithm (LRSP) and a genetic algorithm. LRSP provides a systematic way to generate circuits for approximate state preparation; however, for any given state LRSP can make only very specific approximations, giving us a very limited range of circuits to work with. For this reason our work introduces a genetic algorithm to iterate over the LRSP circuits and to provide a wider range of candidate circuits for approximate state preparation. Using this approach we prepared a range of approximate state preparation circuits for 1000 different Haar-random states and ran them with simulated noise on IBM Qiskit FakeVigo backend. We found that the numerical results matched closely with our theoretical prediction and showed that when run on a noisy quantum computer, the highest fidelity is obtained not for the exact state preparation circuit but for a shorter approximate circuit.
We study the approximate state preparation problem on noisy intermediate-scale quantum (NISQ) computers by applying a genetic algorithm to generate quantum circuits for state preparation. The algorithm can account for the specific characteristics of the physical machine in the evaluation of circuits, such as the native gate set and qubit connectivity. We use our genetic algorithm to optimize the circuits provided by the low-rank state preparation algorithm introduced by Araujo et al., and find substantial improvements to the fidelity in preparing Haar random states with a limited number of CNOT gates. Moreover, we observe that already for a 5-qubit quantum processor with limited qubit connectivity and significant noise levels (IBM Falcon 5T), the maximal fidelity for Haar random states is achieved by a short approximate state preparation circuit instead of the exact preparation circuit. We also present a theoretical analysis of approximate state preparation circuit complexity to motivate our findings. Our genetic algorithm for quantum circuit discovery is freely available at https://github.com/beratyenilen/qc-ga.
We study the approximate state preparation problem on noisy intermediate-scale quantum (NISQ) computers by applying a genetic algorithm to generate quantum circuits for state preparation. The algorithm can account for the specific characteristics of the physical machine in the evaluation of circuits, such as the native gate set and qubit connectivity. We use our genetic algorithm to optimize the circuits provided by the low-rank state preparation algorithm introduced by Araujo et al., and find substantial improvements to the fidelity in preparing Haar random states with a limited number of CNOT gates. Moreover, we observe that already for a 5-qubit quantum processor with limited qubit connectivity and significant noise levels (IBM Falcon 5T), the maximal fidelity for Haar random states is achieved by a short approximate state preparation circuit instead of the exact preparation circuit. We also present a theoretical analysis of approximate state preparation circuit complexity to motivate our findings. Our genetic algorithm for quantum circuit discovery is freely available at https://github.com/beratyenilen/qc-ga .
The efficient preparation of quantum states is an important step in the execution of many quantum algorithms. In the noisy intermediate-scale quantum (NISQ) computing era, this is a significant challenge given quantum resources are scarce and typically only low-depth quantum circuits can be implemented on physical devices. We present a genetic algorithm for state preparation (GASP) which generates relatively low-depth quantum circuits for initialising a quantum computer in a specified quantum state. The method uses a basis set of [Formula: see text], [Formula: see text], [Formula: see text], and CNOT gates and a genetic algorithm to systematically generate circuits to synthesize the target state to the required fidelity. GASP can produce more efficient circuits of a given accuracy with lower depth and gate counts than other methods. This variability of the required accuracy facilitates overall higher accuracy on implementation, as error accumulation in high-depth circuits can be avoided. We directly compare the method to the state initialisation technique based on an exact synthesis technique by implemented in IBM Qiskit simulated with noise and implemented on physical IBM Quantum devices. Results achieved by GASP outperform Qiskit's exact general circuit synthesis method on a variety of states such as Gaussian states and W-states, and consistently show the method reduces the number of gates required for the quantum circuits to generate these quantum states to the required accuracy.
The efficient preparation of quantum states is an important step in the execution of many quantum algorithms. In the noisy intermediate-scale quantum (NISQ) computing era, this is a significant challenge given quantum resources are scarce and typically only low-depth quantum circuits can be implemented on physical devices. We present a genetic algorithm for state preparation (GASP) which generates relatively low-depth quantum circuits for initialising a quantum computer in a specified quantum state. The method uses a basis set of R_x, R_y, R_z, and CNOT gates and a genetic algorithm to systematically generate circuits to synthesize the target state to the required fidelity. GASP can produce more efficient circuits of a given accuracy with lower depth and gate counts than other methods. This variability of the required accuracy facilitates overall higher accuracy on implementation, as error accumulation in high-depth circuits can be avoided. We directly compare the method to the state initialisation technique based on an exact synthesis technique by implemented in IBM Qiskit simulated with noise and implemented on physical IBM Quantum devices. Results achieved by GASP outperform Qiskit's exact general circuit synthesis method on a variety of states such as Gaussian states and W-states, and consistently show the method reduces the number of gates required for the quantum circuits to generate these quantum states to the required accuracy.
Quantum state preparation is a crucial process within numerous quantum algorithms, and the need for efficient initialization of quantum registers is ever increasing as demand for useful quantum computing grows. The problem arises as the number of qubits to be initialized grows, the circuits required to implement the desired state also exponentially increase in size leading to loss of fidelity to noise. This is mainly due to the susceptibility to environmental effects of the non-Clifford T gate, whose use should thus be reduced as much as possible. In this paper, we present and utilize a genetic algorithm for state preparation circuits consisting of gates from the Clifford + T gate set and optimize them in T-Count as to reduce the impact of noise. Whilst the method presented here does not always produce the most accurate circuits in terms of fidelity, it can generate high-fidelity, non-trivial quantum states such as quantum Fourier transform states. In addition, our algorithm does automatically generate fault tolerantly implementable solutions where the number of the most error prone components is reduced. We present an evaluation of the algorithm when trialed against preparing random, Poisson probability distribution, W, GHZ, and quantum Fourier transform states. We also experimentally demonstrate the scalability issues as qubit count increases, which highlights the need for further optimization of the search process.
Ubiquitous in quantum computing is the step to encode data into a quantum state. This process is called quantum state preparation, and its complexity for nonstructured data is exponential on the number of qubits. Several works address this problem, for instance, by using variational methods that train a fixed depth circuit with manageable complexity. These methods have their limitations, as the lack of a back-propagation technique and barren plateaus. This work proposes an algorithm to reduce state preparation circuit depth by offloading computational complexity to a classical computer. The initialized quantum state can be exact or an approximation, and we show that the approximation is better on today’s quantum processors than the initialization of the original state. Experimental evaluation demonstrates that the proposed method enables more efficient initialization of probability distributions in a quantum state.