Abstract In this work, we report a novel quantum state reconstruction process based on the disentanglement algorithm. We propose a sequential disentanglement scheme, which can transform an unknown quantum state into a product of computational zero states. The inverse evolution of the zero states reconstructs the quantum state up to an overall phase. By sequentially disentangling the qubits one by one, we reduce the required measurements with only individual qubit measurement and identify the transformation unitary efficiently. Variational quantum circuit and reinforcement learning methods are used for the quantum circuit design for continuous and discrete quantum gates implementation. Demonstrations with our proposal for the reconstruction of the random states are presented. Our method is universal and imposes no specific ansatz or constraint on the quantum state.
Abstract In this work, we report a novel quantum state reconstruction process based on the disentanglement algorithm. We propose a sequential disentanglement scheme, which can transform an unknown quantum state into a product of computational zero states. The inverse evolution of the zero states reconstructs the quantum state up to an overall phase. By sequentially disentangling the qubits one by one, we reduce the required measurements with only individual qubit measurement and identify the transformation unitary efficiently. Variational quantum circuit and reinforcement learning methods are used for the quantum circuit design for continuous and discrete quantum gates implementation. Demonstrations with our proposal for the reconstruction of the random states are presented. Our method is universal and imposes no specific ansatz or constraint on the quantum state.
Abstract Quantum state reconstruction is an important tool in quantum information science. Based on the idea of sequential disentanglement, we propose a quantum state reconstruction algorithm that reduces the number of parameters to be optimized. For transforming the arbitrary quantum state into a tensor product of 0 states in the computational basis, we give the conclusion that it is not necessary to apply a global unitary transformation in the optimization of sequential disentanglement. In detail, for disentangling arbitrary n-qubit pure state ψ into ψ ˜ 0 , we simply apply the quantum operator U to n − n − 1 2 qubits. This means that the number of parameters that need to be optimized has been further reduced, thereby saving quantum resources. Finally, numerical simulations verify the feasibility of the proposed algorithm.
Using partial knowledge of a quantum state to control multiqubit entanglement is a largely unexplored paradigm in the emerging field of quantum interactive dynamics with the potential to address outstanding challenges in quantum state preparation and compression, quantum control, and quantum complexity. We present a deep reinforcement learning (RL) approach using an actor-critic algorithm for constructing short disentangling circuits for states with up to 16 qubits. With access to only two-qubit reduced density matrices, our agent decides which pairs of qubits to apply two-qubit gates on; requiring only local information makes it directly applicable on modern NISQ devices, as we demonstrated experimentally on a trapped-ion quantum computer. Utilizing a permutation-equivariant transformer architecture, the agent can autonomously identify qubit permutations within the state, and adjusts the disentangling protocol accordingly. Once trained, it provides circuits from different initial states without further optimization. We demonstrate the agent's ability to identify and exploit the entanglement structure of multi-qubit states. We analyze the disentangling circuits constructed by the agent for 4- and 5-qubit Haar-random states, and observe strong correlations between consecutive gates and among the qubits involved. Through extensive benchmarking, we show the efficacy of the RL approach to find disentangling protocols with minimal gate resources. We explore the resilience of our trained agents to noise, highlighting their potential for real-world quantum computing applications. Analyzing optimal disentangling protocols, we report a general circuit to prepare an arbitrary 4-qubit state using at most 5 two-qubit (10 CNOT) gates.
Current experimental quantum computing devices are limited by noise, mainly originating from entangling gates. If an efficient gate sequence for an operation is unknown, one often employs layered parameterized quantum circuits, especially hardware-efficient ansätze, with fixed entangling layer structures. We demonstrate a reinforcement learning algorithm to improve on these by optimizing the entangling gate sequence in the task of quantum state preparation. This allows us to restrict the required number of CNOT gates while taking the qubit connectivity architecture into account. Recent advancements using reinforcement learning have already demonstrated the power of this technique when optimizing the circuit for a sequence of non-parameterized gates. We extend this approach to parameterized gate sets by incorporating general single-qubit unitaries, thus allowing us to consistently reach higher state preparation fidelities at the same number of CNOT gates compared to a hardware-efficient ansatz.
Variational quantum algorithms have been a promising candidate to utilize near-term quantum devices to solve real-world problems. The powerfulness of variational quantum algorithms is ultimately determined by the expressiveness of the underlying quantum circuit ansatz for a given problem. In this work, we propose a sequentially generated circuit ansatz, which naturally adapts to 1D, 2D, 3D quantum many-body problems. Specifically, in 1D our ansatz can efficiently generate any matrix product states with a fixed bond dimension, while in 2D our ansatz generates the string-bond states. As applications, we demonstrate that our ansatz can be used to accurately reconstruct unknown pure and mixed quantum states which can be represented as matrix product states, and that our ansatz is more efficient compared to several alternatives in finding the ground states of some prototypical quantum many-body systems as well as quantum chemistry systems, in terms of the number of quantum gate operations.
Identifying phases of matter is a complicated process, especially in quantum theory, where the complexity of the ground state appears to rise exponentially with system size. Traditionally, physicists have been responsible for identifying suitable order parameters for the identification of the various phases. The entanglement of quantum many-body systems exhibits rich structures and can be determined over the phase diagram. The intriguing question of the relationship between entanglement and quantum phase transition has recently been addressed. As a method that works directly on the entanglement structure, disentanglement can provide factual information on the entanglement structure. In this work, we follow a radically different approach to identifying quantum phases: we utilize reinforcement learning (RL) approaches to develop an efficient variational quantum circuit that disentangles the ground-state of Ising spin chain systems. We show that the specified quantum circuit structure of the tested models correlates to a phase transition in the behaviour of the entanglement. We show a similar universal quantum circuit structure for ground states in the same phase to reduce entanglement entropy. This study sheds light on characterizing quantum phases with the types of entanglement structures of the ground states.
The quantum state generation problem is a major research goal of quantum control and quantum variational algorithms, which use iterative optimization methods to evolve the initial state to the target state. The Twin Delayed Deep Deterministic Policy (TD3) algorithm in reinforcement learning achieves high learning efficiency and better stability in continuous control tasks. Here, using the TD3, we propose a new quantum state preparation method that does not require case-by-case optimization, to find a suitable evolution path to obtain the desired state. Specifically, we input the initial state into the trained actor-network, which can output the parameters of the unitary gates step by step, thus gradually evolving the initial state to the fixed quantum state. According to the reversibility of the unitary transformation, we can obtain a sequence of unitary gates to evolve the fixed state to the desired state. To verify the effectiveness of the algorithm, we perform simulations for one-qubit, two-qubit, and four-qubit cases, and the results show that the trained actor-network can provide appropriate unitary transformations to obtain the fixed state.