Quantum state preparation is an important subroutine in many quantum algorithms. The goal is to encode classical information directly to the quantum state so that it is possible to leverage quantum algorithms for data processing. However, quantum state preparation of arbitrary states scales exponentially in the number of two-qubit gates, and this makes quantum state preparation a very difficult task on quantum computers, especially on near-term noisy devices. This represents a major challenge in achieving quantum advantage. We present and analyze a novel two-step state preparation method where we first minimize the entanglement entropy of the target quantum state, thus transforming the state to one that is easier to prepare. The state with reduced entanglement entropy is then represented as a matrix product state, resulting in a high accuracy preparation of the target state. Our method is suitable for NISQ devices and we give rigorous lower bounds on the accuracy of the prepared state in terms of the entanglement entropy. We benchmark our method with 2D normal distribution and Ricker wavelet states with 6--20 qubits.
Quantum state preparation is an important subroutine in many quantum algorithms. The goal is to encode classical information directly to the quantum state so that it is possible to leverage quantum algorithms for data processing. However, quantum state preparation of arbitrary states scales exponentially in the number of two-qubit gates, and this makes quantum state preparation a very difficult task on quantum computers, especially on near-term noisy devices. This represents a major challenge in achieving quantum advantage. We present and analyze a novel two-step state preparation method where we first minimize the entanglement entropy of the target quantum state, thus transforming the state to one that is easier to prepare. The state with reduced entanglement entropy is then represented as a matrix product state, resulting in a high accuracy preparation of the target state. Our method is suitable for NISQ devices and we give rigorous lower bounds on the accuracy of the prepared state in terms of the entanglement entropy. We benchmark our method with 2D normal distribution and Ricker wavelet states with 6--20 qubits.
Efficient encoding of classical information plays a fundamental role in numerous practical quantum algorithms. However, the preparation of an arbitrary amplitude-encoded state has been proven to be time-consuming, and its deployment on current noisy devices can be challenging. In this work, we propose an improved Matrix Product State(MPS) method preparation protocol with an exponential reduction on the circuit depth, as well as topological adaptability. By refined utilization of the disentangling principle, we also reduce approximately 33% two-qubit gate count. To validate our method, we study various families of functions and distributions with provably bounded MPS rank. Numerical experiments show that our method significantly reduces circuit depth while achieving higher fidelity for states arising in financial and other applications.
Quantum computing promises to provide exponential speed-ups to certain classes of problems. In many such algorithms, a classical vector b is encoded in the amplitudes of a quantum state ∣b⟩. However, efficiently preparing ∣b⟩ is known to be a difficult problem because an arbitrary state of Q qubits generally requires approximately 2Q entangling gates, which results in significant decoherence on today's noisy intermediate-scale quantum (NISQ) computers. We present a deterministic (nonvariational) algorithm that allows us to flexibly reduce the quantum resources required for state preparation in an entanglement-efficient manner. Although this comes at the expense of reduced theoretical fidelity, actual fidelities on current NISQ computers might actually be higher due to reduced decoherence. We show this to be true for various cases of interest, such as the normal and log-normal distributions. For low-entanglement states, our algorithm can prepare states with more than an order of magnitude fewer entangling gates as compared with isometric decomposition.
Quantum circuits for loading probability distributions into quantum states are essential subroutines in quantum algorithms used in physics, finance engineering, and machine learning. The ability to implement these with high accuracy in low-depth quantum circuits is a critical issue. We propose a novel quantum state preparation method for probability distribution with reflection symmetry using matrix product states. By considering reflection symmetry, our method reduces the entanglement of probability distributions and improves the accuracy of approximations by matrix product states. As a result, we improved the accuracy by two orders of magnitude over existing methods using matrix product states. Our approach, characterized by linear scalability with qubit count, is highly advantageous for noisy quantum devices. Also, our demonstration results reveal that the approximation accuracy in tensor networks depends heavily on the bond dimension, with minimal reliance on the number of qubits. Our method is demonstrated for a normal distribution encoded into 10 and 20 qubits on a real quantum processor.
Quantum computing promises to provide exponential speed-ups to certain classes of problems. In many such quantum algorithms, a classical vector b is encoded in the amplitudes of a quantum state ∣b⟩. However, efficient amplitude encoding of an arbitrary vector b in ∣b⟩ is known to be a difficult problem that can reverse the gains of such algorithms. More importantly, an arbitrary quantum state of Q qubits generally requires ∼2Q number of entangling gates, which is problematic for today's Noisy-Intermediate Scale Quantum (NISQ) computers where large numbers of such error-prone gates will result in significant decoherence before initialization is completed. In this work, we demonstrate a deterministic and scalable initialization algorithm that allows for states with low entanglement to be initialized on actual quantum computers with more than an order of magnitude less entangling gates and significantly shallower circuits as compared to isometric decomposition. For states with higher entanglement, optimally approximate states with lower entanglement may be found and initialized with similar performance. We show this to be true for various cases of interest such as the normal and log-normal distributions. Unlike variational approaches, our method requires no classical optimizations in high dimensional spaces and is not plagued with exponentially vanishing gradients or a multitude of local minimas.
Numerous quantum algorithms assume that classical data has already been converted into quantum states, a process known as Quantum State Preparation (QSP). However, achieving precise QSP requires a circuit depth that scales exponentially with the number of qubits, posing a significant challenge to realizing quantum advantage. Recent research explores Parameterized Quantum Circuits (PQCs) as an approximate alternative, offering improved scalability with reduced circuit depth. However, the iterative, state-by-state optimization required by this approach creates substantial runtime overhead, which severely limits its practicality.To improve the efficiency of approximate QSP, we introduce a novel two-stage framework that can potentially generate QSP circuits for arbitrary quantum states. In theoffline training stage, our model learns a direct mapping from target states to circuit parameters, thereby bypassing the need foronline, state-by-state optimizationduring theinference stage. Extensive evaluations show that our approach significantly reduces runtime overhead by up to 132×, making a steady step towards efficient neural approximate QSP.
State preparation algorithms are routines used in many quantum computing applications, from solving a linear system of equations to quantum machine learning. In this paper, we present an exact state preparation algorithm that considers entanglement to reduce the complexity of the generated quantum circuit. The proposed method allows approximation by entanglement reduction. The approximation of an entangled state by two separable states allows a quadratic decrease in the number of CNOT gates in exchange for an approximation error. Through experimental analysis with 7-qubits devices, the approximation error observed through measurements is smaller than the error due to the noise generated by the circuit to prepare the original state.