Numerical analysis of quantum circuits for state preparation and unitary operator synthesis

Abstract

We perform optimal-control-theory calculations to determine the minimum number of two-qubit CNOT gates needed to perform quantum state preparation and unitary operator synthesis for few-qubit systems. By considering all possible gate configurations, we determine the maximum achievable fidelity as a function of quantum circuit size. This information allows us to identify the minimum circuit size needed for a specific target operation and enumerate the different gate configurations that allow a perfect implementation of the operation. We find that there are a large number of configurations that all produce the desired result, even at the minimum number of gates. We also show that the number of entangling gates can be reduced if we use multi-qubit entangling gates instead of two-qubit CNOT gates, as one might expect based on parameter counting calculations. In addition to treating the general case of arbitrary target states or unitary operators, we apply the numerical approach to the special case of synthesizing the multi-qubit Toffoli gate. This approach can be used to investigate any other specific few-qubit task and provides insight into the tightness of different bounds in the literature.

arXiv comment12 pages (two-column), 7 figures

References in corpus (23)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Elementary gates for quantum computation
• Quantum Computing
• Strong quantum computational advantage using a superconducting quantum processor
• Natural and artificial atoms for quantum computation
• Optimal Quantum Circuits for General Two-Qubit Gates
• Optimal Creation of Entanglement Using a Two--Qubit Gate
• Quantum-state preparation with universal gate decompositions
• Minimal Universal Two-qubit Quantum Circuits
• A universal quantum circuit for two-qubit transformations with three CNOT gates
• Efficient decomposition of quantum gates
• Quantum circuits with uniformly controlled one-qubit gates
• Variational Quantum State Eigensolver
• Approximation by Quantum Circuits
• Decompositions of general quantum gates
• Compiling quantum algorithms for architectures with multi-qubit gates
• Linear-Depth Quantum Circuits for n-qubit Toffoli gates with no Ancilla
• Approaching the theoretical limit in quantum gate decomposition
• Approximate Quantum Circuit Synthesis using Block-Encodings
• How many CNOT gates does it take to generate a three-qubit state ?
• Speed limits for two-qubit gates with weakly anharmonic qubits
• Quantum circuit synthesis using Householder transformations
• Measurement-Free Ultrafast Quantum Error Correction by Using Multi-Controlled Gates in Higher-Dimensional State Space

Cited by in corpus (11)

• Quantum circuit synthesis via a random combinatorial search
• Exploring the optimality of approximate state preparation quantum circuits with a genetic algorithm
• Probabilistic state synthesis based on optimal convex approximation
• Numerical circuit synthesis and compilation for multi-state preparation
• Characterization of overparametrization in the simulation of realistic quantum systems
• Quantum Circuit Distillation and Compression
• Multi-target quantum compilation algorithm
• Automated Synthesis of Quantum Algorithms via Classical Numerical Techniques
• A Novel Single-Layer Quantum Neural Network for Approximate SRBB-Based Unitary Synthesis
• Size-Consistent Quantum Chemistry on Quantum Computers
• Quantum circuit synthesis with SQiSW