Nonunitary gates using measurements only

Abstract

Measurement-based quantum computation (MBQC) is a universal platform to realize unitary gates, only using measurements which act on a pre-prepared entangled resource state. By deforming the measurement bases, as well as the geometry of the resource state, we show that MBQC circuits always transmit and act on the input state but generally realize nonunitary logical gates. In contrast to the stabilizer formalism which is often used for unitary gates, we find that ZX calculus is an ideal computation method of these nonunitary gates. As opposed to unitary gates, nonunitary gates can not be applied with certainty, due to the randomness of quantum measurements. We maximize the success probability of realizing nonunitary gates, and discuss applications including imaginary time evolution, which we demonstrate on a noisy intermediate scale quantum device.

References in corpus (51)

• Quantum algorithm for solving linear systems of equations
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• QuTiP: An open-source Python framework for the dynamics of open quantum systems
• Persistent entanglement in arrays of interacting particles
• Measurement-based quantum computation with cluster states
• Predicting Many Properties of a Quantum System from Very Few Measurements
• The ITensor Software Library for Tensor Network Calculations
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Quantum Zeno Effect and the Many-body Entanglement Transition
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Probing entanglement entropy via randomized measurements
• Quantum Steering
• Unitary-projective entanglement dynamics
• Quantum steering: a review with focus on semidefinite programming
• Dynamical purification phase transitions induced by quantum measurements
• The randomized measurement toolbox
• Entanglement of Quantum Evolutions
• Symmetry-resolved entanglement in many-body systems
• Observation of measurement-induced quantum phases in a trapped-ion quantum computer
• Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
• Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems
• Learning the quantum algorithm for state overlap
• Operator space entanglement entropy in transverse Ising chain
• Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
• Real- and imaginary-time evolution with compressed quantum circuits
• Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in many-body quantum states
• Symmetry-protected phases for measurement-based quantum computation
• Operator entanglement entropy of the time evolution operator in chaotic systems
• Identification of symmetry-protected topological states on noisy quantum computers
• Quantum Computation of Finite-Temperature Static and Dynamical Properties of Spin Systems Using Quantum Imaginary Time Evolution
• Unitary $n$-designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of Rényi entropies
• Hadamard-free circuits expose the structure of the Clifford group
• Measurement-induced steering of quantum systems
• A computationally universal phase of quantum matter
• Symmetry-resolved entanglement in symmetry-protected topological phases
• Entanglement barrier and its symmetry resolution: theory and experiment
• Entanglement spectroscopy on a quantum computer
• Nonunitary quantum circuit
• Symmetry-protected topological phases with uniform computational power in one dimension
• Entanglement-magic separation in hybrid quantum circuits
• Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry
• Observing Floquet topological order by symmetry resolution
• Non-Unitary Quantum Computation in the Ground Space of Local Hamiltonians
• Complex Time Evolution in Tensor Networks
• Measurement-Based Time Evolution for Quantum Simulation of Fermionic Systems
• Playing quantum nonlocal games with six noisy qubits on the cloud
• Quantum computational advantage attested by nonlocal games with the cyclic cluster state
• Complete Flow-Preserving Rewrite Rules for MBQC Patterns with Pauli Measurements
• Multipartite entanglement and quantum error identification in $D$-dimensional cluster states
• Redundant string symmetry-based error correction: Demonstrations on quantum devices