Deterministic constant-depth preparation of the AKLT state on a quantum processor using fusion measurements

Abstract

The ground state of the spin-1 Affleck, Kennedy, Lieb and Tasaki (AKLT) model is a paradigmatic example of both a matrix product state and a symmetry-protected topological phase, and additionally holds promise as a resource state for measurement-based quantum computation. Having a nonzero correlation length, the AKLT state cannot be exactly prepared by a constant-depth unitary circuit composed of local gates. In this work, we demonstrate that this no-go limit can be evaded by augmenting a constant-depth circuit with fusion measurements, such that the total preparation time is independent of system size and entirely deterministic. We elucidate our preparation scheme using the language of tensor networks, and furthermore show that the Z2 × Z2 symmetry of the AKLT state directly affords this speed-up over previously known preparation methods. To demonstrate the practical advantage of measurement-assisted preparation on noisy intermediate-scale quantum (NISQ) devices, we carry out our protocol on an IBM Quantum processor. We measure both the string order and entanglement spectrum of prepared AKLT chains and, employing these as metrics, find improved results over the known (purely unitary) sequential preparation approach. We conclude with a demonstration of quantum teleportation using the AKLT state prepared by our measurement-assisted scheme. This work thus serves to provide an efficient strategy to prepare a specific resource in the form of the AKLT state and, more broadly, experimentally demonstrates the possibility for realizable improvement in state preparation afforded by measurement-based circuit depth reduction strategies on NISQ-era devices.

Preparing quantum-many body scars on a quantum computer

“…However, the target states in the four cases (labeled by the four possible states of the adjacent qubits) have different normalization factors due to the Fibonacci constraint; therefore, the state of the qubit chain after feedback will not be an equal-amplitude superposition state as desired. For example, this situation should be contrasted with a recently proposed finite-depth deterministic scheme to prepare the AKLT ground state [68], which is able to correct undesired measurement outcomes with a local circuit. However, the correction operation designed in that work makes use of the fact that the AKLT state is a symmetry-protected topological state [83,84], which is a property that is not shared by the state |ξ .…”

“…Sec. III B shows that a stochastic strategy [63][64][65][66][67][68] using measurements and post-selection can reduce the circuit depth to a constant at the price of an exponential postselection overhead. Finally, in Sec.…”

Sketching phase diagrams using low-depth variational quantum algorithms

“…We use the AKLT state as the initial state for VQE and to enable our ansatz to produce states with different S α total (α = x, y, z) we include the two spin-1/2 degrees of freedom at either end of the chain in the variational parameters. As an MPS with bond dimension 2 the AKLT state can be prepared in linear depth with the use of one ancilla qubit [30] or using its symmetries and fusion measurements even in constant depth [31].…”

Dissipative preparation and stabilization of many-body quantum states in a superconducting qutrit array

“…Since the MPS representation efficiently describes a large variety of low-energy states of manybody Hamiltonians, protocols that can produce the AKLT state may be generalized for a range of applications. Compared with the typical preparation method of the AKLT state based on its matrix product rep-resentation via postselection [15,16], or based on sequential unitary gates [7] and assisted by measurements [17], driven-dissipative methods create the manybody state with robustness and self-correcting features. Here, the system coherence can last much longer than the lifetime of a single component.…”