Observing and braiding topological Majorana modes on programmable quantum simulators

Harle, Nikhil; Shtanko, Oles; Movassagh, Ramis

doi:10.48550/arxiv.2203.15083

“…The combined application of all of these error mitigation techniques enabled us to simulate systems of up to 7 qubits, whereas a previous experiment preparing Majo-rana zero modes used only 3 qubits. We note that References [26,27] also prepared topological Majorana modes on noisy quantum processors but those works took a different approach which is not directly comparable to this work. Our results build on previous experiments suggesting that error mitigation will be crucial to achieving practical applications on NISQ hardware, and they contribute to the growing library of experiments that can serve as device benchmarks as we work towards those practical applications.…”

Section: Discussionmentioning

confidence: 92%

Simulating Majorana zero modes on a noisy quantum processor

Sung¹,

Rančić²,

Lanes³

et al. 2022

Preprint

0

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The simulation of systems of interacting fermions is one of the most anticipated applications of quantum computers. The most interesting simulations will require a fault-tolerant quantum computer, and building such a device remains a long-term goal. However, the capabilities of existing noisy quantum processors have steadily improved, sparking an interest in running simulations that, while not necessarily classically intractable, may serve as device benchmarks and help elucidate the challenges to achieving practical applications on near-term devices. Systems of non-interacting fermions are ideally suited to serve these purposes. While they display rich physics and generate highly entangled states when simulated on a quantum processor, their classical tractability enables experimental results to be verified even at large system sizes that would typically defy classical simulation. In this work, we use a noisy superconducting quantum processor to prepare Majorana zero modes as eigenstates of the Kitaev chain Hamiltonian, a model of non-interacting fermions. Our work builds on previous experiments with non-interacting fermionic systems. Previous work demonstrated error mitigation techniques applicable to the special case of Slater determinants. Here, we show how to extend these techniques to the case of general fermionic Gaussian states, and demonstrate them by preparing Majorana zero modes on systems of up to 7 qubits.

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“…The combined application of all of these error mitigation techniques enabled us to simulate systems of up to seven qubits, whereas a previous experiment preparing MZMs used only three qubits. We note that [27,28] performed larger experiments (up to 21 and 47 qubits, respectively) with Majorana modes on noisy quantum processors by periodically driving the qubits with a Floquet unitary, implementing time-varying Hamiltonians in both non-interacting and interacting regimes. Those works do not directly prepare eigenstates, but rather extract experimental signatures of the Majorana modes via spectroscopic measurements.…”

Section: Discussionmentioning

confidence: 99%

Simulating Majorana zero modes on a noisy quantum processor

Sung¹,

Rančić²,

Lanes³

et al. 2023

Quantum Sci. Technol.

View full text Add to dashboard Cite

The simulation of systems of interacting fermions is one of the most anticipated applications of quantum computers. The most interesting simulations will require a fault-tolerant quantum computer, and building such a device remains a long-term goal. However, the capabilities of existing noisy quantum processors have steadily improved, sparking an interest in running simulations that, while not necessarily classically intractable, may serve as device benchmarks and help elucidate the challenges to achieving practical applications on near-term devices. Systems of non-interacting fermions are ideally suited to serve these purposes. While they display rich physics and generate highly entangled states when simulated on a quantum processor, their classical tractability enables experimental results to be verified even at large system sizes that would typically defy classical simulation. In this work, we use a noisy superconducting quantum processor to prepare Majorana zero modes as eigenstates of the Kitaev chain Hamiltonian, a model of non-interacting fermions. Our work builds on previous experiments with non-interacting fermionic systems. Previous work demonstrated error mitigation techniques applicable to the special case of Slater determinants. Here, we show how to extend these techniques to the case of general fermionic Gaussian states, and demonstrate them by preparing Majorana zero modes on systems of up to 7 qubits.

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“…Furthermore, the braiding of Majorana fermions on quantum computers has been studied in Refs. [15,16].…”

Section: Introductionmentioning

confidence: 99%

Braiding fractional quantum Hall quasiholes on a superconducting quantum processor

Kirmani¹,

Wang²,

Ghaemi³

et al. 2023

Preprint

0

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Direct experimental detection of anyonic exchange statistics in fractional quantum Hall systems by braiding the excitations and measuring the wave-function phase is an enormous challenge. Here, we use a small, noisy quantum computer to emulate direct braiding within the framework of a simplified model applicable to a thin cylinder geometry and measure the topological phase. Our algorithm first prepares the ground state with two quasiholes. It then applies a unitary operation controlled by an ancilla, corresponding to a sequence of adiabatic evolutions that take one quasihole around the other. We finally extract the phase of the wave function from measuring the ancilla with a compound error mitigation strategy. Our results open a new avenue for studying braiding statistics in fractional Hall states.

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Observing and braiding topological Majorana modes on programmable quantum simulators

Cited by 4 publications

References 44 publications

Simulating Majorana zero modes on a noisy quantum processor

Simulating Majorana zero modes on a noisy quantum processor

Simulating Majorana zero modes on a noisy quantum processor

Braiding fractional quantum Hall quasiholes on a superconducting quantum processor

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