Holographic dynamics simulations with a trapped-ion quantum computer

Chertkov, Eli; Bohnet, Justin; Francois, David; Gaebler, John; Gresh, Dan; Hankin, Aaron; Lee, Kenneth; Hayes, David; Neyenhuis, Brian; Stutz, Russell; Potter, Andrew C.; Foss‐Feig, Michael

doi:10.1038/s41567-022-01689-7

Cited by 34 publications

(15 citation statements)

References 35 publications

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“…Moreover, we would like to find an ordering that will yield a qubit-efficient mapping from PEPs networks to quantum circuits. Ideally, we want to make use of mid-circuit measurement and reset so that our circuit contains fewer qubits than are present in the corresponding PEPs state, along the lines of the "holographic" simulation of MPS tensor networks employed in recent works [6][7][8] . To this end, we order the PEPs tensor network in a zig-zag pattern, as depicted in Fig.…”

Section: Mapping Tensor Network To Quantum Channelsmentioning

confidence: 99%

“…Such capability has recently become available on some quantum processors 5 , allowing one to simulate quantum systems consisting of more qubits than are present on the physical device. Several recent works have taken this approach, simulating both static and dynamical one-dimensional (1D) matrix product states (MPS) of quasi-infinite length using a constant number of qubits [6][7][8] . Since most physical quantum states of interest are not maximally entangled, it should not be necessary to use N qubits to simulate most relevant N-qubit states.…”

Section: Introductionmentioning

confidence: 99%

“…Here we take an approach similar to the one used for MPS [6][7][8] , but with two-dimensional (2D) tensor networks. Specifically, we map a subset of projected entangled pair states (PEPs) tensor networks -which represent 2D quantum states on a square lattice -to a quantum circuit, and run the resulting circuit on a trapped-ion quantum device.…”

Section: Introductionmentioning

confidence: 99%

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Simulating Large PEPs Tensor Networks on Small Quantum Devices

MacCormack

Galda²,

Lyon

2022

Preprint

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We systematically map low-bond-dimension PEPs tensor networks to quantum circuits. By measuring and reusing qubits, we demonstrate that a simulation of an N x M square-lattice PEPs network, for arbitrary M, of bond dimension 2 can be performed using N + 2 qubits. We employ this approach to calculate the values of a long-range loop observable in the topological Wen plaquette model by mapping a 3 x 3 PEPs tensor network to a 5-qubit quantum circuit and executing it on the Honeywell System Model H1-1 trapped-ion device. We find that, for this system size, the noisy observable values are sufficient for observing the phase transition from topological to trivial order, as the Wen model is perturbed by a magnetic field term in the Hamiltonian. Our results serve as a proof-of-concept of the utility of the measure-and-reuse approach for simulating large two-dimensional quantum systems on small quantum devices.

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Section: Mapping Tensor Network To Quantum Channelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Simulating Large PEPs Tensor Networks on Small Quantum Devices

MacCormack

Galda²,

Lyon

2022

Preprint

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“…Qubit reuse is an essential ingredient of scalable quantum error correction protocols [9], which require repeated mid-circuit measurements and resets of ancilla qubits to measure error syndromes, and is already available in trapped-ion [10] and superconducting [11] qubit architectures. Recently, qubit-reuse techniques have been used to experimentally prepare and time-evolve large tensor network states on trapped ion quantum computers [12], to study a nonequilibrium phase transition [13], and to perform entanglement spectroscopy of quantum systems [14].…”

Section: Introductionmentioning

confidence: 99%

Qubit-reuse compilation with mid-circuit measurement and reset

DeCross¹,

Chertkov²,

Kohagen³

et al. 2022

Preprint

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A number of commercially available quantum computers, such as those based on trapped-ion or superconducting qubits, can now perform mid-circuit measurements and resets. In addition to being crucial for quantum error correction, this capability can help reduce the number of qubits needed to execute many types of quantum algorithms by measuring qubits as early as possible, resetting them, and reusing them elsewhere in the circuit. In this work, we introduce the idea of qubit-reuse compilation, which takes as input a quantum circuit and produces as output a compiled circuit that requires fewer qubits to execute due to qubit reuse. We present two algorithms for performing qubit-reuse compilation: an exact constraint programming optimization model and a greedy heuristic. We introduce the concept of dual circuits, obtained by exchanging state preparations with measurements and vice versa and reversing time, and show that optimal qubit-reuse compilation requires the same number of qubits to execute a circuit as its dual. We illustrate the performance of these algorithms on a variety of relevant near-term quantum circuits, such as one-dimensional and two-dimensional time-evolution circuits, and numerically benchmark their performance on the quantum adiabatic optimization algorithm (QAOA) applied to the MaxCut problem on random three-regular graphs. To demonstrate the practical benefit of these techniques, we experimentally realize an 80-qubit QAOA MaxCut circuit on the 20-qubit Quantinuum H1-1 trapped ion quantum processor using qubit-reuse compilation algorithms.

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“…While Ĉl is not unitary, implementation of Ll in controlled quantum platforms [29,40,46] seems in reach for the quantum simulation of a MIPT.…”

mentioning

confidence: 99%

Revealing measurement-induced phase transitions by pre-selection

Buchhold

Mueller

Diehl

2022

Preprint

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Pushing forward the understanding of general non-unitary dynamics in controlled quantum platforms has been fueled by the recent discovery of measurement-induced phases and phase transitions. So far, these transi- tions remained largely elusive, since they are masked in standard quantum mechanical observables due to the randomness of measurement outcomes. Here, we establish a general scheme – pre-selection – to make them observable: The outcome randomness is broken explicitly by steering the system towards a representative state, which corresponds to one out of exponentially many possible measurement outcomes. Remarkably, this steer- ing can be chosen so gently that the basic properties of the underlying measurement-induced transition, such as entanglement structure and critical exponents, are not modified. Pre-selection introduces a unique dark or absorbing state with macroscopic order, replacing the maximally mixed stationary state of the unconditioned measurement trajectory ensemble. This creates a link of measurement-induced phase transitions to new forms of quantum absorbing state transitions, which can be detected by standard means via a local order parameter. This insight further enables a quantum simulation strategy, determining the underlying universality class in state-of-the-art quantum platforms without measurement readout.

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Holographic dynamics simulations with a trapped-ion quantum computer

Cited by 34 publications

References 35 publications

Simulating Large PEPs Tensor Networks on Small Quantum Devices

Simulating Large PEPs Tensor Networks on Small Quantum Devices

Qubit-reuse compilation with mid-circuit measurement and reset

Revealing measurement-induced phase transitions by pre-selection

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