Conditions for superdecoherence

Decoherence is the main obstacle to quantum computation. The decoherence rate per qubit is typically assumed to be constant. It is known, however, that quantum registers coupling to a single reservoir can show a decoherence rate per qubit that increases linearly with the number of qubits. This effect has been referred to as superdecoherence, and has been suggested to pose a threat to the scalability of quantum computation. Here, we show that superdecoherence is absent when the spectrum of the single reservoir is continuous, rather than discrete. The reason of this absence, is that, as the number of qubits is increased, a quantum register inevitably becomes susceptible to an ever narrower bandwidth of frequencies in the reservoir. Furthermore, we show that for superdecoherence to occur in a reservoir with a discrete spectrum, one of the frequencies in the reservoir has to coincide exactly with the frequency the quantum register is most susceptible to. We thus fully resolve the conditions that determine the presence or absence of superdecoherence. We conclude that superdecoherence is easily avoidable in practical realizations of quantum computers.Comment: 20 pages, 6 figures, quantum journal accepted versio

Dynamical fidelity susceptibility of decoherence-free subspaces

In idealized models of a quantum register and its environment, quantum information can be stored indefinitely by encoding it into a decoherence-free subspace (DFS). Nevertheless, perturbations to the idealized register-environment coupling will cause decoherence in any realistic setting. Expanding a measure for state preservation, the dynamical fidelity, in powers of the strength of the perturbations, we prove stability to linear order is a generic property of quantum state evolution. The effect of noise perturbation is quantified by a concise expression for the strength of the quadratic, leading order, which we define as the dynamical fidelity susceptibility of DFSs. Under the physical restriction that noise acts on the register $k$-locally, this susceptibility is bounded from above by a polynomial in the system size. These general results are illustrated by two physically relevant examples. Knowledge of the susceptibility can be used to increase coherence times of future quantum computers.Comment: 10 pages, 0 figures, corrected typos, section added, changed notatio

Conditions for superdecoherence

Decoherence is the main obstacle to quantum computation. The decoherence rate perqubit is typically assumed to be constant. It is known, however, that quantum registers coupling to a single reservoir can show a decoherence rate per qubit that increases linearly with the number of qubits. This effect has been referred to as superdecoherence, and has been suggested to pose a threat to the scalability of quantum computation. Here, we show that superdecoherence is absent when the spectrum of the single reservoir is continuous, rather than discrete. The reason of this absence, is that, as the number of qubits is increased, a quantum register inevitably becomes susceptible to an ever narrower bandwidth of frequencies in the reservoir. Furthermore, we show that for superdecoherence to occur in a reservoir with a discrete spectrum, one of the frequencies in the reservoir has to coincide exactly with the frequency the quantum register is most susceptible to. We thus fully resolve the conditions that determine the presence or absence of superdecoherence. We conclude that superdecoherence is easily avoidable in practical realizations of quantum computers

Entangled wavepackets in the vacuum

Motivated by the black hole firewall problem, we find highly entangled pairs of spatially localized modes in quantum field theory. We demonstrate that appropriately chosen wavepackets localized outside the horizon are nearly purified by 'mirror' modes behind the horizon. In addition, we calculate the entanglement entropy of a single localized wavepacket in the Minkowski vacuum. In all cases we study, the quantum state of the system becomes pure in the limit that the wavepackets delocalize; we quantify the trade-off between localization and purity.Comment: 33 pages, 4 figures. v3: typos correcte

Dynamical fidelity susceptibility of decoherence-free subspaces

In idealized models of a quantum register and its environment, quantum information can be stored indefinitely by encoding it into a decoherence-free subspace (DFS). Nevertheless, perturbations to the idealized register-environment coupling will cause decoherence in any realistic setting. Expanding a measure for state preservation, the dynamical fidelity, in powers of the strength of the perturbations, we prove stability to linear order is a generic property of quantum state evolution. The effect of noise perturbation is quantified by a concise expression for the strength of the quadratic leading order, which we define as the dynamical fidelity susceptibility of DFSs. Under the physical restriction that noise acts on the register k-locally, this susceptibility is bounded from above by a polynomial in the system size. These general results are illustrated by two physically relevant examples. Knowledge of the susceptibility can be used to increase coherence times of future quantum computers

Conditions for superdecoherence

Decoherence is the main obstacle to quantum computation. The decoherence rate perqubit is typically assumed to be constant. It is known, however, that quantum registers coupling to a single reservoir can show a decoherence rate per qubit that increases linearly with the number of qubits. This effect has been referred to as superdecoherence, and has been suggested to pose a threat to the scalability of quantum computation. Here, we show that superdecoherence is absent when the spectrum of the single reservoir is continuous, rather than discrete. The reason of this absence, is that, as the number of qubits is increased, a quantum register inevitably becomes susceptible to an ever narrower bandwidth of frequencies in the reservoir. Furthermore, we show that for superdecoherence to occur in a reservoir with a discrete spectrum, one of the frequencies in the reservoir has to coincide exactly with the frequency the quantum register is most susceptible to. We thus fully resolve the conditions that determine the presence or absence of superdecoherence. We conclude that superdecoherence is easily avoidable in practical realizations of quantum computers

Ability of error correlations to improve the performance of variational quantum algorithms

The quantum approximate optimization algorithm (QAOA) has the potential of providing a useful quantum advantage on noisy intermediate-scale quantum (NISQ) devices. The effects of uncorrelated noise on variational quantum algorithms such as QAOA have been studied intensively. Recent experimental results, however, show that the errors impacting NISQ devices are significantly correlated. We introduce a model for both spatially and temporally (non-Markovian) correlated errors based on classical environmental fluctuators. The model allows for the independent variation of the marginalized spacetime-local error probability and the correlation strength. Using this model, we study the effects of correlated stochastic noise on QAOA. We find evidence that the performance of QAOA improves as the correlation time or correlation length of the noise is increased at fixed local error probabilities. This shows that noise correlations in themselves need not be detrimental for NISQ algorithms such as QAOA.Comment: Published version. Parts from the SM moved to the appendix. Improvements to the main text. 16 pages, 5 figure

Line-graph qubit routing: From kagome to heavy-hex and more

Quantum computers have the potential to outperform classical computers, but are currently limited in their capabilities. One such limitation is the restricted connectivity between qubits, as captured by the hardware's coupling graph. This limitation poses a challenge for running algorithms that require a coupling graph different from what the hardware can provide. To overcome this challenge and fully utilize the hardware, efficient qubit routing strategies are necessary. In this paper, we introduce line-graph qubit routing, a general method for routing qubits when the algorithm's coupling graph is a line graph and the hardware coupling graph is a heavy graph. Line-graph qubit routing is fast, deterministic, and effective; it requires a classical computational cost that scales at most quadratically with the number of gates in the original circuit, while producing a circuit with a SWAP overhead of at most two times the number of two-qubit gates in the original circuit. We implement line-graph qubit routing and demonstrate its effectiveness in mapping quantum circuits on kagome, checkerboard, and shuriken lattices to hardware with heavy-hex, heavy-square, and heavy-square-octagon coupling graphs, respectively. Benchmarking shows the ability of line-graph qubit routing to outperform established general-purpose methods, both in the required classical wall-clock time and in the quality of the solution that is found. Line-graph qubit routing has direct applications in the quantum simulation of lattice-based models and aids the exploration of the capabilities of near-term quantum hardware

Variational quantum eigensolver for the Heisenberg antiferromagnet on the kagome lattice

Establishing the nature of the ground state of the Heisenberg antiferromagnet (HAFM) on the kagome lattice is well-known to be a prohibitively difficult problem for classical computers. Here, we give a detailed proposal for a variational quantum eigensolver (VQE) intending to solve this physical problem on a quantum computer. At the same time, this VQE constitutes an explicit experimental proposal for showing a useful quantum advantage on noisy intermediate-scale quantum devices because of its natural hardware compatibility. We classically emulate noiseless and noisy quantum computers with either 2D-grid or all-to-all connectivity and simulate patches of the kagome HAFM of up to 20 sites. In the noiseless case, the ground-state energy, as found by the VQE, approaches the true ground-state energy exponentially as a function of the circuit depth. Furthermore, VQEs for the HAFM on any graph can inherently perform their quantum computations in a decoherence-free subspace that protects against collective longitudinal and collective transversal noise, adding to the noise resilience of these algorithms. Nevertheless, the extent of the effects of other noise types suggests the need for error mitigation and performance targets alternative to high-fidelity ground-state preparation, even for essentially hardware-native VQEs