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arXiv:2402.10173

Universal Quantum Computing with Field-Mediated Unruh--DeWitt Qubits

Eric W. Aspling, Lawler, Michael

Published Feb 15, 2024• 0 citations

Abstract

A set of universal quantum gates is a vital part of the theory of quantum computing, but is absent in the developing theory of Relativistic Quantum Information (RQI). Yet, the Unruh--DeWitt (UDW) detector formalism can be elevated to unitary gates between qubits and quantum fields and has allowed RQI applications in quantum Shannon theory, such as mutual information, coherent information, and quantum capacity in field-mediated quantum channels. Recently, experimental realizations of UDW-style qubits have been proposed in two-dimensional quantum materials, but their value as a quantum technology, including quantum communication and computation, is not yet clear, especially since fields introduce many avenues for decoherence. We introduce controlled-unitary UDW logic gates between qubit and field that are comparable to the two-qubit CNOT gate. We then extend this formalism to demonstrate Quantum State Transfer (QST) (two CNOT gates) and SWAP (three CNOT gates) channels. We illustrate the performance of these quantum operation gates with the diamond distance, a measure of distinguishability between quantum channels. Distinguishability measures like diamond distance allow for a rigorous comparison between field-mediated transduction through UDW detectors and local quantum mechanical operations and so quantify the performance of UDW detectors in quantum technological applications. Using the controlled-unitary qubit-field interactions we define an exact form of the CNOT gate. With this technique we also define quantum field-mediated single qubit operations associated with the Hadamard $H$, the $S$, and $T$ gates. Thus, UDW detectors in simple settings enable a collection of gates known to provide universal quantum computing.

DOI: 10.48550/arxiv.2402.10173

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A set of universal quantum gates is a vital part of the theory of quantum computing, but is absent in the developing theory of Relativistic Quantum Information (RQI). Yet, the Unruh--DeWitt (UDW) detector formalism can be elevated to unitary gates between qubits and quantum fields and has allowed RQI applications in quantum Shannon theory, such as mutual information, coherent information, and quantum capacity in field-mediated quantum channels. Recently, experimental realizations of UDW-style qubits have been proposed in two-dimensional quantum materials, but their value as a quantum technology, including quantum communication and computation, is not yet clear, especially since fields introduce many avenues for decoherence. We introduce controlled-unitary UDW logic gates between qubit and field that are comparable to the two-qubit CNOT gate. We then extend this formalism to demonstrate Quantum State Transfer (QST) (two CNOT gates) and SWAP (three CNOT gates) channels. We illustrate the performance of these quantum operation gates with the diamond distance, a measure of distinguishability between quantum channels. Distinguishability measures like diamond distance allow for a rigorous comparison between field-mediated transduction through UDW detectors and local quantum mechanical operations and so quantify the performance of UDW detectors in quantum technological applications. Using the controlled-unitary qubit-field interactions we define an exact form of the CNOT gate. With this technique we also define quantum field-mediated single qubit operations associated with the Hadamard

H

, the

S

, and

T

gates. Thus, UDW detectors in simple settings enable a collection of gates known to provide universal quantum computing.

Unruh--DeWitt (UDW) detectors implemented as UDW quantum gates provide a framework for evaluating quantum Shannon theory properties of qubit-field systems. UDW quantum channels consist of qubits encoding/decoding quantum information onto/off of quantum fields. With the controlled unitary structure of UDW gates, the encoding/decoding process happens on the diagonals of the coherent state density matrix describing the field. However, given the non-orthogonality of coherent states the output of UDW channels consists of unwanted states and unwanted mixing of states that lower the channel capacity. In idealized models, these appear in the off-diagonals and diagonals of the field's density matrix in the coherent state basis. For this reason, we show that UDW quantum channels have an unexpected representation as certain bosonic dephasing channels with dephasing parameters captured by a combination of the coupling, smearing, and switching functions of the UDW detector model. We demonstrate the unexpected consequence that a larger dephasing parameter results in higher channel capacity and helps alleviate unwanted state mixing. We illustrate these properties through two examples: inserting an additional ideal dephasing channel into the quantum channel and inserting cross-talk noise via a third UDW gate. Remarkably, the cross-talk noise channel qualitatively improves a lower bound on the quantum capacity suggesting UDW gates will have unexpected performance improvements if realized in condensed matter experiments.

The Unruh-DeWitt particle detector model has found success in demonstrating quantum information channels with non-zero channel capacity between qubits and quantum fields. These detector models provide the necessary framework for experimentally realizable Unruh-DeWitt quantum computers with near-perfect channel capacity. We propose spin-qubits with gate-controlled coupling to Luttinger liquids as a laboratory setting for Unruh-DeWitt detectors and explore general design constraints that underpin their feasibility in this and other settings. We present several experimental scenarios including graphene ribbons, edges states in the quantum spin Hall phase of HgTe quantum wells, and the recently discovered quantum anomalous Hall phase in transition metal dichalcogenides. Theoretically, through bosonization, we show that Unruh-DeWitt detectors can carry out quantum computations and identify when they can make perfect quantum communication channels between qubits via the Luttinger liquid. Our results point the way toward an all-to-all connected solid state quantum computer and the experimental study of quantum information in quantum fields via condensed matter physics.

Single qubit rotation gate and the controlled-NOT (CNOT) gate constitute a complete set of gates for universal quantum computation. In general the CNOT gate are only for two nearby qubits. For two qubits which are remote from each other, we need a series of swap gates to transfer these two qubits to the nearest neighboring sites, and then after the CNOT gate we should transfer them to their original sites again. However, a series of swap gates are resource for quantum information processing. One economy way which does not consume so much resource is to implement CNOT gate remotely. The remote CNOT gate is to implement the CNOT gate for two remotely separated qubits with the help of one additional maximally entangled state. The original remote CNOT gate is for two qubits, here we will present the d-dimensional remote CNOT gate. The role of quantum teleportation is identified in the process of the remote CNOT gate.

An essential requirement for any quantum computing architecture is the existence of a universal set of quantum gates. Examples of such sets are the 2-qubit CNOT gate in combination with arbitrary 1-qubit gates, and the 3-qubit Toffoli gate together with the 1-qubit Hadamard. A third set, which has not been implemented so far, is Valiant's 2-qubit matchgate G(A,B) which is universal with the SWAP operation. This paper presents how symmetric Valiant gates are decomposed which are sufficient for universal quantum computation, using another universal class of gates - a controlled-Zthetasgate and single qubit unitaries. Various symmetric matchgates (G(H,H), G(X,X) and G(T,T)) in a two-photon experiment to build quantum logic gates using higher-dimensional Hilbert spaces are implemented. The gate operations are characterized via quantum process tomography.

In quantum computation every unitary operation can be decomposed into quantum circuits---a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-not(cnot) gates. Two measures are important when judging the complexity of the circuit: the total number of cnot gates needed to implement it and the depth of the circuit, measured by the minimal number of computation steps needed to perform it. Here we give an explicit and simple quantum circuit scheme for preparation of arbitrary quantum states, which can directly utilize any decomposition scheme for arbitrary full quantum gates, thus connecting the two problems. Our circuit reduces the depth of the best currently known circuit by a factor of

2

. It also reduces the total number of cnot gates from

{2}^{n}

to

\frac{23}{24}{2}^{n}

in the leading order for even number of qubits. Specifically, the scheme allows us to decrease the upper bound from

11

cnot gates to

9

and the depth from

11

to

5

steps for four qubits. Our results are expected to help in designing and building small-scale quantum circuits using present technologies.

We propose a universal set of magnon-mediated quantum gates applied to a hybrid quantum system of mutually noninteracting qubits coupled to an ancilla magnonic mode. The gates are realized through dynamic manipulation of the frequency of the magnon mode and control of its initial state, without directly changing any qubit parameters. We present protocols for arbitrary single-qubit gates and two-qubit controlled phase gate, which together form a universal set and can be combined to perform any unitary transformation on the qubit subsystem. Our results demonstrate principal possibility of realizing a universal quantum computer controlled solely through manipulation of magnon-qubit interactions.