Mechanism of Universal Quantum Computation in the Brain

In this paper, the authors extend [1] and provide more details of how the brain may act like a quantum computer. In particular, positing the difference between voltages on two axons as the environment for ions undergoing spatial superposition, we argue that evolution in the presence of metric perturbations will differ from that in the absence of these waves. This differential state evolution will then encode the information being processed by the tract due to the interaction of the quantum state of the ions at the nodes with the “controlling’ potential. Upon decoherence, which is equal to a measurement, the final spatial state of the ions is decided and it also gets reset by the next impulse initiation time. Under synchronization, several tracts undergo such processes in synchrony and therefore the picture of a quantum computing circuit is complete. Under this model, based on the number of axons in the corpus callosum alone, we estimate that upwards of 50 million quantum states might be prepared and evolved every second in this white matter tract, far greater processing than any present quantum computer can accomplish.

Blind quantum computation with a client performing different single-qubit gates

In the field of single-server blind quantum computation(BQC), a major focus is to make the client as classical as possible. To achieve this goal, we propose two single-server BQC protocols to achieve verifiable universal quantum computation. In these two protocols, the client only needs to perform either the gate T(in the first protocol) or the gates H and X(in the second protocol). With assistance from a single server, the client can utilize his quantum capabilities to generate some single-qubit states while keeping the actual state of these qubits confidential from others. By using these single-qubit states, the verifiable universal quantum computation can be achieved.

Simulation of Projective Non-Abelian Anyons for Quantum Computation

Fundamental particles in nature can be classified as bosons or fermions,which satisfy their correspondent statistics.However,quasiparticles of condensed matter physics may be neither bosons nor fermions,but can be named as anyons satisfying a generalized statistics.These anyons can be related with topological phases of matter.Interestingly,anyons can be used to encode qubits to perform quantum computations with specific advantages in which the corresponding qubits are naturally fault tolerant due to topological protection.[1,2]This approach is called topological quantum computation.However,its implementation based on natural systems still seems far from realization.

Analysis and improvement of verifiable blind quantum computation

In blind quantum computation(BQC),a client with weak quantum computation capabilities is allowed to delegate its quantum computation tasks to a server with powerful quantum computation capabilities,and the inputs,algorithms and outputs of the quantum computation are confidential to the server.Verifiability refers to the ability of the client to verify with a certain probability whether the server has executed the protocol correctly and can be realized by introducing trap qubits into the computation graph state to detect server deception.The existing verifiable universal BQC protocols are analyzed and compared in detail.The XTH protocol(proposed by Xu Q S,Tan X Q,Huang R in 2020),a recent improvement protocol of verifiable universal BQC,uses a sandglass-like graph state to further decrease resource expenditure and enhance verification capability.However,the XTH protocol has two shortcomings:limitations in the coloring scheme and a high probability of accepting an incorrect computation result.In this paper,we present an improved version of the XTH protocol,which revises the limitations of the original coloring scheme and further improves the verification ability.The analysis demonstrates that the resource expenditure is the same as for the XTH protocol,while the probability of accepting the wrong computation result is reduced from the original minimum(0.866)^(d*)to(0.819)^(d^(*)),where d;is the number of repeated executions of the protocol.

A concise review of Rydberg atom based quantum computation and quantum simulation

Quantum information processing based on Rydberg atoms emerged as a promising direction two decades ago.Recent experimental and theoretical progresses have shined exciting light on this avenue.In this concise review,we will briefly introduce the basics of Rydberg atoms and their recent applications in associated areas of neutral atom quantum computation and simulation.We shall also include related discussions on quantum optics with Rydberg atomic ensembles,which are increasingly used to explore quantum computation and quantum simulation with photons.

Quantum computation and error correction based on continuous variable cluster states

Measurement-based quantum computation with continuous variables,which realizes computation by performing measurement and feedforward of measurement results on a large scale Gaussian cluster state,provides a feasible way to implement quantum computation.Quantum error correction is an essential procedure to protect quantum information in quantum computation and quantum communication.In this review,we briefly introduce the progress of measurement-based quantum computation and quantum error correction with continuous variables based on Gaussian cluster states.We also discuss the challenges in the fault-tolerant measurement-based quantum computation with continuous variables.

Quantum computation with two-dimensional graphene quantum dots

We study an array of graphene nano sheets that form a two-dimensional S = 1/2 Kagome spin lattice used for quantum computation. The edge states of the graphene nano sheets are used to form quantum dots to confine electrons and perform the computation. We propose two schemes of bang-bang control to combat decoherence and realize gate operations on this array of quantum dots. It is shown that both schemes contain a great amount of information for quantum computation. The corresponding gate operations are also proposed.

Universal quantum computation using all-optical hybrid encoding

By employing displacement operations, single-photon subtractions, and weak cross-Kerr nonlinearity, we propose an alternative way of implementing several universal quantum logical gates for all-optical hybrid qubits encoded in both single-photon polarization state and coherent state. Since these schemes can be straightforwardly implemented only using local operations without teleportation procedure, therefore, less physical resources and simpler operations are required than the existing schemes. With the help of displacement operations, a large phase shift of the coherent state can be obtained via currently available tiny cross-Kerr nonlinearity. Thus, all of these schemes are nearly deterministic and feasible under current technology conditions, which makes them suitable for large-scale quantum computing.

Full-Blind Delegating Private Quantum Computation

The delegating private quantum computation(DQC)protocol with the universal quantum gate set{X,Z,H,P,R,CNOT}was firstly proposed by Broadbent et al.[Broadbent(2015)],and then Tan et al.[Tan and Zhou(2017)]tried to put forward a half-blind DQC protocol(HDQC)with another universal set{H,P,CNOT,T}.However,the decryption circuit of Toffoli gate(i.e.T)is a little redundant,and Tan et al.’s protocol[Tan and Zhou(2017)]exists the information leak.In addition,both of these two protocols just focus on the blindness of data(i.e.the client’s input and output),but do not consider the blindness of computation(i.e.the delegated quantum operation).For solving these problems,we propose a full-blind DQC protocol(FDQC)with quantum gate set{H,P,CNOT,T},where the desirable delegated quantum operation,one of{H,P,CNOT,T},is replaced by a fixed sequence(H,P,CZ,CNOT,T)to make the computation blind,and the decryption circuit of Toffoli gate is also optimized.Analysis shows that our protocol can not only correctly perform any delegated quantum computation,but also holds the characteristics of data blindness and computation blindness.

Solid-state quantum computation station

Solid-state quantum computation station belongs to the group 2 of manipulation of quantum state in the Synergetic Extreme Condition User Facility. Here we will first outline the research background, aspects, and objectives of the station, followed by a discussion of the recent scientific as well as technological progress in this field based on similar experimental facilities to be constructed in the station. Finally, a brief summary and research perspective will be presented.

Quantum simulation and quantum computation of noisy-intermediate scale

In the past years, great progresses have been made on quantum computation and quantum simulation. Increasing the number of qubits in the quantum processors is expected to be one of the main motivations in the next years, while noises in manipulation of quantum states may still be inevitable even the precision will improve. For research in this direction, it is necessary to review the available results about noisy multiqubit quantum computation and quantum simulation. The review focuses on multiqubit state generations, quantum computational advantage, and simulating physics of quantum many-body systems. Perspectives of near term noisy intermediate-quantum processors will be discussed.

Quantum computation and simulation with vibrational modes of trapped ions

Vibrational degrees of freedom in trapped-ion systems have recently been gaining attention as a quantum resource,beyond the role as a mediator for entangling quantum operations on internal degrees of freedom,because of the large available Hilbert space.The vibrational modes can be represented as quantum harmonic oscillators and thus offer a Hilbert space with infinite dimensions.Here we review recent theoretical and experimental progress in the coherent manipulation of the vibrational modes,including bosonic encoding schemes in quantum information,reliable and efficient measurement techniques,and quantum operations that allow various quantum simulations and quantum computation algorithms.We describe experiments using the vibrational modes,including the preparation of non-classical states,molecular vibronic sampling,and applications in quantum thermodynamics.We finally discuss the potential prospects and challenges of trapped-ion vibrational-mode quantum information processing.

Low-temperature environments for quantum computation and quantum simulation

This review summarizes the requirement of low temperature conditions in existing experimental approaches to quantum computation and quantum simulation.

Quantum computation and simulation with superconducting qubits

Superconducting circuits based on Josephson junctions are regarded as one of the most promising technologies for the implementation of scalable quantum computers.This review presents the basic principles of superconducting qubits and shows the progress of quantum computing and quantum simulation based on superconducting qubits in recent years.The experimental realization of gate operations,readout,error correction codes,as well as some quantum algorithms are summarized,followed by an introduction of quantum simulation.And then some important applications in fields including condensed matter physics,quantum annealing,and quantum chemistry are discussed.

Efficient self-testing system for quantum computations based on permutations

Verification in quantum computations is crucial since quantum systems are extremely vulnerable to the environment.However,verifying directly the output of a quantum computation is difficult since we know that efficiently simulating a large-scale quantum computation on a classical computer is usually thought to be impossible.To overcome this difficulty,we propose a self-testing system for quantum computations,which can be used to verify if a quantum computation is performed correctly by itself.Our basic idea is using some extra ancilla qubits to test the output of the computation.We design two kinds of permutation circuits into the original quantum circuit:one is applied on the ancilla qubits whose output indicates the testing information,the other is applied on all qubits(including ancilla qubits) which is aiming to uniformly permute the positions of all qubits.We show that both permutation circuits are easy to achieve.By this way,we prove that any quantum computation has an efficient self-testing system.In the end,we also discuss the relation between our self-testing system and interactive proof systems,and show that the two systems are equivalent if the verifier is allowed to have some quantum capacity.

Quantum Computation with Two-Level Systems in Current-Biased Josephson Junction

We present a feasible scheme that realizes quantum computation using the two-level systems （TLSs） in Current-biased Josephson junction （CBJJ） under the present experimental technology. Effective manipulation of the TLSs by CBJJ serving as register qubit can be obtained, such as initialization, single-qubit rotations, two-qubit gates, entanglement generation, and read out, etc. In addition, we also discuss the experimental feasibility and efficiency of the scheme.

Nonadiabatic Geometric Quantum Computation with Asymmetric Superconducting Quantum Interference Device

We propose a method of controlling the dc-SQUID (superconducting quantum interference device) system by changing the gate voltages, which controls the amplitude of the fictitious magnetic fields B-z, and the externally applied current that produces the piercing magnetic flux Phi(x) for the dc-SQUID system. We have also introduced a physical model for the dc-SQUID system. Using this physical model, one can obtain the non-adiabatic geometric phase gate for the single qubit and the non-adiabatic conditional geometric phase gate (controlled NOT gate) for the two qubits. It is shown that when the gate voltage and the externally applied current of the dc-SQUID system satisfies an appropriate constraint condition, the charge state evolution can be controlled exactly on a dynamic phase free path. The non-adiabatic evolution of the charge states is given as well.

Quantum Computation with Nonlinear Optics

We propose a scheme of quantum computation with nonlinear quantum optics. Polarization states of photons are used for qubits. Photons with different frequencies represent different qubits. Single qubit rotation operation is implemented through optical elements like the Faraday polarization rotator. Photons are separated into different optical paths, or merged into a single optical path using dichromatic mirrors. The controlled-NOT gate between two qubits is implemented by the proper combination of parametric up and down conversions. This scheme has the following features： （1） No auxiliary qubits are required in the controlled-NOT gate operation; （2） No measurement is required in the course of the computation; （3） It is resource efficient and conceptually simple.

Nonadiabatic Geometric Quantum Computation with Asymmetric Superconducting Quantum Interference Device

We propose a method of controlling the dc-SQUID (superconducting quantum interference device) systemby changing the gate voltages, which controls the amplitude of the fictitious magnetic fields Bz, and the externallyapplied current that produces the piercing magnetic fiux φx for the dc-SQUID system. We have also introduced aphysical model for the dc-SQUID system. Using this physical model, one can obtain the non-adiabatic geometric phasegate for the single qubit and the non-adiabatic conditional geometric phase gate (controlled NOT gate) for the twoqubits. It is shown that when the gate voltage and the externally applied current of the dc-SQUID system satisfies anappropriate constraint condition, the charge state evolution can be controlled exactly on a dynamic phase free path. Thenon-adiabatic evolution of the charge states is given as well.

One-Way Quantum Computation with Cluster State and Probabilistic Gate

We present a scheme for efficiently constructing a two-dimensional cluster state,which serves as the central physical resource for one-way quantum computation.In this scheme,we successfully make the required computational overhead scale efficiently with the qubit number by using a probabilistic entangling quantum gate.