The construction of large, coherent quantum systems necessary for quantum computation remains an entreating but elusive goal, due to the ubiquitous nature of decoherence. Recent progress in quantum error correction schemes have given new hope to this field, but thus far, the codes presented in the literature assume a restricted number of errors and error free encoding, decoding, and measurement. We investigate a specific scenario without these assumptions; in particular, we evaluate a scheme to preserve a single quantum bit against phase damping using a three-qubit encoding based on Shor. By applying a new formalism which gives simple operators for decoherence and noisy logic gates, we find the fidelity of the stored qubit as a function of time, including decoherence which occurs not only during storage but also during processing. We generalize our results to include any source of error, and derive an upper limit on the allowable decoherence per timestep. Physically, our results suggest the feasibility of engineering artificial metastable states through repeated error correction.
Persistent homology is a powerful mathematical tool that summarizes useful information about the shape of data allowing one to detect persistent topological features while one adjusts the resolution. However, the computation of such topological features is often a rather formidable task necessitating the subsampling the underlying data. To remedy this, we develop an efficient quantum computation of persistent Betti numbers, which track topological features of data across different scales. Our approach employs a persistent Dirac operator whose square yields the persistent combinatorial Laplacia…
Topological data analysis (TDA) is an emergent field of data analysis. The critical step of TDA is computing the persistent Betti numbers. Existing classical algorithms for TDA are limited if we want to learn from high-dimensional topological features because the number of high-dimensional simplices grows exponentially in the size of the data. In the context of quantum computation, it has been previously shown that there exists an efficient quantum algorithm for estimating the Betti numbers even in high dimensions. However, the Betti numbers are less general than the persistent Betti numbers, …
We present two experimental schemes that can be used to implement the Factorized Quantum Lattice-Gas Algorithm for the 1D Diffusion Equation with Persistent-Current Qubits. One scheme involves biasing the PC Qubit at multiple flux bias points throughout the course of the algorithm. An implementation analogous to that done in Nuclear Magnetic Resonance Quantum Computing is also developed. Errors due to a few key approximations utilized are discussed and differences between the PC Qubit and NMR systems are highlighted.
Classical rotations of asymmetric rigid bodies are unstable around the axis of intermediate momentof inertia, causing a flipping of rotor orientation. This effect, known as the tennis racket effect,quickly averages to zero in classical ensembles since the flipping period varies significantly uponapproaching the separatrix. Here, we explore the quantum rotations of rapidly spinning thermalasymmetric nanorotors and show that classically forbidden tunnelling gives rise to persistent tennisracket dynamics, in stark contrast to the classical expectation. We characterise this effect, demon-strating …
Quantum protocols for bit commitment have been proposed and it is largely accepted that unconditionally secure quantum bit commitment is not possible; however, it can be more secure than classical bit commitment. In despite of its usefulness, quantum bit commitment protocols have not been experimentally implemented. The main reason is the fact that all proposed quantum bit commitment protocols require quantum memory. In this work, we show a quantum bit commitment protocol that does not require quantum memory and can be implemented with present technology.
This article describes a quantum bit commitment protocol, QBC1, based on entanglement destruction via forced measurements and proves its unconditional security.
A quantum protocol for bit commitment the security of which is based on technological limitations on nondemolition measurements and long-term quantum memory is presented.
Calibration of quantum computing technologies is essential to the effective utilization of their quantum resources. Specifically, the performance of quantum annealers is likely to be significantly impaired by noise in their programmable parameters, effectively misspecification of the computational problem to be solved, often resulting in spurious suboptimal solutions. We developed a strategy to determine and correct persistent, systematic biases between the actual values of the programmable parameters and their user-specified values. We applied the recalibration strategy to two D-Wave Two quan…
In this letter, it is proposed that cryogenic quantum bits can operate based on the nonlinearity due to the quantum capacitance of two-dimensional Dirac materials, and in particular graphene. The anharmonicity of a typical superconducting quantum bit is calculated, and the sensitivity of quantum bit frequency and anharmonicity with respect to temperature are found. Reasonable estimates reveal that a careful fabrication process can reveal expected properties, putting the context of quantum computing hardware into new perspectives.
The evolution of a quantum oscillator, with periodically varying frequency and damping, is studied in the two cases of parametric resonance (PR) producing a limited, or unlimited stretching of the wave function. The different asymptotic behaviors of the energy distribution, show the non trivial interplay between PR and the initial quantum state. In the first case, the oscillator's mean energy tends asymptotically to a fully classical value, independent of the initial state, with vanishing relative quantum fluctuations. In the second case, the memory of the initial state persists over arbitrary…
Under rather general assumptions about the properties of a noisy quantum channel, a first quantum protocol is proposed which allows to implement the secret bit commitment with the probability arbitrarily close to unity.
We propose a framework of bit commitment protocol using a comparison scheme and present a compound comparison scheme based on counterfactual cryptography. Finally, we propose a counterfactual quantum bit commitment protocol. In security analysis, we give the proper security parameters for counterfactual quantum bit commitment and prove that intercept attack and intercept/resend attack are ineffective attack for our protocol. In addition, we explain that counterfactual quantum bit commitment protocol cannot be attacked with no-go theorem attack by current technology.
Spontaneous synchronisation is a collective phenomenon that can occur in both dynamical classical and quantum systems. Here, we analyse the spontaneous synchronisation dynamics of vibrations assisting energy transfer in a bio-inspired system. We find the emergence of a constant non-zero `synchronisation phase' between synchronised vibrational displacements as the natural frequencies of the oscillators are detuned. This phase difference arises from the asymmetric participation of local modes in the long-lived synchronised state. Furthermore, we investigate the relationships between the synchron…
The commitment of bits between two mutually distrustful parties is a powerful cryptographic primitive with which many cryptographic objectives can be achieved. It is widely believed that unconditionally secure quantum bit commitment is impossible due to quantum entanglement cheating, which is codified in a general impossibility theorem. Gaps in the proof of this impossibility theorem are found. An unconditionally secure bit commitment protocol utilizing anonymous quantum states and the no-clone theorem is presented below with a full security proof.
In this paper, we introduce a new quantum bit commitment protocol which is practically secure against entanglement attacks. A general cheating strategy is discussed and shown to be practically ineffective against the proposed approach.
The desire to obtain an unconditionally secure bit commitment protocol in quantum cryptography was expressed for the first time thirteen years ago. Bit commitment is sufficient in quantum cryptography to realize a variety of applications with unconditional security. In 1993, a quantum bit commitment protocol was proposed together with a security proof. However, a basic flaw in the protocol was discovered by Mayers in 1995 and subsequently by Lo and Chau. Later the result was generalized by Mayers who showed that unconditionally secure bit commitment is impossible. A brief review on quantum bit…
In this work, we propose a quantum bit string commitment protocol using polarization of mesoscopic coherent states. The protocol is described and its security against brute force and quantum cloning machine attack is analyzed.
The impossibility proof on unconditionally secure quantum bit commitment is critically reviewed. Different ways of obtaining secure protocols are indicated.
We present a scheme for multi-bit quantum random number generation using a single qubit discrete-time quantum walk in one-dimensional space. Irrespective of the initial state of the qubit, quantum interference and entanglement of particle with the position space in the walk dynamics certifies high randomness in the system. Quantum walk in a position space of dimension $2^l+1$ ensures string of $(l+ 2)$-bits of random numbers from a single measurement. Bit commitment with the position space and control over the spread of the probability distribution in position space enable us with options to e…
CALA-$n$: A Quantum Library for Realizing Cost-Effective 2-, 3-, 4-, and 5-bit Gates on IBM Quantum Computers using Bloch Sphere Approach, Clifford+T Gates, and Layouts
We present an n-bit Toffoli gate quantum circuit based on the realization proposed by Barenco, where some of the Toffoli gates in their construction are replaced with Peres gates. This results in a significant cost reduction. Our main contribution is a quantum circuit which simulates the (m+1)-bit Toffoli gate with 32m-96 elementary quantum gates and one garbage bit which is passed unchanged. This paper is a corrected and expanded version of our recent journal publication.
Though it was proven that secure quantum sealing of a single classical bit is impossible in principle, here we propose an unconditionally secure quantum sealing protocol which seals a classical bit string. Any reader can obtain each bit of the sealed string with an arbitrarily small error rate, while reading the string is detectable. The protocol is simple and easy to be implemented. The possibility of using this protocol to seal a single bit in practical is also discussed.
The relationship between the quantum bit commitment (QBC) and quantum seal (QS) is studied. It is elaborated that QBC and QS are not equivalent, but QS protocols satisfying a stronger unconditional security requirement can lead to an unconditionally secure QBC. In this sense, QS is strictly stronger than QBC in security requirements. Based on an earlier proposal on sealing a single bit, a feasible QBC protocol is also put forward, which is secure in practice even if the cheater has a strong quantum computational power.
We propose a prepare-and-measure scheme for quantum key distribution with 2-bit quantum codes. The protocol is unconditionally secure under whatever type of intercept-and-resend attack. Given the symmetric and independent errors to the transmitted qubits, our scheme can tolerate a bit error rate up to 26% in 4-state protocol and 30% in 6-state protocol, respectively. These values are higher than all currently known threshold values for prepare-and-measure protocols. A specific realization with linear optics is given.
This article describes a quantum bit commitment protocol, QBC3, based on entanglement destruction via forced measurements and proves its unconditional security. Some comments on the current status of the field are also made.
We define an anti-quantum bit state via analogous way as the anti-state in Particle Physics.We show the quantum information Feymann diagrams for the teleportations and superdense coding, which preserve the information flow. The role of information vacuum and anihilation between error information and anti-information is mentioned for the stability of quantum computing.
We propose a practical quantum oblivious transfer and a bit commitment protocols which replace the single-photon source with weak coherent pulses and allow error and loss in channel and detectors. These protocols can be realized with available optoelectronic apparatus.
Based on the fact that the entanglement can not be created locally, we proposed a quantum bit commitment protocol, in which entangled states and quantum algorithms is used. The bit is not encoded with the form of the quantum states, and delaying the measurement is required. Therefore the protocol will not be denied by the Mayers-Lo-Chau no-go theorem, and unconditional security is achieved.
Digital signature scheme is commonly employed in modern electronic commerce and quantum digital signature (QDS) offers the information-theoretical security by the laws of quantum mechanics against attackers with unreasonable computation resources. The focus of previous QDS was on the signature of 1-bit message. In contrast, based on quantum ghost imaging with security test, we propose a scheme of QDS in which a multi-bit message can be signed at a time. Our protocol is no more demanding than the traditional cases for the requirements of quantum resources and classical communications. The multi…
This paper proposes a cheat sensitive quantum bit commitment (CSQBC) scheme based on single photons, in which Alice commits a bit to Bob. Here, Bob only can cheat the committed bit with probability close to $0$ with the increasing of used single photons' amount. And if Alice altered her committed bit after commitment phase, she will be detected with probability close to $1$ with the increasing of used single photons' amount. The scheme is easy to be realized with nowadays technology.
We prove the existence of a class of two--input, two--output gates any one of which is universal for quantum computation. This is done by explicitly constructing the three--bit gate introduced by Deutsch [Proc.~R.~Soc.~London.~A {\bf 425}, 73 (1989)] as a network consisting of replicas of a single two--bit gate.
Quantum bit seal is a way to encode a classical bit quantum mechanically so that everyone can obtain non-zero information on the value of the bit. Moreover, such an attempt should have a high chance of being detected by an authorized verifier. Surely, a reader looks for a way to get the maximum amount of information on the sealed bit and at the same time to minimize her chance of being caught. And a verifier picks a sealing scheme that maximizes his chance of detecting any measurement of the sealed bit. Here, I report a strategy that passes all measurement detection procedures at least half of…
The nature and scope of various impossibility proofs as they relate to real-world situations are discussed. In particular, it is shown in words without technical symbols how secure quantum bit commitment protocols may be obtained with testing that exploits the multiple possibilities of cheating entanglement formation.
We demonstrate a five-bit nuclear-magnetic-resonance quantum computer that distinguishes among various functions on four bits, making use of quantum parallelism. Its construction draws on the recognition of the sufficiency of linear coupling along a chain of nuclear spins, the synthesis of a suitably coupled molecule, and the use of a multi-channel spectrometer.
In a recent letter (Phys. Lett. A 377 (2013) 1076, arXiv:0905.3801), the authors presented an impossibility proof of quantum bit commitment, which attempted to cover all possible protocols that involve both quantum and classical information. Here we show that there are many errors in the proof, thus it fails to exhaust all conceivable protocols.
This work uses a simple quantum computer model to discuss the randomness of bit strings originated from integer sequences. The considered quantum computer model has three elements: a processing unit responsible for a mathematical operation, an initial equally weighted superposition and a quantum state used as resource. The randomness depends on the last.
Zero-knowledge proof system is an important protocol that can be used as a basic block for construction of other more complex cryptographic protocols. Quantum zero-knowledge protocols have been proposed but, since their implementation requires advanced quantum technology devices, experimental implementation of zero-knowledge protocols have not being reported. In this work, we present a quantum zero-knowledge protocol based on a quantum bit commitment protocol that can be implemented with today technology. Hence, our quantum zero-knowledge protocol can be readily implemented.
The ``impossibility proof'' on unconditionally secure quantum bit commitment is critically analyzed. Many possibilities for obtaining a secure bit commitment protocol are indicated, purely on the basis of two-way quantum communications, which are not covered by the impossibility proof formulation. They are classified under six new types of protocols, with security proofs for specific examples on four types. Reasons for some previously failed attempts at obtaining secure protocols are also indicated.
In this paper we consider the purification of a quantum state using the information obtained from a continuous measurement record, where the classical measurement record is digitized to a single bit per measurement after the measurements have been made. Analysis indicates that efficient and reliable state purification is achievable for one- and two-qubit systems. We also consider quantum feedback control based on the discrete one-bit measurement sequences.
We proposed a new quantum bit commitment scheme in which secret key need not to be provided by other quantum key distribution system. We can get the bit commitment with probability p by adding a waiting time in a frame during operating the BB84 protocol. Then the measurement outcomes can be encrypted by one-time pad with the key generated by BB84 protocol. We can also obtain the redundant secret keys to encrypt other information in this quantum key distribution system.
An $n$-bit string is encoded as a sequence of non-orthogonal quantum states. The parity bit of that $n$-bit string is described by one of two density matrices, $ρ_0^{(n)}$ and $ρ_1^{(n)}$, both in a Hilbert space of dimension $2^n$. In order to derive the parity bit the receiver must distinguish between the two density matrices, e.g., in terms of optimal mutual information. In this paper we find the measurement which provides the optimal mutual information about the parity bit and calculate that information. We prove that this information decreases exponentially with the length of the string i…
Bit commitment is a fundamental cryptographic primitive with numerous applications. Quantum information allows for bit commitment schemes in the information theoretic setting where no dishonest party can perfectly cheat. The previously best-known quantum protocol by Ambainis achieved a cheating probability of at most 3/4[Amb01]. On the other hand, Kitaev showed that no quantum protocol can have cheating probability less than 1/sqrt{2} [Kit03] (his lower bound on coin flipping can be easily extended to bit commitment). Closing this gap has since been an important and open question. In this pape…
We show here that the recent work of Wolf and Wullschleger (quant-ph/0502030) on oblivious transfer apparently opens the possibility that non-local correlations which are stronger than those in quantum mechanics could be used for bit-commitment. This is surprising, because it is the very existence of non-local correlations which in quantum mechanics prevents bit-commitment. We resolve this apparent paradox by stressing the difference between non-local correlations and oblivious transfer, based on the time-ordering of their inputs and outputs, which prevents bit-commitment.
A new cryptographic tool, anonymous quantum key technique, is introduced that leads to unconditionally secure key distribution and encryption schemes that can be readily implemented experimentally in a realistic environment. If quantum memory is available, the technique would have many features of public-key cryptography; an identification protocol that does not require a shared secret key is provided as an illustration. The possibility is also indicated for obtaining unconditionally secure quantum bit commitment protocols with this technique.
Very recently [Phys. Rev. E 82, 021921 (2010)] a simple mechanism was presented by which a molecule subjected to forced oscillations, out of thermal equilibrium, can maintain quantum entanglement between two of its quantum degrees of freedom. Crucially, entanglement can be maintained even in the presence of very intense noise, so intense that no entanglement is possible when the forced oscillations cease. This mechanism may allow for the presence of non-trivial quantum entanglement in biological systems. Here we significantly enlarge the study of this model. In particular, we show that the per…
Bit commitment involves the submission of evidence from one party to another so that the evidence can be used to confirm a later revealed bit value by the first party, while the second party cannot determine the bit value from the evidence alone. It is widely believed that secure quantum bit commitment is impossible due to quantum entanglement cheating, which is codified in a general impossibility theorem. In this paper, the scope of this general impossibility proof is extended and analyzed, and gaps are found. Three specific protocols are described for which the entanglement cheating as given…
