We construct a new error-suppression scheme that makes use of the adjoint of reversible quantum algorithms. For decoherence induced errors such as depolarization, it is presented that provided the depolarization error probability is less than 1, our scheme can exponentially reduce the final output error rate to zero using a number of cycles, and the output state can be coherently sent to another stage of quantum computation process. Besides, experimental set-ups via optical approach have been proposed using Grover's search algorithm as an example. Some further discussion on the benefits and limitations of the scheme is given in the end.
A critical analysis of the feasibility of reversible computing is performed. The key question is: Is it possible to build a completely reversible computer? A closer look into the internal aspects of the reversible computing as well as the external constraints such as the second law of thermodynamics has demonstrated that several difficulties would have to be solved before reversible computer is being built. It is shown that a conventional reversible computer would require energy for setting up the reversible inputs from irreversible signals, for the reading out of the reversible outputs, for t…
The relation between entropy and information has great significance for computation. Based on the strict reversibility of the laws of microphysics, Landauer (1961), Bennett (1973), Priese (1976), Fredkin and Toffoli (1982), Feynman (1985) and others envisioned a reversible computer that cannot allow any ambiguity in backward steps of a calculation. It is this backward capacity that makes reversible computing radically different from ordinary, irreversible computing. The proposal aims at a higher kind of computer that would give the actual output of a computation together with the original inpu…
It has been shown (Arxiv: quant-ph/0507236) that a universal quantum computer could be powerful enough to solve efficiently the quantum search problem, and the reversible and unitary halting protocol based on the state-locking pulse field is the key component to construct the efficient quantum search processes, while the state-locking pulse field is the key component to generate the reversible and unitary halting protocol. In this paper the reversible and unitary halting protocol and the generalized state-locking pulse field have been extensively investigated theoretically. The basic principle…
Proposed below is a reversible digital computer modeled after the natural behavior of a quantum system. Using approaches usually reserved for idealized quantum computers, the Reversible CAM, or State Vector Parallel (RSVP) processor can easily find keywords in an unstructured database (that is, it can solve a needle in a haystack problem). The RSVP processor efficiently solves a SAT (Satisfiability of Boolean Formulae) problem; also it can aid in the solution of a GP (Global Properties of Truth Table) problem. The power delay product of the RSVP processor is exponentially lower than that of a …
It has long been known that to minimise the heat emitted by a deterministic computer during it's operation it is necessary to make the computation act in a logically reversible manner\cite{Lan61}. Such logically reversible operations require a number of auxiliary bits to be stored, maintaining a history of the computation, and which allows the initial state to be reconstructed by running the computation in reverse. These auxiliary bits are wasteful of resources and may require a dissipation of energy for them to be reused. A simple procedure due to Bennett\cite{Ben73} allows these auxiliary bi…
We demonstrate that reversible dephasing via inhomogeneous broadening can greatly reduce collective quantum state rotation errors, and observe the suppression of rotation errors by more than 21 dB in the context of collective population measurements of the spin states of an ensemble of $2.1 \times 10^5$ laser cooled and trapped $^{87}$Rb atoms. The large reduction in rotation noise enables direct resolution of spin state populations 13(1) dB below the fundamental quantum projection noise limit. Further, the spin state measurement projects the system into an entangled state with 9.5(5) dB of di…
The paper introduces dual Toffoli and Peres reversible gates, which operate under disjunctive control, and shows their functionality based on the Barenco et al. quantum model. Both uniform and mixed polarity are considered for the controls. Rewriting rules are presented, which provide a possible reduction of the number of gates and quantum cost of reversible (sub)circuits using standard Toffoli or Peres gates. Finally, a Clifford+T realization of a dual Toffoli and a dual Peres gate is shown, which may be used when mapping reversible circuits to the IBM quantum computers.
Liquid-state NMR quantum computer has demonstrated the possibility of quantum computation and supported its development. Using NMR quantum computer techniques, we observed phase decoherence under two kinds of artificial noise fields; one a noise with a long period, and the other with shorter random period. The first one models decoherence in a quantum channel while the second one models transverse relaxation. We demonstrated that the bang-bang control suppresses decoherence in both cases.
It is discussed the decoherence problems in ensemble large-scale solid state NMR quantum computer based on the array of P donor atoms having nuclear spin I = 1/2. It is considered here, as main mechanisms of decoherence for low temperature (< 0.1 K), the adiabatic processes of random modulation of qubit resonance frequency determined by secular part of nuclear spin interaction with electron spin of the basic atoms, with impurity paramagnetic atoms and also with nuclear spins of impurity diamagnetic atoms. It was made estimations of allowed concentrations of magnetic impurities and of spin temp…
The question of finding a lower bound on the number of Toffoli gates in a classical reversible circuit is addressed. A method based on quantum information concepts is proposed. The method involves solely concepts from quantum information - there is no need for an actual physical quantum computer. The method is illustrated on the example of classical Shannon data compression.
Reversible entanglement transfer between light and matter is a crucial requisite for the ongoing developments of quantum information technologies. Quantum networks and their envisioned applications, e.g., secure communications beyond direct transmission, distributed quantum computing or enhanced sensing, rely on entanglement distribution between nodes. Although entanglement transfer has been demonstrated, a current roadblock is the limited efficiency of this process that can compromise the scalability of multi-step architectures. Here we demonstrate the efficient transfer of heralded single-ph…
A hierarchical, reversible mapping between levels of tree structured computation, applicable for structuring the Quantum Computation algorithm for NP-complete problem is presented. It is proven that confining the state of a quantum computer to a subspace of the available Hilbert space, where states are consistent with the problem constraints, can be done in polynomial time. The proposed mapping, together with the method of state reduction can be potentially used for solving NP-complete problems in polynomial time.
Reversible algorithms play a crucial role both in classical and quantum computation. While for a classical bit the only nontrivial reversible operation is the bit-flip, nature is far more versatile in what it allows to do to a quantum bit. The reversible operations that a quantum computer can perform on a qubit are group of linear unitary transformations. However, laws of quantum mechanics prohibit implementation of anti-linear anti-unitary gates, even though they are perfectly reversible. Here we show that such a restriction on possible set of reversible operations is, remarkably, a fundament…
Crosstalk between target and neighboring spectator qubits due to spillover of control signals represents a major error source limiting the fidelity of two-qubit entangling gates in quantum computers. We show that in our laser-driven trapped-ion system coherent crosstalk error can be modelled as residual $X\hatσ_ϕ$ interaction and can be actively cancelled by single-qubit echoing pulses. We propose and demonstrate a crosstalk suppression scheme that eliminates all first-order crosstalk, yet only requires local control by driving rotations solely on the target qubits. We report a two-qubit Bell …
A major hurdle to the deployment of quantum linear systems algorithms and recent quantum simulation algorithms lies in the difficulty to find inexpensive reversible circuits for arithmetic using existing hand coded methods. Motivated by recent advances in reversible logic synthesis, we synthesize arithmetic circuits using classical design automation flows and tools. The combination of classical and reversible logic synthesis enables the automatic design of large components in reversible logic starting from well-known hardware description languages such as Verilog. As a prototype example for ou…
We describe the construction of quantum gates (unitary operators) from boolean functions and give a number of applications. Both non-reversible and reversible boolean functions are considered. The construction of the Hamilton operator for a quantum gate is also described with the Hamilton operator expressed as spin system. Computer algebra implementations are provided.
We introduce a model of computation based on read only memory (ROM), which allows us to compare the space-efficiency of reversible, error-free classical computation with reversible, error-free quantum computation. We show that a ROM-based quantum computer with one writable qubit is universal, whilst two writable bits are required for a universal classical ROM-based computer. We also comment on the time-efficiency advantages of quantum computation within this model.
Quantum computers require quantum processors. An important part of the processor of any computer is the arithmetic unit, which performs binary addition, subtraction, division and multiplication, however multiplication can be performed using repeated addition, while division can be performed using repeated subtraction. In this paper we present two designs using the reversible $R^3$ gate to perform the quantum half adder/ subtractor and the quantum full adder/subtractor. The proposed half adder/subtractor design can be used to perform different logical operations, such as $AND$, $XOR$, $NAND$, $…
We present numerical and analytical studies of a quantum computer proposed by the Yamamoto group in Phys. Rev. Lett. 89, 017901 (2002). The stable and quantum chaos regimes in the quantum computer hardware are identified as a function of magnetic field gradient and dipole-dipole couplings between qubits on a square lattice. It is shown that a strong magnetic field gradient leads to suppression of quantum chaos.
Controlling quantum systems is crucial for quantum computation and a variety of new quantum technologies. The control is typically achieved by breaking down the target dynamics into a sequence of elementary gates,whose description can be stored into the memory of a classical computer. Here we explore a different approach, initiated by Nielsen and Chuang, where the target dynamics is encoded in the state of a quantum system, regarded as a "quantum program". We show that quantum strategies based on coherent interactions between the quantum program and the target system offer an advantage over al…
Reversible or information-lossless circuits have applications in digital signal processing, communication, computer graphics and cryptography. They are also a fundamental requirement in the emerging field of quantum computation. We investigate the synthesis of reversible circuits that employ a minimum number of gates and contain no redundant input-output line-pairs (temporary storage channels). We prove constructively that every even permutation can be implemented without temporary storage using NOT, CNOT and TOFFOLI gates. We describe an algorithm for the synthesis of optimal circuits and stu…
This paper discusses how to implement certain classes of quantum computer algorithms using classical discrete switching networks that are amenable to implementation in main stream CMOS transistor IC technology. The methods differ from other classical approaches in that asynchronous feedback is exploited in classical transistor reversible logic circuits to implement the Hadamard transform in one simultaneous step over all qubits as in a true quantum computer. The Simon problem is used as an example. The method is used to provide an order n execution speed method for the Gaussian elimination ste…
Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search…
A remarkable feature of quantum theory is non-locality (i.e. the presence of correlations which violate Bell inequalities). However, quantum correlations are not maximally non-local, and it is natural to ask whether there are compelling reasons for rejecting theories in which stronger violations are possible. To shed light on this question, we consider post-quantum theories in which maximally non-local states (non-local boxes) occur. It has previously been conjectured that the set of dynamical transformations possible in such theories is severely limited. We settle the question affirmatively i…
This article is an attempt to generalize the classical theory of reversible computing, principally developed by Bennet [IBM J. Res. Develop., 17(1973)] and by Fredkin and Toffoli [Internat. J. Theoret. Phys., 21(1982)], to the quantum case. This is a fundamental step towards the construction of a quantum computer because a time efficient quantum computation is a reversible physical process. The paper is organized as follows. The first section reviews the classical theory of reversible computing. In the second section it is showed that the designs used in the classical framework to decrease the…
Manipulating quantum computing hardware in the presence of imperfect devices and control systems is a central challenge in realizing useful quantum computers. Susceptibility to noise limits the performance and capabilities of noisy intermediate-scale quantum (NISQ) devices, as well as any future quantum computing technologies. Fortunately quantum control enables efficient execution of quantum logic operations and algorithms with built-in robustness to errors, without the need for complex logical encoding. In this manuscript we introduce software tools for the application and integration of qua…
We propose a new class of quantum computing algorithms which generalize many standard ones. The goal of our algorithms is to estimate probability distributions. Such estimates are useful in, for example, applications of Decision Theory and Artificial Intelligence, where inferences are made based on uncertain knowledge. The class of algorithms that we propose is based on a construction method that generalizes a Fredkin-Toffoli (F-T) construction method used in the field of classical reversible computing. F-T showed how, given any binary deterministic circuit, one can construct another binary de…
Quantum computers are considered as a part of the family of the reversible, lineary-extended, dynamical systems (Quanputers). For classical problems an operational reformulation is given. A universal algorithm for the solving of classical and quantum problems on quanputers is formulated.
In this paper we consider adversarial noise models that will fail quantum error correction and fault-tolerant quantum computation. We describe known results regarding high-rate noise, sequential computation, and reversible noisy computation. We continue by discussing highly correlated noise and the "boundary," in terms of correlation of errors, of the "threshold theorem." Next, we draw a picture of adversarial forms of noise called (collectively) "detrimental noise." Detrimental noise is modeled after familiar properties of noise propagation. However, it can have various causes. We start by po…
We study the application of decoupling techniques to the case of a damped vibrational mode of a chain of trapped ions, which can be used as a quantum bus in linear ion trap quantum computers. We show that vibrational heating could be efficiently suppressed using appropriate ``parity kicks''. We also show that vibrational decoherence can be suppressed by this decoupling procedure, even though this is generally more difficult because the rate at which the parity kicks have to applied increases with the effective bath temperature.
Future quantum repeater architectures, capable of efficiently distributing information encoded in quantum states of light over large distances, will benefit from multiplexed photonic quantum memories. In this work we demonstrate a temporally multiplexed quantum repeater node in a laser-cooled cloud of $^{87}$Rb atoms. We employ the DLCZ protocol where pairs of photons and single collective spin excitations (so called spin waves) are created in several temporal modes using a train of write pulses. To make the spin waves created in different temporal modes distinguishable and enable selective re…
Linear reversible circuits represent a subclass of reversible circuits with many applications in quantum computing. These circuits can be efficiently simulated by classical computers and their size is polynomially bounded by the number of qubits, making them a good candidate to deploy efficient methods to reduce computational costs. We propose a new algorithm for synthesizing any linear reversible operator by using an optimized version of the Gaussian elimination algorithm coupled with a tuned LU factorization. We also improve the scalability of purely greedy methods. Overall, on random operat…
Even if a logical network consists of thermodynamically reversible gate operations, the computation process may have high dissipation rate if the gate implementation is controlled by external clock signals. It is an open question whether the global clocking mechanism necessarily envolves irreversible processes. However, one can show that it is not possible to extract any timing information from a micro-physical clock without disturbing it. Applying recent results of quantum information theory we can show a hardware-independent lower bound on the timing information that is necessarily destroyed…
Most of the work on implementing arithmetic on a quantum computer has borrowed from results in classical reversible computing (e.g. [VBE95], [BBF02], [DKR04]). These quantum networks are inherently classical, as they can be implemented with only the Toffoli gate. Draper [D00] has proposed an inherently "quantum" network for addition based on the quantum Fourier transform. His approach has the advantage that it requires no carry qubits (the previous approaches required O(n) carry qubits). The network in [D00] uses quantum rotation gates, which must either be implemented with exponential precisi…
The search problem is to find a state satisfying certain properties out of a given set. Grover's algorithm drives a quantum computer from a prepared initial state to the target state and solves the problem quadratically faster than a classical computer. The algorithm uses selective transformations to distinguish the initial state and target state from other states. It does not succeed unless the selective transformations are very close to phase-inversions. Here we show a way to go beyond this limitation. An important application lies in quantum error-correction, where the errors can cause the …
We have analyzed an efficient integration of the multi-qubit echo quantum memory into the quantum computer scheme on the atomic resonant ensembles in quantum electrodynamics cavity. Here, one atomic ensemble with controllable inhomogeneous broadening is used for the quantum memory node and other atomic ensembles characterized by the homogeneous broadening of the resonant line are used as processing nodes. We have found optimal conditions for efficient integration of multi-qubit quantum memory modified for this analyzed physical scheme and we have determined a specified shape of the self tempor…
The Hidden Weighted Bit function plays an important role in the study of classical models of computation. A common belief is that this function is exponentially hard for the implementation by reversible ancilla-free circuits, even though introducing a small number of ancillae allows a very efficient implementation. In this paper, we refute the exponential hardness conjecture by developing a polynomial-size reversible ancilla-free circuit computing the Hidden Weighted Bit function. Our circuit has size $O(n^{6.42})$, where $n$ is the number of input bits. We also show that the Hidden Weighted B…
Quantum computer possesses quantum parallelism and offers great computing power over classical computer \cite{er1,er2}. As is well-know, a moving quantum object passing through a double-slit exhibits particle wave duality. A quantum computer is static and lacks this duality property. The recently proposed duality computer has exploited this particle wave duality property, and it may offer additional computing power \cite{r1}. Simply put it, a duality computer is a moving quantum computer passing through a double-slit. A duality computer offers the capability to perform separate operations on t…
For the implementation of a quantum computer it is necessary to exercise complete control over the Hamiltonian of the used physical system. For NMR quantum computing the effectively acting Hamiltonian can be manipulated via pulse sequences. Here we examine a register consisting of N selectively addressable spins with pairwise coupling between each spin pair. We show that complete decoupling of the spins is possible independent of the particular form of the spin-spin interaction. The proposed method based on orthogonal arrays is efficient in the sense that the effort regarding time and amount o…
Randomized compiling reduces the effects of errors on quantum computers by tailoring arbitrary Markovian errors into stochastic Pauli noise. Here we prove that randomized compiling also tailors non-Markovian errors into local stochastic Pauli noise and investigate the technique's limitations. We show through analysis and numerical results that randomized compiling alters errors in three distinct helpful ways. First, it prevents the coherent accumulation of errors (including hard to remove crosstalk effects) across gate cycles by destroying intercycle coherent correlations. Second, it converts …
The first realization of solid state quantum computer was demonstrated recently by using artificial atoms -- transmons in superconducting resonator. Here, we propose a novel architecture of flexible and scalable quantum computer based on a waveguide circuit coupling many quantum nodes of controlled atomic ensembles. For the first time, we found the optimal practically attainable parameters of the atoms and circuit for 100{%} efficiency of quantum memory for multi qubit photon fields and confirmed experimentally the predicted perfect storage. Then we revealed self modes for reversible transfer …
First solid state quantum computer was built using transmons (cooper pair boxes). The operation of the computer is limited because of using a number of the rigit cooper boxes working with fixed frequency at temperatures of superconducting material. Here, we propose a novel architecture of quantum computer based on a flexible wire circuit of many coupled quantum nodes containing controlled atomic (molecular) ensembles. We demonstrate wide opportunities of the proposed computer. Firstly, we reveal a perfect storage of external photon qubits to multi-mode quantum memory node and demonstrate a rev…
Problems in realization of silicon-based solid-state NMR quantum computer with ensemble addressing to qubits are considered. It is presented the extension of Kane's scheme to ensemble approach version with strip gates. For the initialization of nuclear quantum states it is proposed to use the solid-state effect in ENDOR technique whereby the nuclear spins can be practically fully polarized or, that is the same, indirect cooled to the spin temperature less than ~ 1 mK. It is suggested the possible planar silicon topology of such ensemble quantum computer and shown that the measurement with stan…
It has been recently proved that a quantum jump may be reversed by a unitary process provided the initial state is restricted by some conditions. The application of such processes for preventing decoherence, for example in quantum computers, was suggested. We shall show that in the situation when the quantum jump is reversible it supplies no information about the initial state additional to the information known beforehand. Therefore the reversibility of this type does not contradict the general statement of quantum measurement theory: a measurement cannot be reversed. As a consequence of this…
Achieving a practical advantage with near-term quantum computers hinges on having effective methods to suppress errors. Recent breakthroughs have introduced methods capable of exponentially suppressing errors by preparing multiple noisy copies of a state and virtually distilling a more purified version. Here we present an alternative method, the Resource-Efficient Quantum Error Suppression Technique (REQUEST), that adapts this breakthrough to much fewer qubits by making use of active qubit resets, a feature now available on commercial platforms. Our approach exploits a space/time trade-off to …
We consider the logical assertions of a hypothetical observer who is inside a quantum computer and performs a reversible quantum measurement, obtaining a symmetric couple of new axioms, valid only inside the quantum computer. The result is that, in this logical framework, symmetry and paraconsistency hold.
As quantum computers mature, quantum error correcting codes (QECs) will be adopted in order to suppress errors to any desired level $E$ at a cost in qubit-count $n$ that is merely poly-logarithmic in $1/E$. However in the NISQ era, the complexity and scale required to adopt even the smallest QEC is prohibitive. Instead, error mitigation techniques have been employed; typically these do not require an increase in qubit-count but cannot provide exponential error suppression. Here we show that, for the crucial case of estimating expectation values of observables (key to almost all NISQ algorithms…
We propose an effective realization of the universal set of elementary quantum gates in solid state quantum computer based on macroscopic (or mesoscopic) resonance systems - multi-atomic coherent ensembles, squids or quantum dots in quantum electrodynamic cavity. We exploit an encoding of logical qubits by the pairs of the macroscopic two- or three-level atoms that is working in a Hilbert subspace of all states inherent to these atomic systems. In this subspace, logical single qubit gates are realized by the controlled reversible transfer of single atomic excitation in the pair via the exchang…
As an ensemble scheme of solid-state NMR quantum computers the extension of Kane's many-qubits silicon scheme based on the array of 31 P donor atoms are spaced lengthwise of the strip gates is considered. The possible planar topology of such ensemble quantum computer is suggested. The estimation of the output NMR signal was performed and it was shown that for the number N>=10^5 of ensemble elements involving L~10^3 qubits each, the standard NMR methods are usable. As main mechanisms of decoherence for low temperature (<0.1K), the adiabatic processes of random modulation of qubit resonance freq…
A key goal of digital quantum computing is the simulation of fermionic systems such as molecules or the Hubbard model. Unfortunately, for present and near-future quantum computers the use of quantum error correction schemes is still out of reach. Hence, the finite error rate limits the use of quantum computers to algorithms with a low number of gates. The variational Hamiltonian ansatz (VHA) has been shown to produce the ground state in good approximation in a manageable number of steps. Here we study explicitly the effect of gate errors on its performance. The VHA is inspired by the adiabatic…
